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January 21, 2011 feature

Which-way detector unlocks some mystery of the double-slit experiment

By Lisa Zyga , Phys.org

(PhysOrg.com) -- One of the greatest puzzles of the double-slit experiment – and quantum physics in general – is why electrons seem to act differently when being observed. While electrons traveling through a barrier with two slits create interference patterns when unobserved, these interference patterns disappear when scientists detect which slit each electron travels through. By designing a modified version of the double-slit experiment with a new "which-way" electron detector at one of the slits, a team of scientists from Italy has found a clue as to why electron behavior appears to change when being observed.

As one of the most famous experiments in quantum physics, the double-slit experiment demonstrates how the quantum world is very different from the classical world. When macroscale objects are shot at a barrier with two slits, the objects travel straight through the slits and leave two straight lines on the wall behind the barrier. But when electrons are used instead of macroscale objects, they do not leave two straight lines on the wall but an interference pattern of many lines. Because the interference pattern remains even when the electrons are shot one at a time, the experiment seems to suggest that each electron somehow travels through both slits at the same time and interferes with itself, like a wave instead of a particle.

The second unusual part of the double-slit experiment is that the electrons stop creating an interference pattern when scientists set up a detector near one of the slits to determine which slit(s) an electron is passing through. Under these circumstances, the electrons simply create two straight lines, the same as classical particles.

Throughout the years, scientists have demonstrated different versions of the two-slit experiment. In the new study, physicists Stefano Frabboni from the University of Modena and Reggio Emilia and the CNR-Institute of Nanoscience in Modena, Italy; Gian Carlo Gazzadi from the CNR-Institute of Nanoscience; and Giulio Pozzi from the University of Bologna have presented another version of the two-slit experiment using a transmission electron microscope.

“Over the last few years, we tried to use our expertise in transmission electron microscopy and focused ion beam specimen preparation to realize some basic experiments related to some of the ‘mysteries’ of quantum mechanics, as pointed out by Feynman in his celebrated lectures and books,” Frabboni told PhysOrg.com .

First, the scientists used focused ion beam milling to make two nanoslits on a barrier. Then they modified one of the slits by covering it with a filter made of several layers of “low atomic number” material to create a which-way detector for the electrons passing through.

Although the electrons (which were shot one by one) could still pass through the filtered slit, the filter caused more of the electrons to undergo inelastic scattering rather than elastic scattering. As the physicists explained, an electron undergoing inelastic scattering is localized at the covered slit, and acts like a spherical wave after passing through the slit. In contrast, an electron passing through the unfiltered slit is more likely to undergo elastic scattering, and act like a cylindrical wave after passing through that slit. The spherical wave and cylindrical wave do not have any phase correlation, and so even if an electron passed through both slits, the two different waves that come out cannot create an interference pattern on the wall behind them.

The physicists also found that the thickness of the filter determined the interference effects: the thicker the filter, the greater the probability for inelastic scattering rather than elastic scattering, and so the fewer the interference effects. They could make the filter thick enough so that the interference effects canceled out almost completely.

“When the electron suffers inelastic scattering, it is localized; this means that its wavefunction collapses and after the measurement act, it propagates roughly as a spherical wave from the region of interaction, with no phase relation at all with other elastically or inelastically scattered electrons,” Frabboni said. “The experimental results show electrons through two slits (so two bright lines in the image when elastic and inelastic scattered electrons are collected) with negligible interference effects in the one-slit Fraunhofer diffraction pattern formed with elastic electrons.”

In a separate study, the physicists covered both slits to see if two spherical waves would create an interference pattern. They found that, in the very faint inelastic intensity, no fringes seem present, whereas interference fringes are recovered, at a very low intensity, when the elastic image is taken.

Overall, the results suggest that the type of scattering an electron undergoes determines the mark it leaves on the back wall, and that a detector at one of the slits can change the type of scattering. The physicists concluded that, while elastically scattered electrons can cause an interference pattern, the inelastically scattered electrons do not contribute to the interference process.

Copyright 2010 PhysOrg.com. All rights reserved. This material may not be published, broadcast, rewritten or redistributed in whole or part without the express written permission of PhysOrg.com.

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The double-slit experiment: Is light a wave or a particle?

The double-slit experiment is universally weird.

How does the double-slit experiment work?

Interference patterns from waves, particle patterns, double-slit experiment: quantum mechanics, history of the double-slit experiment, additional resources.

The double-slit experiment is one of the most famous experiments in physics and definitely one of the weirdest. It demonstrates that matter and energy (such as light) can exhibit both wave and particle characteristics — known as the particle-wave duality of matter — depending on the scenario, according to the scientific communication site Interesting Engineering .

According to the University of Sussex , American physicist Richard Feynman referred to this paradox as the central mystery of quantum mechanics. 

We know the quantum world is strange, but the two-slit experiment takes things to a whole new level. The experiment has perplexed scientists for over 200 years, ever since the first version was first performed by British scientist Thomas Young in 1801.

Related: 10 mind-boggling things you should know about quantum physics  

Christian Huygens was the first to describe light as traveling in waves whilst Isaac Newton thought light was composed of tiny particles according to Las Cumbres Observatory . But who is right? British polymath Thomas Young designed the double-slit experiment to put these theories to the test. 

To appreciate the truly bizarre nature of the double-split experiment we first need to understand how waves and particles act when passing through two slits. 

When Young first carried out the double-split experiment in 1801 he found that light behaved like a wave. 

Firstly, if we were to shine a light on a wall with two parallel slits — and for the sake of simplicity, let's say this light has only one wavelength. 

As the light passes through the slits, each, in turn, becomes almost like a new source of light. On the far side of the divider, the light from each slit diffracts and overlaps with the light from the other slit, interfering with each other. 

According to Stony Brook University , any wave can create an interference pattern, whether it be a sound wave, light wave or waves across a body of water. When a wave crest hits a wave trough they cancel each other out — known as destructive interference — and appear as a dark band. When a crest hits a crest they amplify each other — known as constructive interference — and appear as a bright band. The combination of dark and bright bands is known as an interference pattern and can be seen on the sensor screen opposite the slits. 

This interference pattern was the evidence Young needed to determine that light was a wave and not a particle as Newton had suggested. 

But that is not the whole story. Light is a little more complicated than that, and to see how strange it really is we also need to understand what pattern a particle would make on a sensor field. 

If you were to carry out the same experiment and fire grains of sand or other particles through the slits, you would end up with a different pattern on the sensor screen. Each particle would go through a slit end up in a line in roughly the same place (with a little bit of spread depending on the angle the particle passed through the slit).  

Clearly, waves and particles produce a very different pattern, so it should be easy to distinguish between the two right? Well, this is where the double-slit experiment gets a little strange when we try and carry out the same experiment but with tiny particles of light called photons. Enter the realm of quantum mechanics. 

The smallest constituent of light is subatomic particles called photons. By using photons instead of grains of sand we can carry out the double-slit experiment on an atomic scale. 

If you block off one of the slits, so it is just a single-slit experiment, and fire photons through to the sensor screen, the photons will appear as pinprick points on the sensor screen, mimicking the particle patterns produced by sand in the previous example. From this evidence, we could suggest that photons are particles. 

Now, this is where things start to get weird. 

If you unblock the slit and fire photons through both slits, you start to see something very similar to the interference pattern produced by waves in the light example. The photons appear to have gone through the pair of slits acting like waves. 

But what if you launch photons one by one, leaving enough time between them that they don't have a chance of interfering with each other, will they behave like particles or waves? 

At first, the photons appear on the sensor screen in a random scattered manner, but as you fire more and more of them, an interference pattern begins to emerge. Each photon by itself appears to be contributing to the overall wave-like behavior that manifests as an interference pattern on the screen — even though they were launched one at a time so that no interference between them was possible.

It's almost as though each photon is "aware" that there are two slits available. How? Does it split into two and then rejoin after the slit and then hit the sensor? To investigate this, scientists set up a detector that can tell which slit the photon passes through. 

Again, we fire photons one at a time at the slits, as we did in the previous example. The detector finds that about 50% of the photons have passed through the top slit and about 50% through the bottom, and confirms that each photon goes through one slit or the other. Nothing too unusual there. 

But when we look at the sensor screen on this experiment, a different pattern emerges. 

This pattern matches the one we saw when we fired particles through the slits. It appears that monitoring the photons triggers them to switch from the interference pattern produced by waves to that produced by particles. 

If the detection of photons through the slits is apparently affecting the pattern on the sensor screen, what happens if we leave the detector in place but switch it off? (Shh, don't tell the photons we're no longer spying on them!) 

This is where things get really, really weird. 

Same slits, same photons, same detector, just turned off. Will we see the same particle-like pattern? 

No. The particles again make a wave-like interference pattern on the sensor screen. 

The atoms appear to act like waves when you're not watching them, but as particles when you are. How? Well, if you can answer that, a Nobel Prize is waiting for you. 

In the 1930s, scientists proposed that human consciousness might affect quantum mechanics. Mathematician John Von Neumann first postulated this in 1932 in his book " The Mathematical Foundations of Quantum Mechanics ." In the 1960s, theoretical physicist, Eugene Wigner conceived a thought experiment called Wigner's friend — a paradox in quantum physics that describes the states of two people, one conducting the experiment and the observer of the first person, according to science magazine Popular Mechanics . The idea that the consciousness of a person carrying out the experiment can affect the result is knowns as the Von Neumann–Wigner interpretation.

Though a spiritual explanation for quantum mechanic behavior is still believed by a few individuals, including author and alternative medicine advocate Deepak Chopra , a majority of the science community has long disregarded it. 

As for a more plausible theory, scientists are stumped. 

Furthermore —and perhaps even more astonishingly — if you set up the double-slit experiment to detect which slit the photon went through after the photon has already hit the sensor screen, you still end up with a particle-type pattern on the sensor screen, even though the photon hadn't yet been detected when it hit the screen. This result suggests that detecting a photon in the future affects the pattern produced by the photon on the sensor screen in the past. This experiment is known as the quantum eraser experiment and is explained in more detail in this informative video from Fermilab . 

We still don't fully understand how exactly the particle-wave duality of matter works, which is why it is regarded as one of the greatest mysteries of quantum mechanics. 

The first version of the double-slit experiment was carried out in 1801 by British polymath Thomas Young, according to the American Physical Society (APS). His experiment demonstrated the interference of light waves and provided evidence that light was a wave, not a particle. 

Young also used data from his experiments to calculate the wavelengths of different colors of light and came very close to modern values.

Despite his convincing experiment that light was a wave, those who did not want to accept that Isaac Newton could have been wrong about something criticized Young. (Newton had proposed the corpuscular theory, which posited that light was composed of a stream of tiny particles he called corpuscles.) 

According to APS, Young wrote in response to one of the critics, "Much as I venerate the name of Newton, I am not therefore obliged to believe that he was infallible."

Since the development of quantum mechanics, physicists now acknowledge light to be both a particle and a wave. 

Explore the double-slit experiment in more detail with this article from the University of Cambridge, which includes images of electron patterns in a double-slit experiment. Discover the true nature of light with Canon Science Lab . Read about fragments of energy that are not waves or particles — but could be the fundamental building blocks of the universe — in this article from The Conversation . Dive deeper into the two-slit experiment in this article published in the journal Nature . 

Bibliography

Grangier, Philippe, Gerard Roger, and Alain Aspect. " Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences. " EPL (Europhysics Letters) 1.4 (1986): 173.

Thorn, J. J., et al. "Observing the quantum behavior of light in an undergraduate laboratory. " American Journal of Physics 72.9 (2004): 1210-1219.

Ghose, Partha. " The central mystery of quantum mechanics. " arXiv preprint arXiv:0906.0898 (2009).

Aharonov, Yakir, et al. " Finally making sense of the double-slit experiment. " Proceedings of the National Academy of Sciences 114.25 (2017): 6480-6485.

Peng, Hui. " Observations of Cross-Double-Slit Experiments. " International Journal of Physics 8.2 (2020): 39-41. 

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27.3 Young’s Double Slit Experiment

Learning objectives.

By the end of this section, you will be able to:

• Explain the phenomena of interference.
• Define constructive interference for a double slit and destructive interference for a double slit.

Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see Figure 27.10 ).

Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent. By coherent , we mean waves are in phase or have a definite phase relationship. Incoherent means the waves have random phase relationships. Why did Young then pass the light through a double slit? The answer to this question is that two slits provide two coherent light sources that then interfere constructively or destructively. Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. We illustrate the double slit experiment with monochromatic (single λ λ ) light to clarify the effect. Figure 27.11 shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 27.12 (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in Figure 27.12 (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

To understand the double slit interference pattern, we consider how two waves travel from the slits to the screen, as illustrated in Figure 27.13 . Each slit is a different distance from a given point on the screen. Thus different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively as shown in Figure 27.13 (a). If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively as shown in Figure 27.13 (b). More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths [ ( 1 / 2 ) λ ( 1 / 2 ) λ , ( 3 / 2 ) λ ( 3 / 2 ) λ , ( 5 / 2 ) λ ( 5 / 2 ) λ , etc.], then destructive interference occurs. Similarly, if the paths taken by the two waves differ by any integral number of wavelengths ( λ λ , 2 λ 2 λ , 3 λ 3 λ , etc.), then constructive interference occurs.

Take-Home Experiment: Using Fingers as Slits

Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?

Figure 27.14 shows how to determine the path length difference for waves traveling from two slits to a common point on a screen. If the screen is a large distance away compared with the distance between the slits, then the angle θ θ between the path and a line from the slits to the screen (see the figure) is nearly the same for each path. The difference between the paths is shown in the figure; simple trigonometry shows it to be d sin θ d sin θ , where d d is the distance between the slits. To obtain constructive interference for a double slit , the path length difference must be an integral multiple of the wavelength, or

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

where λ λ is the wavelength of the light, d d is the distance between slits, and θ θ is the angle from the original direction of the beam as discussed above. We call m m the order of the interference. For example, m = 4 m = 4 is fourth-order interference.

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in Figure 27.15 . The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation

For fixed λ λ and m m , the smaller d d is, the larger θ θ must be, since sin θ = mλ / d sin θ = mλ / d . This is consistent with our contention that wave effects are most noticeable when the object the wave encounters (here, slits a distance d d apart) is small. Small d d gives large θ θ , hence a large effect.

Example 27.1

Finding a wavelength from an interference pattern.

Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of 10 . 95º 10 . 95º relative to the incident beam. What is the wavelength of the light?

The third bright line is due to third-order constructive interference, which means that m = 3 m = 3 . We are given d = 0 . 0100 mm d = 0 . 0100 mm and θ = 10 . 95º θ = 10 . 95º . The wavelength can thus be found using the equation d sin θ = mλ d sin θ = mλ for constructive interference.

The equation is d sin θ = mλ d sin θ = mλ . Solving for the wavelength λ λ gives

Substituting known values yields

To three digits, this is the wavelength of light emitted by the common He-Ne laser. Not by coincidence, this red color is similar to that emitted by neon lights. More important, however, is the fact that interference patterns can be used to measure wavelength. Young did this for visible wavelengths. This analytical technique is still widely used to measure electromagnetic spectra. For a given order, the angle for constructive interference increases with λ λ , so that spectra (measurements of intensity versus wavelength) can be obtained.

Example 27.2

Calculating highest order possible.

Interference patterns do not have an infinite number of lines, since there is a limit to how big m m can be. What is the highest-order constructive interference possible with the system described in the preceding example?

Strategy and Concept

The equation d sin θ = mλ (for m = 0, 1, − 1, 2, − 2, … ) d sin θ = mλ (for m = 0, 1, − 1, 2, − 2, … ) describes constructive interference. For fixed values of d d and λ λ , the larger m m is, the larger sin θ sin θ is. However, the maximum value that sin θ sin θ can have is 1, for an angle of 90º 90º . (Larger angles imply that light goes backward and does not reach the screen at all.) Let us find which m m corresponds to this maximum diffraction angle.

Solving the equation d sin θ = mλ d sin θ = mλ  for  m m gives

Taking sin θ = 1 sin θ = 1 and substituting the values of d d and λ λ from the preceding example gives

Therefore, the largest integer m m can be is 15, or

The number of fringes depends on the wavelength and slit separation. The number of fringes will be very large for large slit separations. However, if the slit separation becomes much greater than the wavelength, the intensity of the interference pattern changes so that the screen has two bright lines cast by the slits, as expected when light behaves like a ray. We also note that the fringes get fainter further away from the center. Consequently, not all 15 fringes may be observable.

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Double-slit Experiment

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Plane wave representing a particle passing through two slits, resulting in an interference pattern on a screen some distance away from the slits. [1] .

The double-slit experiment is an experiment in quantum mechanics and optics demonstrating the wave-particle duality of electrons , photons , and other fundamental objects in physics. When streams of particles such as electrons or photons pass through two narrow adjacent slits to hit a detector screen on the other side, they don't form clusters based on whether they passed through one slit or the other. Instead, they interfere: simultaneously passing through both slits, and producing a pattern of interference bands on the screen. This phenomenon occurs even if the particles are fired one at a time, showing that the particles demonstrate some wave behavior by interfering with themselves as if they were a wave passing through both slits.

Niels Bohr proposed the idea of wave-particle duality to explain the results of the double-slit experiment. The idea is that all fundamental particles behave in some ways like waves and in other ways like particles, depending on what properties are being observed. These insights led to the development of quantum mechanics and quantum field theory , the current basis behind the Standard Model of particle physics , which is our most accurate understanding of how particles work.

The original double-slit experiment was performed using light/photons around the turn of the nineteenth century by Thomas Young, so the original experiment is often called Young's double-slit experiment. The idea of using particles other than photons in the experiment did not come until after the ideas of de Broglie and the advent of quantum mechanics, when it was proposed that fundamental particles might also behave as waves with characteristic wavelengths depending on their momenta. The single-electron version of the experiment was in fact not performed until 1974. A more recent version of the experiment successfully demonstrating wave-particle duality used buckminsterfullerene or buckyballs , the \(C_{60}\) allotrope of carbon.

Waves vs. Particles

Double-slit experiment with electrons, modeling the double-slit experiment.

To understand why the double-slit experiment is important, it is useful to understand the strong distinctions between wave and particles that make wave-particle duality so intriguing.

Waves describe oscillating values of a physical quantity that obey the wave equation . They are usually described by sums of sine and cosine functions, since any periodic (oscillating) function may be decomposed into a Fourier series . When two waves pass through each other, the resulting wave is the sum of the two original waves. This is called a superposition since the waves are placed ("-position") on top of each other ("super-"). Superposition is one of the most fundamental principles of quantum mechanics. A general quantum system need not be in one state or another but can reside in a superposition of two where there is some probability of measuring the quantum wavefunction in one state or another.

Left: example of superposed waves constructively interfering. Right: superposed waves destructively interfering. [2]

If one wave is \(A(x) = \sin (2x)\) and the other is \(B(x) = \sin (2x)\), then they add together to make \(A + B = 2 \sin (2x)\). The addition of two waves to form a wave of larger amplitude is in general known as constructive interference since the interference results in a larger wave.

If one wave is \(A(x) = \sin (2x)\) and the other is \(B(x) = \sin (2x + \pi)\), then they add together to make \(A + B = 0\) \(\big(\)since \(\sin (2x + \pi) = - \sin (2x)\big).\) This is known as destructive interference in general, when adding two waves results in a wave of smaller amplitude. See the figure above for examples of both constructive and destructive interference.

Two speakers are generating sounds with the same phase, amplitude, and wavelength. The two sound waves can make constructive interference, as above left. Or they can make destructive interference, as above right. If we want to find out the exact position where the two sounds make destructive interference, which of the following do we need to know?

a) the wavelength of the sound waves b) the distances from the two speakers c) the speed of sound generated by the two speakers

This wave behavior is quite unlike the behavior of particles. Classically, particles are objects with a single definite position and a single definite momentum. Particles do not make interference patterns with other particles in detectors whether or not they pass through slits. They only interact by colliding elastically , i.e., via electromagnetic forces at short distances. Before the discovery of quantum mechanics, it was assumed that waves and particles were two distinct models for objects, and that any real physical thing could only be described as a particle or as a wave, but not both.

In the more modern version of the double slit experiment using electrons, electrons with the same momentum are shot from an "electron gun" like the ones inside CRT televisions towards a screen with two slits in it. After each electron goes through one of the slits, it is observed hitting a single point on a detecting screen at an apparently random location. As more and more electrons pass through, one at a time, they form an overall pattern of light and dark interference bands. If each electron was truly just a point particle, then there would only be two clusters of observations: one for the electrons passing through the left slit, and one for the right. However, if electrons are made of waves, they interfere with themselves and pass through both slits simultaneously. Indeed, this is what is observed when the double-slit experiment is performed using electrons. It must therefore be true that the electron is interfering with itself since each electron was only sent through one at a time—there were no other electrons to interfere with it!

When the double-slit experiment is performed using electrons instead of photons, the relevant wavelength is the de Broglie wavelength \(\lambda:\)

\[\lambda = \frac{h}{p},\]

where \(h\) is Planck's constant and \(p\) is the electron's momentum.

Calculate the de Broglie wavelength of an electron moving with velocity \(1.0 \times 10^{7} \text{ m/s}.\)

Usain Bolt, the world champion sprinter, hit a top speed of 27.79 miles per hour at the Olympics. If he has a mass of 94 kg, what was his de Broglie wavelength?

Express your answer as an order of magnitude in units of the Bohr radius \(r_{B} = 5.29 \times 10^{-11} \text{m}\). For instance, if your answer was \(4 \times 10^{-5} r_{B}\), your should give \(-5.\)

Image Credit: Flickr drcliffordchoi.

While the de Broglie relation was postulated for massive matter, the equation applies equally well to light. Given light of a certain wavelength, the momentum and energy of that light can be found using de Broglie's formula. This generalizes the naive formula \(p = m v\), which can't be applied to light since light has no mass and always moves at a constant velocity of \(c\) regardless of wavelength.

The below is reproduced from the Amplitude, Frequency, Wave Number, Phase Shift wiki.

In Young's double-slit experiment, photons corresponding to light of wavelength \(\lambda\) are fired at a barrier with two thin slits separated by a distance \(d,\) as shown in the diagram below. After passing through the slits, they hit a screen at a distance of \(D\) away with \(D \gg d,\) and the point of impact is measured. Remarkably, both the experiment and theory of quantum mechanics predict that the number of photons measured at each point along the screen follows a complicated series of peaks and troughs called an interference pattern as below. The photons must exhibit the wave behavior of a relative phase shift somehow to be responsible for this phenomenon. Below, the condition for which maxima of the interference pattern occur on the screen is derived.

Left: actual experimental two-slit interference pattern of photons, exhibiting many small peaks and troughs. Right: schematic diagram of the experiment as described above. [3]

Since \(D \gg d\), the angle from each of the slits is approximately the same and equal to \(\theta\). If \(y\) is the vertical displacement to an interference peak from the midpoint between the slits, it is therefore true that

\[D\tan \theta \approx D\sin \theta \approx D\theta = y.\]

Furthermore, there is a path difference \(\Delta L\) between the two slits and the interference peak. Light from the lower slit must travel \(\Delta L\) further to reach any particular spot on the screen, as in the diagram below:

Light from the lower slit must travel further to reach the screen at any given point above the midpoint, causing the interference pattern.

The condition for constructive interference is that the path difference \(\Delta L\) is exactly equal to an integer number of wavelengths. The phase shift of light traveling over an integer \(n\) number of wavelengths is exactly \(2\pi n\), which is the same as no phase shift and therefore constructive interference. From the above diagram and basic trigonometry, one can write

\[\Delta L = d\sin \theta \approx d\theta = n\lambda.\]

The first equality is always true; the second is the condition for constructive interference.

Now using \(\theta = \frac{y}{D}\), one can see that the condition for maxima of the interference pattern, corresponding to constructive interference, is

\[n\lambda = \frac{dy}{D},\]

i.e. the maxima occur at the vertical displacements of

\[y = \frac{n\lambda D}{d}.\]

The analogous experimental setup and mathematical modeling using electrons instead of photons is identical except that the de Broglie wavelength of the electrons \(\lambda = \frac{h}{p}\) is used instead of the literal wavelength of light.

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How to Perform Young's Double Slit Experiment

Last Updated: August 10, 2021

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 18 people, some anonymous, worked to edit and improve it over time. This article has been viewed 41,262 times.

Thomas Young's double slit experiment was extremely important in the area of wave theory . His experiment proves that light exhibits wavelike properties. Monochromatic light, light consisting of one color, is split using two slits placed close together. Two coherent light waves emerge on the other side of the slits. Coherent light, meaning the waves have the same frequency and phase , will both constructively and destructively interact. This interaction causes light and dark fringes based on simple geometry. If this pattern is in fact the result of the experiment, light is proven to have wavelike properties.

The light and dark fringes are caused by the difference in phase of the light when it is incident on an object (i.e. light sensor). The light from the bottom slit has farther to travel and therefore a phase difference exists between the two rays of light. This interaction between these two waves creates a light, dark, or intermediate fringe.

An area where a light fringe occurs, the phase difference between the two coherent light waves is zero degrees. For example, there is no phase difference and the waves add together to create a fringe with maximum intensity. An area where a dark fringe occurs, the phase difference between the two coherent light waves is equal to 180 degrees. At this point, the waves add together and completely cancel each other out. Intermediate fringes occur when the phase difference is somewhere between zero and 180 degrees. In general, intensity of the fringe decreases as the phase difference between the two light waves increases from zero to 180 degrees.

• Begin with the optics bench in front of you with the 0 centimeter (0.0 in) mark on your left.
• Install the diode laser at the 0 centimeter (0.0 in) mark facing towards the right. This should require little effort.
• Mount the multi-slit apparatus to its appropriate mount. This may require some force and will make a clicking sound when properly installed. Assembly should prove to be rather simple.
• Install the newly assembled multi-slit apparatus on the optics bench between the 5 and 10 cm mark. Adjustment will be made later in the experiment to both position and slit settings.

• Remove one of the screws from the linear translator that secures the grooved bar and pull it out away from frame of the linear translator.
• Install the rotary motion sensor onto the grooved bar. This can be achieved by sliding the grooved bar into the square hole in the center of the rotary motion sensor. One important note is that the set of mounted pulleys on the rotary motion sensor should be facing upwards when installed properly.
• Replace the grooved bar to its original position and reinsert the screw.
• You should notice that one end of the connecting rod is slightly smaller in diameter and is threaded. In one hand hold the connecting rod with the threaded end up. Place the aperture mount on the rod followed by the light sensor making sure that the aperture of the light sensor is firmly against the rotating disk consisting of varying sized apertures.
• Simply screw in the connecting rod (Hand tighten only).
• Mount this newly created piece by placing the connecting rod into the last remaining hole of the rotary motion sensor, so that the light sensor apparatus is upright.
• Tighten the retention screw on the rotary motion sensor (Hand tighten only).

• Adjust the position of the nut until it enters the highest channel and the linear translator is resting on the raised surface of the optics bench.
• Slide the linear translator down the track until the light sensor is approximately 1 meter (3.3 ft) from the multi-slit apparatus. This may require moving the multi-slit apparatus closer to the diode laser.

• Select one of the double slits from the multi-slit apparatus, at this point it doesn't matter which one, by spinning the multi-slit wheel until the appropriate slit is mostly in line with the diode laser. You will be able to feel a slight popping as each slit grouping reaches this position.
• Turn the diode laser on by connecting the power supply and flipping the switch on the back of the diode laser. Note that beside the on/off switch there are two knobs. One will adjust the diode laser in the vertical direction and the other in the horizontal direction.
• At the other end of the optics bench adjust the aperture setting of the light sensor mount until slit #3 is selected.
• With the laser on, adjust both the horizontal and vertical knobs until you have created an interference and diffraction pattern (looks like a line of light) that shines through the narrow slit of the light sensor apparatus that you just adjusted, insuring that that the pattern is also perpendicular to slit #3.
• Setup your computer, including a graph on Data Studio plotting intensity vs. distance.

• Select a set of appropriate double slits from the multi-slit apparatus and spin them into position. One thing to keep in mind when choosing is that the smaller the slit size the harder it will be to detect maximums of higher m values.
• Turn off the lights and adjust the computer screen in order to reduce ambient light.
• Turn on the diode laser.
• Move the rotary motion sensor to one side of the linear translator.
• Click 'Start' on Data Studio to begin collecting data.
• Slowly and smoothly move the rotary motion sensor to the other side of the linear translator.
• Click 'Stop' to finish collecting data.
• Slit Distance = d (Values may be found on the multi-slit apparatus)
• Slit Size = a (Values may be found on the multi-slit apparatus)
• Distance from multi-slit apparatus to the light sensor = l
• Distances from central maximum to other maximums (see graph) = x
• Wavelength = λ

Expert Q&A

• Move the rotary motion sensor at a slow and constant speed. Thanks Helpful 0 Not Helpful 0
• Make the room as dark as possible. This can not be stressed enough and also includes the computer screen. Thanks Helpful 0 Not Helpful 1
• Start with larger double slit settings and work your way down. Thanks Helpful 0 Not Helpful 1
• Do not look directly into the diode laser. It causes permanent damage. Thanks Helpful 4 Not Helpful 1

Things You'll Need

• Optics bench
• diode laser & power cord
• light sensor
• light sensor aperture mounting apparatus with connecting rod
• linear translator
• multi-slit apparatus & apparatus mount
• Data Studios
• rotary motion sensor

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• Do the "Double Slit" Experiment the Way it Was Originally Done

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• Quantum mechanics
• Opinion and reviews

The double-slit experiment

This article is an extended version of the article “The double-slit experiment” that appeared in the September 2002 issue of Physics World (p15). It has been further extended to include three letters about the history of the double-slit experiment with single electrons that were published in the May 2003 issue of the magazine.

What is the most beautiful experiment in physics? This is the question that Robert Crease asked Physics World readers in May – and more than 200 replied with suggestions as diverse as Schrödinger’s cat and the Trinity nuclear test in 1945. The top five included classic experiments by Galileo, Millikan, Newton and Thomas Young. But uniquely among the top 10, the most beautiful experiment in physics – Young’s double-slit experiment applied to the interference of single electrons – does not have a name associated with it.

Most discussions of double-slit experiments with particles refer to Feynman’s quote in his lectures: “We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery.” Feynman went on to add: “We should say right away that you should not try to set up this experiment. This experiment has never been done in just this way. The trouble is that the apparatus would have to be made on an impossibly small scale to show the effects we are interested in. We are doing a “thought experiment”, which we have chosen because it is easy to think about. We know the results that would be obtained because there are many experiments that have been done, in which the scale and the proportions have been chosen to show the effects we shall describe”.

It is not clear that Feynman was aware that the first double-slit experiment with electrons had been carried out in 1961, the year he started his lectures (which were published in 1963). More surprisingly, perhaps, Feynman did not stress that an interference pattern would build up even if there was just one electron in the apparatus at a time. (This lack of emphasis was unusual because in the same lecture Feynman describes the electron experiment – and other double-slit experiments with water waves and bullets – in considerable detail).

So who actually carried out the first double-slit experiment with single electrons? Not surprisingly many thought or gedanken experiments are named after theorists – such as the Aharonov-Bohm effect, Bell’s inequality, the Casimir force, the Einstein-Podolsky-Rosen paradox, Schrödinger’s cat and so on – and these names rightly remain even when the experiment has been performed by others in the laboratory. However, it seems remarkable that no name whatsoever is attached to the double-slit experiment with electrons. Standard reference books are silent on this question but a study of the literature reveals several unsung experimental heroes.

Back to Young

Young carried out his original double-slit experiment with light some time in the first decade of the 1800s, showing that the waves of light from the two slits interfered to produce a characteristic fringe pattern on a screen. In 1909 Geoffrey Ingram (G I) Taylor conducted an experiment in which he showed that even the feeblest light source – equivalent to “a candle burning at a distance slightly exceeding a mile” – could lead to interference fringes. This led to Dirac’s famous statement that “each photon then interferes only with itself”.

In 1927 Clinton Davisson and Lester Germer observed the diffraction of electron beams from a nickel crystal – demonstrating the wave-like properties of particles for the first time – and George (G P) Thompson did the same with thin films of celluloid and other materials shortly afterwards. Davisson and Thomson shared the 1937 Nobel prize for “discovery of the interference phenomena arising when crystals are exposed to electronic beams”, but neither performed a double-slit experiment with electrons.

In the early 1950s Ladislaus Laszlo Marton of the US National Bureau of Standards (now NIST) in Washington, DC demonstrated electron interference but this was in a Mach-Zehnder rather than a double-slit geometry. These were the early days of the electron microscope and physicists were keen to exploit the very short de Broglie wavelength of electrons to study objects that were too small to be studied with visible light. Doing gedanken or thought experiments in the laboratory was further down their list of priorities.

A few years later Gottfried Möllenstedt and Heinrich Düker of the University of Tübingen in Germany used an electron biprism – essentially a very thin conducting wire at right angles to the beam – to split an electron beam into two components and observe interference between them. (Möllenstedt made the wires by coating fibres from spiders’ webs with gold – indeed, it is said that he kept spiders in the laboratory for this purpose). The electron biprism was to become widely used in the development of electron holography and also in other experiments, including the first measurement of the Aharonov-Bohm effect by Bob Chambers at Bristol University in the UK in 1960.

But in 1961 Claus Jönsson of Tübingen, who had been one of Möllenstedt’s students, finally performed an actual double-slit experiment with electrons for the first time ( Zeitschrift für Physik 161 454). Indeed, he demonstrated interference with up to five slits. The next milestone – an experiment in which there was just one electron in the apparatus at any one time – was reached by Akira Tonomura and co-workers at Hitachi in 1989 when they observed the build up of the fringe pattern with a very weak electron source and an electron biprism ( American Journal of Physics 57 117-120). Whereas Jönsson’s experiment was analogous to Young’s original experiment, Tonomura’s was similar to G I Taylor’s. (Note added on 7 May: Pier Giorgio Merli, Giulio Pozzi and GianFranco Missiroli carried out double-slit interference experiments with single electrons in Bologna in the 1970s; see Merli et al. in Further reading and the letters from Steeds, Merli et al. , and Tonomura at the end of this article.)

Since then particle interference has been demonstrated with neutrons, atoms and molecules as large as carbon-60 and carbon-70. And earlier this year another famous experiment in optics – the Hanbury Brown and Twiss experiment – was performed with electrons for the first time (again at Tübingen!). However, the results are profoundly different this time because electrons are fermions – and therefore obey the Pauli exclusion principle – whereas photons are bosons and do not.

Credit where it’s due

So why are Jönsson, Tonomura and the other pioneers of the double-slit experiment not well known? One obvious reason is that Jönsson’s results were first published in German in a German journal. Another reason might be that there was little incentive to perform the ultimate thought experiment in the lab, and little recognition for doing so. When Jönsson’s paper was translated into English 13 years later and published in the American Journal of Physics in 1974 (volume 42, pp4-11), the journal’s editors, Anthony (A P) French and Edwin Taylor, described it as a “great experiment”, but added that there are “few professional rewards” for performing what they describe as “real, pedagogically clean fundamental experiments.”

It is worth noting that the first double-slit experiment with single electrons by Tonomura and co-workers was also published in the American Journal of Physics , which publishes articles on the educational and cultural aspects of physics, rather than being a research journal. Indeed, the journal’s information for contributors states: “We particularly encourage manuscripts on already published contemporary research that can be used directly or indirectly in the classroom. We specifically do not publish articles announcing new theories or experimental results.”

French and Taylor’s editorial also confirms how little known Jönsson’s experiment was at the time: “For decades two-slit electron interference has been presented as a thought experiment whose predicted results are justified by their remote and somewhat obscure relation to real experiments in which electrons are diffracted by crystals. Few such recent presentations acknowledge that the two-slit electron interference experiment has now been done and that the results agree with the expectation of quantum physics in all detail.”

However, it should be noted that the history of physics is complicated and that events are rarely as clear-cut as we might like. For instance, it is widely claimed that Young performed his double-slit experiment in 1801 but he did not publish any account of it until his Lectures on Natural Philosophy in 1807. It also appears as if Davisson and a young collaborator called Charles Kunsman observed electron diffraction in 1923 – four years before Davisson and Germer – without realising it.

Final thoughts

Gedanken or thought experiments have played an important role in the history of quantum physics. It is unlikely that the whole area of quantum information would be as lively as it is today – both theoretically and experimentally – if a small band of physicists had not persevered and actually demonstrated quantum phenomena with individual particles.

At one time the Casimir force, which has yet to be measured with an accuracy of better than 15% in the geometry first proposed by Hendrik Casimir in 1948, might also have been viewed as purely a pedagogical experiment – a gedanken experiment with little relevance to real experimental physics. However, it is now clear that applications as varied as nanotechnology and experimental tests of theories of “large” extra dimensions require a detailed knowledge of the Casimir force .

The need for “real, pedagogically clean fundamental experiments” is clearly as great as ever.

This is a longer version of the article “The double-slit experiment” that appeared in the print version of the September issue of Physics World, on page 15. Three letters that appeared in the May 2003 issue of the magazine have been added to the end of this version of the article.

T Young 1802 On the theory of light and colours (The 1801 Bakerian Lecture) Philosophical Transactions of the Royal Society of London 92 12-48

T Young 1804 Experiments and calculations relative to physical optics (The 1803 Bakerian Lecture) Philosophical Transactions of the Royal Society of London 94 1-16

T Young 1807 A Course of Lectures on Natural Philosophy and the Mechanical Arts (J Johnson, London)

G I Taylor 1909 Interference fringes with feeble light Proceedings of the Cambridge Philosophical Society 15 114-115

P A M Dirac 1958 The Principles of Quantum Mechanics (Oxford University Press) 4th edn p9

R P Feynman, R B Leighton and M Sands 1963 The Feynman Lecture on Physics (Addison-Wesley) vol 3 ch 37 (Quantum behaviour)

A Howie and J E Fowcs Williams (eds) 2002 Interference: 200 years after Thomas Young’s discoveries Philosophical Transactions of the Royal Society of London 360 803-1069

R P Crease 2002 The most beautiful experiment Physics World September pp19-20. This article contains the results of Crease’s survey for Physics World ; the first article about the survey appeared on page 17 of the May 2002 issue.

Electron interference experiments

Visit www.nobel.se/physics/laureates/1937/index.html for details of the Nobel prize awarded to Clinton Davisson and George Thomson

L Marton 1952 Electron interferometer Physical Review 85 1057-1058

L Marton, J Arol Simpson and J A Suddeth 1953 Electron beam interferometer Physical Review 90 490-491

L Marton, J Arol Simpson and J A Suddeth 1954 An electron interferometer Reviews of Scientific Instruments 25 1099-1104

G Möllenstedt and H Düker 1955 Naturwissenschaften 42 41

G Möllenstedt and H Düker 1956 Zeitschrift für Physik 145 377-397

G Möllenstedt and C Jönsson 1959 Zeitschrift für Physik 155 472-474

R G Chambers 1960 Shift of an electron interference pattern by enclosed magnetic flux Physical Review Letters 5 3-5

C Jönsson 1961 Zeitschrift für Physik 161 454-474

C Jönsson 1974 Electron diffraction at multiple slits American Journal of Physics 42 4-11

A P French and E F Taylor 1974 The pedagogically clean, fundamental experiment American Journal of Physics 42 3

P G Merli, G F Missiroli and G Pozzi 1976 On the statistical aspect of electron interference phenomena American Journal of Physics 44 306-7

A Tonomura, J Endo, T Matsuda, T Kawasaki and H Ezawa 1989 Demonstration of single-electron build-up of an interference pattern American Journal of Physics 57 117-120

H Kiesel, A Renz and F Hasselbach 2002 Observation of Hanbury Brown-Twiss anticorrelations for free electrons Nature 418 392-394

Atoms and molecules

O Carnal and J Mlynek 1991 Young’s double-slit experiment with atoms: a simple atom interferometer Physical Review Letters 66 2689-2692

D W Keith, C R Ekstrom, Q A Turchette and D E Pritchard 1991 An interferometer for atoms Physical Review Letters 66 2693-2696

M W Noel and C R Stroud Jr 1995 Young’s double-slit interferometry within an atom Physical Review Letters 75 1252-1255

M Arndt, O Nairz, J Vos-Andreae, C Keller, G van der Zouw and A Zeilinger 1999 Wave-particle duality of C 60 molecules Nature 401 680-682

B Brezger, L Hackermüller, S Uttenthaler, J Petschinka, M Arndt and A Zeilinger 2002 Matter-wave interferometer for large molecules Physical Review Letters 88 100404

Review articles and books

G F Missiroli, G Pozzi and U Valdrè 1981 Electron interferometry and interference electron microscopy Journal of Physics E 14 649-671. This review covers early work on electron interferometry by groups in Bologna, Toulouse, Tübingen and elsewhere.

A Zeilinger, R Gähler, C G Shull, W Treimer and W Mampe 1988 Single- and double-slit diffraction of neutrons Reviews of Modern Physics 60 1067-1073

A Tonomura 1993 Electron Holography (Springer-Verlag, Berlin/New York)

H Rauch and S A Werner 2000 Neutron Interferometry: Lessons in Experimental Quantum Mechanics (Oxford Science Publications)

The double-slit experiment with single electrons

The article “A brief history of the double-slit experiment” (September 2002 p15; correction October p17) describes how Claus Jönsson of the University of Tübingen performed the first double-slit interference experiment with electrons in 1961. It then goes on to say: “The next milestone – an experiment in which there was just one electron in the apparatus at any one time – was reached by Akira Tonomura and co-workers at Hitachi in 1989 when they observed the build up of the fringe pattern with a very weak electron source and an electron biprism ( Am. J. Phys. 57 117-120)”.

In fact, I believe that “the first double-slit experiment with single electrons” was performed by Pier Giorgio Merli, GianFranco Missiroli and Giulio Pozzi in Bologna in 1974 – some 15 years before the Hitachi experiment. Moreover, the Bologna experiment was performed under very difficult experimental conditions: the intrinsic coherence of the thermionic electron source used by the Bologna group was considerably lower than that of the field-emission source used in the Hitachi experiment.

The Bologna experiment is reported in a film called “Electron Interference” that received the award in the physics category at the International Festival on Scientific Cinematography in Brussels in 1976. A selection of six frames from the film ( see figure ) was also used for a short paper, “On the statistical aspect of electron interference phenomena”, that was submitted for publication in May 1974 and published two years later (P G Merli, G F Missiroli and G Pozzi 1976 Am. J. Phys. 44 306-7).

John Steeds Department of Physics, University of Bristol [email protected]

The history of science is not restricted to the achievements of big scientists or big scientific institutions. Contributions can also be made by researchers with the necessary background, curiosity and enthusiasm. In the period 1973-1974 we were investigating practical applications of electron interferometry with a Siemens Elmiskop 101 electron microscope that had been carefully calibrated at the CNR-LAMEL laboratory in Bologna, where one of us (PGM) was based ( J. Phys. E7 729-32).

These experiments followed earlier work at the Istituto di Fisica in 1972-73 in which the electron biprism was inserted in a Siemens Elmiskop IA and then used both for didactic ( Am. J. Phys. 41 639-644) and research experiments ( J. Microscopie 18 103-108). We used the Elmiskop 101 for many experiments including, for instance, the observation of the electrostatic field associated with p-n junctions ( J. Microscopie 21 11-20).

During this period we learnt that Professors Angelo and Aurelio Bairati in the Institute of Anatomy at the University of Milan had bought an image intensifier that could be used with the Elmiskop 101. Out of curiosity, and also realizing the conceptual importance of interference experiments with single photons or electrons, we asked if we could attempt to perform an interference experiment with single electrons in the Milan laboratory. Our results formed the basis of the film “Electron interference” and were also published in 1976 ( Am. J. Phys. 44 306-7).

Following the publication of the paper by Tonomura and co-workers in 1989, which did not refer to our 1976 paper (although it did contain an incorrect reference to our film), the American Journal of Physics published a letter from Greyson Gilson of Submicron Structures Inc. The letter stated: “Tonomura et al. seem to believe that they were the first to perform a successful two-slit interference experiment using electrons and also that they were the first to observe the cumulative build-up of the resulting electron interference pattern. Although their demonstration is very admirable, reports of similar work have appeared in this Journal for about 30 years (see, for examples, Refs. 2-7.) It seems inappropriate to permit the widespread misconception that such experiments have not been performed and perhaps cannot be performed to continue.” (G Gilson 1989 Am. J. Phys. 57 680). Three of the seven papers that Gilson refers to were from our group in Bologna.

The main subject of our 1976 paper and the 1989 paper from the Hitachi group are the same: the single-electron build-up of the interference pattern and the statistical aspect of the phenomena. Obviously the electron-detection system used by the Hitachi group in 1989 was more sophisticated than the one we used in 1974. However, the sentence on page 118 of the paper by Tonomura et al. , which states that in our film we “showed the electron arrival in each frame without recording the cumulative arrivals”, is not correct: this can be seen by watching the film and looking at figure 1 of our 1976 paper (a version of which is shown here ).

Finally, it is also worth noting that the first double-slit experiment with single electrons was actually a by-product of research into the practical applications of electron interferometry.

Pier Giorgio Merli LAMEL, CNR Bologna, Italy [email protected] Giulio Pozzi Department of Physics, University of Bologna [email protected] GianFranco Missiroli Department of Physics, University of Bologna [email protected]

The Bologna group photographed the monitor of a sensitive TV camera as they changed the intensity of an electron beam. They observed that a few light flashes of electrons appeared at low intensities, and that interference fringes were formed at high intensities. They also mentioned that they were able to increase the storage time up to “values of minutes”. Historically, they are the first to report such experiments concerning the formation of interference patterns as far as I know.

Later, similar experiments were conducted by Hannes Lichte, then at Tübingen and now at Dresden. Important experiments on electron interference were also carried out by Valentin Fabrikant and co-workers at the Moscow Institute for Energetics in 1949 and later by Takeo Ichinokawa of Waseda University in Tokyo.

Our experiments at Hitachi (A Tonomura, J Endo, T Matsuda, T Kawasaki and H Ezawa 1989 Demonstration of single-electron buildup of an interference pattern Am. J. Phys. 57 117–120) differed from these experiments in the following respects:

(a) Our experiments were carried out from beginning to end with constant and extremely low electron intensities – fewer than 1000 electrons per second – so there was no chance of finding two or more electrons in the apparatus at the same time. This removed any possibility that the fringes might be due to interactions between the electrons, as had been suspected by some physicists, such as Sin-Itiro Tomonaga.

(b) We developed a position-sensitive electron-counting system that was modified from the photon-counting image acquisition system produced by Hamamatsu Photonics. In this system, the formation of fringes could be observed as a time series; the electrons were accumulated over time to gradually form an interference pattern on the monitor (similar to a long exposure with a photographic film). The electrons arrived at random positions on the detector only once in a while and it took more than 20 minutes for the interference pattern to form (see figure). To film the build-up process, the electron source, the electron biprism and the rest of the experiment therefore had to be extremely stable: if the interference pattern had drifted by a fraction of fringe spacing over the exposure time, the whole fringe pattern would have disappeared.

(c) The electrons arriving at the detector were detected with almost 100% efficiency. Counting losses and noise in conventional TV cameras mean that it is difficult to know if each flash of the screen really corresponds to an individual electron. Therefore, the detection error in our experiment was limited to less than 1%.

We believe that we carried out the first experiment in which the build-up process of an interference pattern from single-electron events could be seen in real time as in Feynman’s famous double-slit Gedanken experiment under the condition, we emphasize, that there was no chance of finding two or more electrons in the apparatus.

Akira Tonomura Hitachi Advanced Research Laboratory, Saitama, Japan [email protected]

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• Published: 10 July 2020

Quantum double-double-slit experiment with momentum entangled photons

• Manpreet Kaur 1 &
• Mandip Singh 1  

Scientific Reports volume  10 , Article number:  11427 ( 2020 ) Cite this article

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Double-double-slit thought experiment provides profound insight on interference of quantum entangled particles. This paper presents a detailed experimental realisation of quantum double-double-slit thought experiment with momentum entangled photons and theoretical analysis of the experiment. Experiment is configured in such a way that photons are path entangled and each photon can reveal the which-slit path information of the other photon. As a consequence, single photon interference is suppressed. However, two-photon interference pattern appears if locations of detection of photons are correlated without revealing the which-slit path information. It is also shown experimentally and theoretically that two-photon quantum interference disappears when the which-slit path of a photon in the double-double-slit is detected.

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Introduction.

Wave nature of light was first experimentally demonstrated by the famous Young’s double-slit experiment 1 , 2 . In quantum physics, light is quantised in the form of energy quanta known as photon. According to the statement of P.A.M. Dirac, “Each photon interferes only with itself” 3 . This self interference of a photon is a consequence of quantum superposition principle. If photons are incident on a double-slit one by one then the interference pattern of a photon gradually emerges. Where detection of each photon corresponds to a point on the screen. Young’s double-slit experiment provides profound insight on the wave-particle duality if it is imagined for individual particles 4 . Interference pattern of a single particle is not formed if the path information of a particle i.e. a slit through which a particle has passed, is known. According to Copenhagen interpretation, an observation on the quantum superposition of paths of a particle corresponds to a measurement that collapses quantum superposition therefore, no interference pattern is formed. On the other hand, what happens if we modify the experiment in such a way that the which-path information of a particle is not available during its passage through a double-slit but can be obtained even after its detection. In this case, the which-path information can be carried out by the quantum state of another particle if total quantum state of particles is an entangled quantum state. By knowing its path by a measurement, the path information of the other particle is immediately determined. Because of path revealing quantum entanglement of particles the single particle interference is suppressed. However, quantum interference can be recovered even after completion of experiment by making correlated selection of measurement outcomes.

The first experiment to show the interference of light with very low intensity in the Young’s double-slit experiment was performed in 1909 by G.I. Taylor 5 . Interesting experiments showing the Young’s double-slit interference are performed with neutrons from the foundational perspective of quantum mechanics 6 , with electron beams 7 and with a single electron passing through a double-slit 8 , 9 , 10 . Recently, a first experimental demonstration of interference of antiparticles with a double-slit is reported 11 . Interference of macromolecules is the subject of great interest in the quest to realise quantum superposition of mesoscopic and macroscopic objects 12 , 13 . In this context, number of interesting experiments have been performed to produce a path superposition of large molecules similar to the double-slit type interference experiments 14 , 15 , 16 .

The main concept of a quantum single double-slit experiment was extended to a quantum double-double-slit thought experiment by Greenberger, Horne and Zeilinger 17 to provide foundational insight on the multiparticle quantum interference. In their paper. they have considered two double-slits and a source of particles placed in the middle of double-slits. Each particle is detected individually after it traverses a double-slit. Quantum entanglement of particles appears naturally in their considerations 18 , 19 and it is shown, when single particle interference disappears and two-particle interference appears. An experimental realisation of quantum double-double-slit thought experiment showing a two-photon interference has been demonstrated with quantum correlated photons produced by spontaneous parametric down conversion (SPDC) process 20 . However, in this paper, we present a detailed experimental realisation of the quantum double-double-slit thought experiment with momentum entangled photon pairs, where a virtual double-double-slit configuration is realised with two Fresnel biprisms. This paper provides a detailed conceptual, theoretical and experimental analysis of the quantum double-double-slit experiment. In addition, an experiment of detection of a which-slit path of a photon is presented where it is shown that the two-photon interference disappears when a which-slit path of a photon is detected.

In this paper, experiments are presented in the context of a quantum double-double-slit thought experiment. However, experiments of foundational significance with polarization entangled photons 21 , 22 , 23 and momentum entangled photons 24 have been intensively studied. In addition, interesting experiments on delayed choice path erasure 25 , 26 , 27 , 28 , 29 , 30 and two-photon interference 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 are performed. Similar experiments have been proposed with Einstein–Podolsky–Rosen (EPR) entangled pair of atoms 41 .

Quantum double-double-slit experiment

Quantum double-double-slit experiment consists of two double-slits and a source of photon pairs. In this experimental situation, a single photon passes through each double-slit and detected individually on screens positioned behind the double-slits as shown in Fig.  1 . However, interference of photons depends on the quantum state of two photons. To understand quantum interference of two photons in a double-double-slit experiment, consider a source is producing photons in pairs and both the photons have same linear polarisation. Double-slit 1 and double-slit 2 are aligned parallel to y -axis and positioned at distances \(l_{1}\) and \(l_{2}\) , respectively along the x -axis from the source. Single slits \(a_{1}\) and \(b_{1}\) of double-slit 1 are separated by a distance \(d_{1}\) and single slits \(a_{2}\) and \(b_{2}\) of double-slit 2 are separated by a distance \(d_{2}\) as shown in Fig.  1 where each slit width is considered to be infinitesimally small. A single photon of a photon pair is detected on screen 1, which is positioned at a distance \(s_{1}\) from double-slit 1 and a second photon is detected on screen 2, which is positioned at a distance \(s_{2}\) from double-slit 2. There are four different possible paths by which photons can arrive at the respective screens i.e. a photon can arrive at a point \(o_{1}\) on screen 1 via double-slit 1 and the other photon can arrive at a point \(o_{2}\) on screen 2 via double-slit 2. Therefore, possible paths of photons are (i) a first photon can pass through slit \(a_{1}\) and the second photon can pass through slit \(a_{2}\) , or (ii) a first photon can pass through slit \(b_{1}\) and the second photon can pass through slit \(b_{2}\) , or (iii) a first photon can pass through slit \(a_{1}\) and the second photon can pass through slit \(b_{2}\) , or (iv) a first photon can pass through slit \(b_{1}\) and the second photon can pass through slit \(a_{2}\) . Since all the possible paths are indistinguishable and not revealing any which-path information therefore, total amplitude \(A_{12}\) to find a photon at \(o_{1}\) and a photon at \(o_{2}\) together is a quantum superposition of all the possible paths, which can be successively written as

where \(t_{a1}\) , \(t_{b1}\) , \(t_{a2}\) , \(t_{b2}\) are amplitudes of transmission of slits \(a_{1}\) , \(b_{1}\) , \(a_{2}\) , \(b_{2}\) , respectively. Quantum states \(|a_{1}\rangle\) , \(|b_{1}\rangle\) \(|a_{2}\rangle\) , \(|b_{2}\rangle\) are position space basis states of locations on the slits on double-slit 1 and double-slit 2, respectively where a photon can be found. Similarly, \(|o_{1}\rangle\) and \(|o_{2}\rangle\) are the position space basis states of locations on the screens. However, position basis states corresponding to points on each double-slit and a screen form a different basis set such that \(\langle o_{1}|a_{1}\rangle\) represents the amplitude of transmitted photon to go from slit \(a_{1}\) to a location \(o_{1}\) on screen 1. Same terminology is applied for other amplitudes in Eq.  1 .

A schematic diagram of a double-double-slit experiment. Photons are individually detected on screens after they pass through the double-slits separately. Which-slit path information of photons can be detected by blocking any single slit by closing the shutter.

Further, consider photon pairs produced by a source of finite size are emitted in opposite directions w.r.t. each other such that they are momentum entangled, their net momentum is zero and momentum of each photon is definitely unknown. Consider the spatial extension of source is much smaller than the slit separation but large to produce momentum entanglement. As a consequence of momentum entanglement, if a photon passes through slit \(a_{1}\) then the other photon passes through slit \(b_{2}\) and if a photon passes through slit \(b_{1}\) then the other photon passes through slit \(a_{2}\) after their transmission through the slits. For momentum entangled photons, both these possibilities are quantum superimposed, as result of it both the photons are path entangled via the slits and first two terms in the summation of Eq.  1 become zero. The last two terms in the summation are due to path entanglement via the slits, these two amplitudes interfere with each other and produce a two-photon interference of momentum entangled photons. When all four slits are opened, a two-photon path information is not revealed and a two-photon interference can be observed by recording detection locations of a photon corresponding to a particular location of detection of other photon on the other screen during each repetition of the experiment.

On the other hand, if one measures the direction of momentum of any single photon prior to its passage through double-slits then the momentum entangled state is collapsed. This measurement outcome reveals momentum direction of a photon on which a measurement is performed and the direction of momentum of the other photon is also revealed instantly after the collapse even without making any measurement on it. This measurement reveals which-slit path information of photons. On the other hand, which-slit path of photons in the double-double-slit can be detected by closing any single slit with a shutter. A shutter shown in Fig.  1 is considered as a photon measuring detector, if shutter is closed to block a slit \(a_{2}\) and a photon is detected on screen 2 then it reveals that a photon is passed through a slit \(b_{2}\) due to collapse of quantum entangled state caused by the shutter detector. As a consequence, one can find out that the other photon is passed through a slit \(a_{1}\) if it is detected at \(o_{1}\) . Since a path of both photons is known therefore, two-photon interference is suppressed. Interesting situation appears when double-slit 2 and screen 2 are removed to allow a photon to propagate in space while other photon is passed through double-slit 1 and detected on screen 1. A single-photon interference not produced on screen 1 because of path entanglement the which-slit path information of photons can be obtained by measuring momentum of the propagating photon even after the detection of a photon on screen 1.

Furthermore, when all slits are opened and which-slit path is not detected, a photon can be detected at any location on a screen randomly during each repetition of the experiment and its detection location is not known prior to a measurement on screen. Once a photon is detected on a screen, its detection location instantly determines the amplitude to find other photon on other screen if it is not reached there. Individual photons show no interference on a screen because a well defined phase coherent amplitude to find a photon on a screen depends on a particular detection location of other photon. In this case, a single photon amplitude is completely incoherent. The information of detection location of a photon determines a particular two-photon interference pattern. In other words, in this type of joint and correlated registration of detection locations of photons, if a different detection location of a photon is selected the two-photon interference pattern exhibits a shift. If only single photons are registered on each screen without making any correlation between their detection locations then the interference pattern is not formed on each screen.

Two-photon interference

To find out a two-photon interference in the double-double-slit experiment for a finite width of each slit, consider a source of photons located at origin is producing a two-photon quantum state \(|\Psi \rangle\) as shown in Fig.  1 . Double-slits can be defined by amplitude transmission functions \(t_{1}(y')\) and \(t_{2}(y'')\) of double-slit 1 and double-slit 2 respectively. Where \(y'\) and \(y''\) are the arbitrary points on double-slit 1 and double-slit 2, respectively such that the position basis states corresponding to these points located on the double-slits where a photon can be found are \(|l_{1}, y'\rangle\) and \(|l_{2}, y''\rangle\) . Therefore, the amplitude \(A_{12}\) to find photons at points \(o_{1}\) and \(o_{2}\) together on screens can be written as

Consider photon source has finite size and two-photon quantum state \(|\Psi \rangle\) is a momentum entangled quantum state, where both the photons have same linear polarisation and frequency. Such a two-photon quantum entangled state can be produced by degenerate noncollinear SPDC with type-I phase matching in a beta-barium-borate (BBO) crystal which is pumped by a laser beam propagating along the z -axis (longitudinal direction), where the z -axis (not shown in Fig.  1 ) is perpendicular to the xy -plane (transverse plane). Photons known as the signal and the idler photons are emitted from the source with opposite momenta with nearly equal in magnitude in the transverse plane such that their two-photon momentum entangled state in the transverse momentum space is 42 , 43 , 44 , 45 , 46

where \(|\mathbf {q_{s}}\rangle\) , \(|\mathbf {q_{i}}\rangle\) are the transverse momentum quantum states of the signal and the idler photons of momentum \(\mathbf {q_{s}}\) and \(\mathbf {q_{i}}\) , respectively and N is a normalisation constant. Two-photon wavefunction \(\Phi (\mathbf {q_{s},\mathbf {q_{i}}})\) represents the amplitude to find a signal photon in momentum state \(|\mathbf {q_{s}}\rangle\) and an idler photon in momentum state \(|\mathbf {q_{i}}\rangle\) . Quantum entanglement is manifested by non separability of \(\Phi (\mathbf {q_{s},\mathbf {q_{i}}})\) . For the pump laser beam with gaussian intensity profile of finite width in the transverse plane, the two-photon wavefunction \(\Phi (\mathbf {q_{s},\mathbf {q_{i}}})\) is prominent only for momentum states of photons with opposite transverse momenta. Since source size is finite therefore, if momentum of a photon is measured precisely then the quantum state of the other photon corresponds to a momentum state of opposite momentum with finite uncertainty. Further detail on momentum entanglement of photons produced by degenerate noncollinear SPDC in the BBO crystal is given in methods.

There are two possibilities that can result in a joint detection of photons on screen 1 and screen 2. These indistinguishable possibilities are (i) the signal photon is passed through double-slit 1 and detected on screen 1 and the idler photon is passed through double-slit 2 and detected on screen 2 and (ii) the idler photon is passed through double-slit 1 and detected on screen 1 and the signal photon is passed through double-slit 2 and detected on screen 2. Any single photon (signal or idler) that can be detected after passing through the double-slit 1 is labeled as photon 1 and any single photon that can be detected after passing through the double-slit 2 is labeled as photon 2. Photon 1 and photon 2 are indistinguishable as they have same frequency and polarisation. Consider, transmission function of double-slit 1 is \(t_{1}(y')= a'_{t}\left( \frac{e^{-(y'-d_{1}/2)^2/2\sigma _{1}^2}}{(2\pi )^{1/2}\sigma _{1}}+\frac{e^{-(y'+d_{1}/2)^2/2\sigma _{1}^2}}{(2\pi )^{1/2}\sigma _{1}}\right)\) , which represents two gaussian slits with separation between them \(d_{1}\) and slit width \(\sigma _{1}\) of each slit is such that \(d_{1}\) is considerably larger than \(\sigma _{1}\) . Similarly, transmission function of double-slit 2 is \(t_{2}(y'')= a''_{t}\left( \frac{e^{-(y''-d_{2}/2)^2/2\sigma _{2}^2}}{(2\pi )^{1/2}\sigma _{2}}+\frac{e^{-(y''+d_{2}/2)^2/2\sigma _{2}^2}}{(2\pi )^{1/2}\sigma _{2}}\right)\) , which represents two gaussian slits with separation between them \(d_{2}\) and slit width \(\sigma _{2}\) of each slit is such that \(d_{2}\) is considerably larger than \(\sigma _{2}\) . Where, \(a'_{t}\) and \(a''_{t}\) are the complex multipliers of transmission functions, they include the phase shift introduced by the slits and limit the maximum transmission to one. For \(a'_{t}= a''_{t}=0\) , the transmission of slits is zero. Each double-slit is positioned far away from the source as compared to its slit separation. Therefore, slits are located at close inclination with the x -axis such that photons coming from source are incident on slits almost close to the normal incidence. To have two-photon path entanglement via the slits the double-slits are positioned such that \(d_{1}/l_{1}=d_{2}/l_{2}\) and \(\sigma _{1}/l_{1}=\sigma _{2}/l_{2}\) . In addition, uncertainty \(\Delta q_{\parallel }\) of momentum component of each photon parallel to the double-slits, provided momentum of other photon is precisely determined, is small such that \(\Delta q_{\parallel }/q\ll d_{1}/l_{1}= d_{2}/l_{2}\) to suppress single photon interference by each double-slit, where q is the magnitude of momentum of a photon 41 . However, \(\Delta q_{\parallel }/q\approx \sigma _{1}/l_{1}=\sigma _{2}/l_{2}\) . These conditions implies, if a photon is passed through slit \(a_{1}\) then the other photon is most likely passed through slit \(b_{2}\) and if a photon is passed through slit \(b_{1}\) the other photon is most likely passed through slit \(a_{2}\) . Therefore, photons contributing to the joint detection on screens are path entangled via the slits. However, if a photon is absorbed far away from slits at an arbitrary location \(y'\) on double-slit 1 then the other photon is most probably absorbed at \(y''=-y'l_{2}/l_{1}\) far away from slits of double-slit 2. Transmission of each slit is considered to be gaussian with very small width that allows a photon to pass through it. Under these considerations, the amplitude \(A_{12}\) of joint detection of photons on screens gets a major contribution from a small range of momentum states of quantum state \(|\Psi \rangle\) . Remaining momentum states in \(|\Psi \rangle\) are absorbed at double-slits. Therefore, to evaluate \(A_{12}\) by using Eq.  2 , a following approximation can be applied

where \(c_{w}\) is a constant of proportionality that depends on the two-photon wavefunction. Since photons are incident on each slit close to the normal incidence therefore, \(e^{i q (r_{a1}+ r_{b2})/\hslash }\) is the two-photon amplitude of a photon to go from source to slit \(a_{1}\) located at a distance \(r_{a1}\) and other photon to go from source to slit \(b_{2}\) located at a distance \(r_{b2}\) . Similarly, \(e^{i q (r_{b1}+ r_{a2})/\hslash }\) is the two-photon amplitude of a photon to go from source to slit \(b_{1}\) located at a distance \(r_{b1}\) and other photon to go from source to slit \(a_{2}\) located at a distance \(r_{a2}\) . The transmitted amplitude of photons via the slits \(a_{1}\) and \(a_{2}\) or via the slits \(b_{1}\) and \(b_{2}\) is negligible because \(\Phi (\mathbf {q_{s},\mathbf {q_{i}}})\) is very small for these paths. Photons are path entangled via the slits and Eq.  4 represents the amplitude of transmitted photons on the double-slits that leads to the joint detection of photons.

Transmitted photon amplitude of a photon further emanates from a point on a double-slit such that it corresponds to an uniform probability distribution of the photon to be found on the screen. The amplitudes of transmitted photons to go from a point location on a double-slit to a point location on the nearest screen are \(\langle o_{1}| l_{1},y'\rangle \propto e^{iq|R'|/\hslash }/|R'|^{1/2}\) and \(\langle o_{2}| l_{2},y''\rangle \propto e^{iq|R''|/\hslash }/|R''|^{1/2}\) for photon 1 and photon 2, respectively. Where \(R'\) and \(R''\) are the distances of \(o_{1}\) and \(o_{2}\) from arbitrary points \(y'\) and \(y''\) located on double-slit 1 and double-slit 2, respectively. Since distances \(s_{1}\) and \(s_{2}\) of the screens from the nearest double-slits are much larger than the slit separations therefore, \(\langle o_{1}| l_{1},y'\rangle \propto e^{iq(r_{1}-y'\sin (\theta _{1}))/\hslash }/r^{1/2}_{1}\) and \(\langle o_{2}| l_{2},y''\rangle \propto e^{iq(r_{2}-y''\sin (\theta _{2}))/\hslash }/r^{1/2}_{2}\) , where \(r_{1}\) and \(r_{2}\) are the distances of \(o_{1}\) and \(o_{2}\) from the middle points of double-slit 1 and double-slit 2, respectively as shown in Fig.  1 . After solving Eq.  2 by using Eq.  4 the amplitude of joint detection of photons can be written as

where \(\delta =q (r_{a1}+r_{b2}-r_{a2}-r_{b1})/2\hslash\) and \(c_{n}\) is a proportionality constant. Therefore, probability of coincidence detection \(p_{12}=|A_{12}|^{2}\) of photons is

Probability of coincidence detection of photons is a product of two functions, where the exponential functions corresponds to a single-photon diffraction of photons from single slits and a cosine function corresponds to two-photon interference from the double-double-slit. Since photons are path entangled via the slits therefore, Eq.  6 can not be written as a product of two separate functions of variables of photon 1 and photon 2, respectively. If only the single photon detection locations on each screen are recorded without making any correlation among them then no interference pattern is formed. A single photon interference is suppressed due to quantum entanglement of paths of photons in the double-double-slit. Both photons can be detected anywhere randomly on the respective screens however, a two-photon quantum interference pattern appears only in the position correlated measurements. Probability of detection of a single photon on the respective screens can be calculated by integrating all possible paths of a single photon. However, due to quantum entanglement of paths this integral results in an addition of probability of detection of a single photon via each slit of a double-slit. Therefore, probabilities \(p_{1}\) and \(p_{2}\) to find a single photon on screen 1 and screen 2 are

where each probability distribution of a single photon detection is gaussian and single photon interference pattern is not exhibited.

Actual experiment is performed in the three-dimensional position space, where momentum of photons and distances of detectors from double-slits are measured in the three-dimensional position space. Therefore, projection of momentum and distances onto the transverse plane should be considered in order to be consistent with Eqs.  6 and 7 . In actual experiment the slits are located parallel to the transverse plane, detector displacement is parallel to the transverse plane and displacement range is such that \(y_{1}\ll s_{1}\) , \(y_{2}\ll s_{2}\) therefore, \(\sin {\theta _{1}}\sim y_{1}/s_{1}\) and \(\sin \theta _{2}\sim y_{2}/s_{2}\) . Under these considerations, terms in the form of a ratio, of transverse momentum and distance of a screen from a corresponding double slit, appears in Eqs.  6 and 7 . Therefore, photon momentum and distances of detectors from double-slits measured in the three-dimensional position space can be placed in these equations to calculate the patterns.

Double-double-slit experiment presented in this paper is performed with momentum entangled photons produced by type-I degenerate noncollinear SPDC 21 , 24 , 39 , 42 , 43 , 44 , 45 , 47 . A BBO crystal is pumped by an extraordinary linearly polarised laser beam of wavelength 405 nm and down converted photon pairs of wavelength 810 nm with ordinary polarisation are produced in the forward direction in a conical emission pattern according to momentum and energy conservation as shown in Fig.  2 . To produce a virtual double-double-slit configuration, two Fresnel biprisms are placed in the path of photons and photons are detected by single photon avalanche photodetectors \(D_{1}\) and \(D_{2}\) . Optical narrow band pass filters are placed in front of each photon detector to stop the background light. Down converted photons have same frequency and linear polarisation, which is perpendicular to the polarisation of the pump laser beam. Pump laser intensity is such that probability of more than single photon pair production is extremely small. Number of photon counts of each single photon detector and their mutual coincidence photon counts are measured with a two channel single photon counting module. Transverse mode extension of the pump laser beam is reduced to keep the source size much smaller than the slit separation but it is large so that momentum entanglement of photons is preserved.

A schematic diagram of the experimental configuration of the double-double-slit experiment. Momentum entangled photon pairs are produced in a conical emission pattern by a nonlinear crystal. A double-double-slit configuration is realised with two Fresnel biprisms.

An unfolded diagram of the double-double-slit experiment realised with Fresnel biprisms. Virtual sources correspond to virtual slits. To detect which-slit path information of photons, a shutter can be placed in a path of photon 1 in such a way that a virtual slit \(b_{1}\) is blocked.

Two-photon interference pattern obtained by measuring the coincidence photon counts when measurement location \(y_{2}\) of photon 2 is stationary. Experimental measurements are represented by open circles and solid line interference pattern is the two-photon interference calculated from theory. There is no interference exhibited by the individual photons as shown by single photon counts of single photon detectors \(D_{1}\) and \(D_{2}\) . Where ( a ) for \(y_{2}=~0~{\text {mm}}\) and ( b ) for \(y_{2}=~0.07~{\text {mm}}\) . Two-photon interference pattern is shifted as the location \(y_{2}\) of photon detector \(D_{2}\) is displaced.

Two-photon interference pattern obtained by measuring the coincidence photon counts when measurement location \(y_{1}\) of photon 1 is stationary. Experimental measurements are represented by open circles and solid line interference pattern is the two-photon interference calculated from theory. There is no interference exhibited by the individual photons as shown by single photon counts of single photon detectors \(D_{1}\) and \(D_{2}\) . Where ( a ) for \(y_{1}=~0~{\text {mm}}\) and ( b ) for \(y_{1}=~0.07~{\text {mm}}\) . Two-photon interference pattern is shifted as the location \(y_{1}\) of photon detector \(D_{1}\) is displaced.

For type-I phase matching, the BBO emits two degenerate photons with opposite transverse momenta in the transverse plane as shown in Fig.  2 and quantum state of photons of a pair corresponds to a continuous variable momentum entangled quantum state. A two-dimensional unfolded diagram of the experimental schematic given in Fig.  2 is shown in Fig.  3 , where a source S positioned at origin is a BBO crystal that emits momentum entangled photons pairs. Two virtual double-slits are realised with two Fresnel biprisms positioned in the path of both photons. Fresnel biprisms are aligned in such a way that after passing through each Fresnel biprism, paths of a photon can be extrapolated in the backward direction such that it appears as if the photon is originated from two virtual sources which are considered as slits. Each Fresnel biprism produces a virtual double-slit with gaussian slits of finite size. In this way, a double-double-slit configuration is realised with slit separation \(d_{1}\) and \(d_{2}\) of a virtual double-slit 1 and a virtual double-slit-2, respectively as shown in Fig.  3 . The virtual double-double-slit is parallel to the transverse plane and both photon detectors are displaced parallel to the transverse plane. Photon 1 is detected at location \(o_{1}\) and photon 2 is detected at location \(o_{2}\) by single photon detectors. Shortest distance of \(D_{1}\) , \(D_{2}\) are \(L_{1}\) , \(L_{2}\) from double-slit 1 and double-slit 2, respectively as shown in Fig.  3 . Single photon counts of single photon detectors positioned at different locations \(y_{1}\) and \(y_{2}\) and the corresponding coincidence photons counts are recorded. Experimental results on the double-double-slit interference of momentum entangled photons are shown in Fig.  4 , where the coincidence and single photon counts of photons are measured at different \(y_{1}\) positions of single photon detector \(D_{1}\) when single photon detector \(D_{2}\) a kept stationary at a location \(y_{2}\) . Single photon counts of each single photon detector and the coincidence photon counts are presented by open circles in Fig.  4 a for \(y_{2}\) = 0 mm where each data point is the mean of photon counts acquired for 5 s and twenty five repetitions of the experiment. The coincidence photon counts represent a two-photon interference pattern and the corresponding theoretically calculated interference given by Eq.  6 with a consideration of finite size of photon detectors is shown by a solid line. Effect of finite size of detectors raises the minima of the interference pattern. Single photon counts show no interference pattern as presented by the theoretical analysis also. According to the experimental considerations, \(\sin \theta _{1}\sim y_{1}/s_{1}\) and \(\sin \theta _{2}\sim y_{2}/s_{2}\) . The coincidence interference pattern exhibits a shift when measurement location \(y_{2}\) of photon 2 is shifted to another position by displacing single photon detector \(D_{2}\) . A shift in the two-photon interference pattern is shown in Fig.  4 b for \(y_{2}\) = 0.07 mm. In the opposite case, photon 1 is detected at a stationary location \(y_{1}\) and photon 2 is detected at different locations \(y_{2}\) . Results of the coincidence measurements of photon counts and single photon counts are shown in Fig.  5 a for \(y_{1}\) = 0 mm and Fig.  5 b for \(y_{1}\) = 0.07 mm. Solid line in each plot of coincidence measurements is the two-photon interference calculated from Eq.  6 by including the effect of finite size of detectors. A two-photon interference shows a shift with the displacement of position of detection location \(y_{1}\) of photon 1, while single photon counts show no interference as theoretically shown in the previous section. In the experiment, each virtual double-slit has a same slit separation \(d_{1}=d_{2}=~0.67~\hbox {mm}\) and \(L_{1}=L_{2}=528\)  mm.

It is evident from the probability of coincidence photon detection given in Eq.  6 that for \(d_{1}=d_{2}\) , the fringe separation of the two-photon interference pattern will reduce to half if the coincidence photon counts are measured for \(y_{2}=-y_{1}\) i.e. when both single photon detectors are displaced in the opposite direction. For this case, a two-photon interference pattern and a single photon pattern are shown in Fig.  6 , where each measured data point of photon counts is the mean of data acquired for 5 s and twenty five repetitions of the experiment. It is a different experimental set-up than the previous case and in this case \(d_{1}=d_{2}=~0.682~\hbox {mm}\) and \(L_{1}=L_{2}=520\) mm. Solid line represents a theoretically calculated two-photon interference by including the effect of finite size of photon detectors. It is evident that the fringe separation is reduced to half and therefore, the number of fringes are increased within the same gaussian envelop. There is no formation of coincidence interference pattern if both the single photon detectors are displaced in the same direction such that \(y_{2}=y_{1}\) as it is evident from Eq.  6 .

In this experiment both the single photon detectors \(D_{1}\) and \(D_{2}\) are displaced in the opposite direction such that \(y_{2}=-y_{1}\) . Fringe separation of two-photon interference is reduced and individual photons exhibit no interference.

Detection of which-slit path of photons

In the double-double-slit experiment, photons are momentum entangled and they can reveal the which-slit path information of each other if one of them is detected close to any double-slit. If one blocks a single slit of a double-slit then the which-slit path can be detected from the coincidence detection of photons. Consider a slit \(a_{2}\) is blocked by closing a shutter shown in Fig.  1 .

Two-photon coincidence pattern when a virtual slit \(b_{1}\) is blocked. It is evident that two-photon interference is suppressed. Solid line is a theoretically calculated two-photon pattern.

If photons of a single pair are detected on screen 1 and screen 2 together then it is evident that photon 2 has passed through slit \(b_{2}\) . One can consider a path blocking shutter as another single photon detector \(D_{3}\) . If \(D_{3}\) detects a photon 2 then the path entangled state of photons collapses and the which-slit path of photon 1 in the double-slit 1 is also determined. In this case, the which-slit path of photon 1 is through the single slit \(b_{1}\) . Since each photon is passed through a single slit therefore, neither a single photon nor a two-photon interference of joint detections of photons on screen 1 and a path blocking single photon detector \(D_{3}\) will occur. On the other hand, if photon 2 is detected on screen 2 then the path entangled state is collapsed by \(D_{3}\) such that photon 2 is passed though slit \(b_{2}\) and photon 1 is passed through slit \(a_{1}\) . Single photon detection probability of photon 2 on screen 2 will reduce by half in comparison to the case when both slits were open. Probability of a single photon detection of photon 1 on screen 1 will remain unchanged because detection of photon 1 does not reveal any information whether a photon 2 is detected at screen 2 or by \(D_{3}\) . In the experiment, shutter is placed after the Fresnel biprism 1 such that a virtual slit \(b_{1}\) shown in Fig.  3 is blocked. This configuration resembles to a double-double-slit schematic shown in Fig.  1 where the slit \(a_{2}\) can be blocked by a shutter. Photon counts are measured for different locations \(y_{2}\) of single photon detector \(D_{2}\) by keeping single photon detector \(D_{1}\) stationary at \(y_{1}\) . Experimental results of a path detection experiment are shown in Fig.  7 . Experimental parameters in this case are same as for the experiment described in the previous section. It is evident from the experimental results, if a which-slit path information of photons is extracted by blocking any single slit then both single and two-photon interferences are suppressed.

This paper has presented experimental and conceptual insights on the quantum double-double-slit thought experiment first introduced by Greenberger, Horne and Zeilinger 17 . Experiments presented in this paper are performed with momentum entangled photons produced by type-I degenerate noncollinear SPDC process in a BBO crystal. In the experiment, once both photons traverse the respective double-slits, they can be detected anywhere on screens randomly because when a photon strikes a screen its quantum state collapses to one location randomly. Patterns emerge in many repetitions of the same experiment. Since paths of photons in the double-double-slit configuration are quantum entangled, their individual quantum states are phase incoherent therefore, formation of a single photon interference is suppressed. However, if a photon is detected on a screen at a well defined location, the quantum state of other photon, which is not detected, corresponds to a phase coherent amplitude to find it on second screen. Therefore, knowledge of detection locations of a photon labels the different phase coherent amplitudes to find other photon on second screen. However, in subsequent repetitions of the experiment, detection locations of photons can vary randomly. For a given location of detection of a photon the other photon shows interference pattern which corresponds to the conditional interference pattern of two photons. As a detection location of a photon is varied the conditional interference pattern is shifted. On the other hand, if no correlations of detection locations of photons are made then there is no way to select a particular phase coherent amplitude in repeated measurements. Eventually, a single photon interference pattern does not appear. It is also shown experimentally and conceptually, if a which-slit path information of any one of the photons is detected then a single photon interference and a two-photon interference disappear because of random collapse of quantum superposition of paths.

Two-photon momentum entangled state

Two-photon momentum entangled state is produced by a negative uniaxial second order nonlinear BBO crystal by type-I SPDC process. A pump photon of frequency \(\omega _{p}\) is split into two photons known as the signal photon and the idler photon of frequency \(\omega _{s}\) and \(\omega _{i}\) , respectively. A linearly polarised extraordinary pump laser beam propagating along the z -axis is incident on the crystal. A planar surface of the crystal is in the xy -plane with origin at the centre, where \(l_{x}\) , \(l_{y}\) , \(l_{z}\) are the spatial extensions of the crystal along each axis. Ordinary photons produced by SPDC are linearly polarised with propagation vectors in three dimensions \(\mathbf {k_{s}}\) and \(\mathbf {k_{i}}\) . In type-I phase matching, due to dispersion and anisotropy of the crystal, the signal and the idler photons are produced with non zero angle of their propagation vectors with the propagation vector \(\mathbf {k_{p}}\) of the pump laser beam to conserve momentum of photons. For a thin crystal and a narrow pump laser beam, it produces a conical emission pattern of down converted photons. Pump laser beam is considered to be a continuous beam and due to low down conversion efficiency the pump laser beam amplitude is considered to be constant. The amplitude to produce more than one photon pair is extremely small, which is desirable in experiments with a single quantum entangled pair of photons during each cycle of the experiment. Pump laser beam is considered to be monochromatic, frequencies of the signal and the idler photons are same in the experiment and their propagation vectors are making a nonzero angle with the propagation direction of pump photons. Narrow band pass filters are placed after the crystal and prior to the detectors to increase coherence length. Due to sufficiently long interaction time, energy conservation condition is fulfilled such that \(\hslash \omega _{p}=\hslash \omega _{s}+\hslash \omega _{i}\) . Since polarisation of down converted photons is same therefore, two-photon quantum state produced by degenerate type-I noncollinear SPDC process can be written as 42 , 43 , 44 , 45 , 46 , 47

where \(c_{0}\) , \(c_{1}\) are complex coefficients, \(c_{1}\) depends on the pump laser beam intensity and second order nonlinear coefficient of the crystal. The quantum states \(|\mathbf {p_{s}}\rangle\) and \(|\mathbf {p_{i}}\rangle\) represent single photon momentum states of the signal and the idler modes of momentum vectors \(\mathbf {p_{s}}=\hslash \mathbf {k_{s}}\) and \(\mathbf {p_{i}}=\hslash \mathbf {k_{i}}\) , respectively. The quantum state \(|0\rangle\) is a vacuum state of the signal and the idler modes without any photon. A two-photon wavefunction \(\Phi (\mathbf {p_{s},\mathbf {p_{i}}})\) in the momentum space can be written as

where \(c_{p}\) is a constant and the integration is carried out in transverse momentum space which is a projection of three-dimensional momenta onto the transverse two-dimensional xy -plane, \(\Delta p_{j}\) = \(p_{sj}+p_{ij}-p_{pj}\) for \(j\in \{x,y,z\}\) and \(p_{sj}\) , \(p_{ij}\) , \(p_{pj}\) represent components of momentum of the signal, the idler and pump photons along the j -axis, respectively. A function \(\mathbf {\nu }(\mathbf {q_{p}})\) is the normalised amplitude of pump laser beam corresponding to momentum projection \(\mathbf {q_{p}}\) in the transverse plane. For a plane wave, \(\mathbf {\nu }(\mathbf {q_{p}})\) is a Dirac delta function. If crystal extensions \(l_{x}\) and \(l_{y}\) are much larger than the wavelength of pump laser beam then \(\Delta p_{x}\) and \(\Delta p_{y}\) should be very small otherwise \(\Phi (\mathbf {p_{s},\mathbf {p_{i}}})\) diminishes. Therefore, \(\mathbf {q_{p}}\) = \(\mathbf {q_{s}}+\mathbf {q_{i}}\) for transverse momentum \(\mathbf {q_{s}}\) of the signal photon and transverse momentum \(\mathbf {q_{i}}\) of the idler photon. It corresponds to conservation of transverse momentum of photons. For a gaussian transverse momentum profile of the pump laser beam with radius \(\sigma _{p}\) in the position-space and for a very small angle between the pump photon momentum and the signal photon or the idler photon momentum, the two-photon wavefunction is given in Ref. 44 ,

where, \(c_{\Phi }\) is a constant of proportionality. Two-photon wavefunction \(\Phi (\mathbf {q_{s},\mathbf {q_{i}}})\) is prominent if transverse momenta of photons are equal and opposite to each other.

Two-photon quantum entangled state in the transverse momentum space can be written as

where N is a normalisation constant and the vacuum state is not relevant in the context of present experiment. In general the momentum entanglement is manifested by non separability of two-photon wavefunction \(\Phi (\mathbf {q_{s},\mathbf {q_{i}}})\) .

Experimental details

A linearly polarised pump laser light of wavelength 405 nm of gaussian beam profile is incident on a BBO crystal at room temperature. Two orthogonally polarised momentum entangled photons of wavelength 810 nm are emitted in a conical emission pattern and single photons are detected by avalanche single photon detectors. Each photon pair is passed through two Fresnel biprisms to realise a virtual double-double-slit configuration. After the crystal, pump light at 405 nm is blocked by an optical band pass filter with transmission window peak at 810 nm where the full-width-half-maximum of the transmission window is about 10 nm. Two multimode optical fibers carry photons from points \(o_{1}\) and \(o_{2}\) to each single photon detector. The other end of each optical fiber is mounted on separate three-dimensional precision displacement stages and photons are coupled to each optical fiber with an objective lens. Narrow apertures are positioned at \(o_{1}\) and \(o_{2}\) prior to the objective lens to allow photons to be detected at these two points only. Prior to each fiber coupler two optical band pass filters (filter 1 and filter 2) are placed in the path of each photon to block scattered photon of wavelength 405 nm and background photons reaching each single photon detector. Photon correlations are measured by counting electrical pulses produced by each single photon detector. Experimentally measured coincidence and single photon counts are shown by open circles data points in the figures. Each data point is acquired for 5 s with twenty five repetitions of the same experiment. Experimental results are compared with theoretical calculations considering the effect of finite size of photon detectors.

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Acknowledgements

Mandip Singh acknowledges research funding by the Department of Science and Technology, Quantum Enabled Science and Technology grant for project No. Q.101 of theme title “Quantum Information Technologies with Photonic Devices”. DST/ICPS/QuST/Theme-1/2019 (General).

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M.S. designed and setup the experiment, M.K. took data and also aligned the experiment. M.S. did theory, analysed data and wrote the manuscript, both authors discussed the experiment.

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Kaur, M., Singh, M. Quantum double-double-slit experiment with momentum entangled photons. Sci Rep 10 , 11427 (2020). https://doi.org/10.1038/s41598-020-68181-1

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What Is The Double-Slit Experiment?

The double-slit experiment, observation affects reality, the various interpretations:.

The double-slit experiment shows the duality of the quantum world. A photon’s wave/particle duality is affected when it is observed.

Light has been one of the major areas of inquiry for physicists since we first began questioning the world around us. Understandably so, as it is the medium by which we see, measure and understand the world. It holds a powerful symbolism in our imaginations, is reflected in our religions and is famously quoted in our scriptures.

Rigorous science has enlightened our ignorance about Light. Until the 1800s, light was thought to be made up of particles, attested by Newtonian physics.

This came rather intuitively, as we see light traveling in a straight line, like bullets coming out of a gun.

However, nature is often weirder than our expectations and light’s weird behavior was first shown by Thomas Young in his now heavily worked upon and immortalized double-slit experiment. This experiment provides some fascinating insights into the minute workings of nature and has challenged everything we know about light, matter, and reality itself. Let’s revisit the experiment that has baffled legendary scientists – including Einstein!

Recommended Video for you:

The experiment is pretty straightforward, with very few parts. There are three main components:

• A source of light or matter – photons, electrons, bullets

• Two narrow slits for the source to pass-through.

• A projection screen, where the source makes its impression. The pattern of the impression tells us if it is a wave or a particle.

The objective of the experiment is to see the underlying make-up of light and matter.

Let’s start with something familiar, bullets from a machine gun. Our gun fires bullets at regular intervals towards the range of the two slits.

Two straight lines appear on the projector. The graph pattern is that of two mountains; where the crests imply the impression points, and the troughs imply empty places.

The thing to note here is, if we close S2 and fire the gun, only one line appears. Thus, we can safely say that S is equal to the sum of S1 and S2, i.e., S = S1 + S2.

Light is the next source for the experiment. The impression appears as bundles of photons fire through the two slits. What is the pattern you think will emerge? Is it similar to that of bullets? Well, light consists of bullet-like particles, so it isn’t farfetched to say the pattern will be the same.

To everyone’s surprise, however, the impression isn’t of two straight lines. The graph pattern that emerges is an interference pattern; there is the brightest impression in the center, and recedes on both sides. An interference pattern is only made when two waves interfere with each other; there is no other possible explanation to it. The pattern shows that the light is moving in waves.

The waves from the two slits are colliding with each other. There is a peculiar formation that develops when two waves collide. A wave has a crest (the part above) and a trough (the part below).

When the crest of one wave collides with the crest of another, it adds and forms constructive interference, seen as a bright spot on the projector. When the crest of one wave and trough of another collide, they cancel each other out and form a destructive pattern, which results in dark spots between the impressions on the projector.

The second slit is closed and the experiment is done again. Now with one slit to move through, the photons form a straight line. Note, here S is not equal to the sum of S1 and S2, and this is also where light’s wave-particle duality comes into focus.

This revelation changed our thinking about light, but the rabbit hole doesn’t end there; things just get weirder when we further iterate the experiment. Now, instead of flashing a bunch of photons together, only single photons are fired through the slits at regular intervals. Given that it is a single photon, and has no other wave to interact with, we can say that the photon will make a single line on the projector, yet the result is counter-intuitive; the formation on the projector is still an interference pattern!

How can this be? How can a single photon know about the photons coming after it and form a pattern resembling that of the group being shot together?

This is where quantum spookiness begins and things get pretty far out. It appears that a single photon is traveling through both the slits and colliding with itself to form the interference pattern. This has bothered physicists a lot, as it does not obey the laws that we see in our Newtonian scale. It turns out that a large assemblage appears to behave in a way that is different from the behavior of its minuscule components.

Now, let’s hit a home run and take this weirdness to another level. This last iteration of the experiment will make you appreciate nature’s absurdness and how totally wacky our world truly is.

Also Read: Wave-Particle Duality: Is An Electron A Particle Or A Wave?

At this point, we have established that a single photon travels from both the slit at the same time and collides with itself to form the interference pattern. As classical physics dictates, it is impossible for the same photon to move through the two slits at the same time. Perhaps it is splitting itself into two parts and interacting with itself. The only way to know is to watch. A detector is placed in one of the slits so when the photon passes through the slit, the detector identifies it.

As the photon passes through the slit, the detector identifies it. The pattern that emerges on the projector is a single line.

Just when you think you’re coming to terms with the quantum scale, things slip over your head. The act of measuring or observing the photon makes it go through only one path, making the impression on the projector of a particle. It doesn’t interact with itself anymore and no interference pattern emerges. When the experiment is carried out with varying degrees of detection, so that the detection is dimmer on every passing photon (say 7-10 photons are being detected and that number keeps decreasing), then the interference pattern starts to slowly emerge again. The photons act as a wave when not being observed and act as particles when they are being observed.

Also Read: What Is The Observer Effect In Quantum Mechanics?

The double-slit experiments is one of the most iterated experiments in scientific history. Electrons, atoms, molecules and even complex fullerenes like Buckyballs have been used as sources for the experiment. The same results are obtained using every source; the pattern is consistent in both light and matter.

Things on the quantum scale don’t follow the deterministic laws of the macro scale. There are many interpretations of this quantum phenomenon. The Copenhagen Interpretation states that the interference pattern is all the probable functions of the photon (a wave function) and the act of observing or measuring it makes the wave select one of the many alternatives (collapsing of the wave function).

Another interpretation is the many-worlds theory, which states that all the possible states of the photon’s wave function exist simultaneously and our detection is just this particular instance of the wave function.

The theories tend to run wild and it’s safe to say that the quantum realm is a little slippery to wrap your head around. However, there’s no need to feel bad, as you’re in good company. As Richard Feynman said:

Also Read: Why Is Quantum Mechanics So Difficult To Understand?

• Copenhagen Interpretation. The University of Oregon
• A Review and Response to the Book "The Grand Design" by ... - TASC. tasc-creationscience.org
• Chapter 14 Interference and Diffraction. web.mit.edu
• Young’s Double Slit Experiment - pressbooks.online.ucf.edu
• Lecture Notes | Quantum Physics III - MIT OpenCourseWare. MIT OpenCourseWare

Vishal is an Architect and a design aficionado. He likes making trippy patterns in his computer. Fascinated by technology’s role in humanity’s evolution, he is constantly thinking about how the future of our species would turn out – sometimes at the peril of what’s currently going on around him.

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Physics in a minute: The double slit experiment

One of the most famous experiments in physics is the double slit experiment. It demonstrates, with unparalleled strangeness, that little particles of matter have something of a wave about them, and suggests that the very act of observing a particle has a dramatic effect on its behaviour.

To start off, imagine a wall with two slits in it. Imagine throwing tennis balls at the wall. Some will bounce off the wall, but some will travel through the slits. If there's another wall behind the first, the tennis balls that have travelled through the slits will hit it. If you mark all the spots where a ball has hit the second wall, what do you expect to see? That's right. Two strips of marks roughly the same shape as the slits.

In the image below, the first wall is shown from the top, and the second wall is shown from the front.

The pattern you get from particles.

Now imagine shining a light (of a single colour, that is, of a single wavelength) at a wall with two slits (where the distance between the slits is roughly the same as the light's wavelength). In the image below, we show the light wave and the wall from the top. The blue lines represent the peaks of the wave. As the wave passes though both slits, it essentially splits into two new waves, each spreading out from one of the slits. These two waves then interfere with each other. At some points, where a peak meets a trough, they will cancel each other out. And at others, where peak meets peak (that's where the blue curves cross in the diagram), they will reinforce each other. Places where the waves reinforce each other give the brightest light. When the light meets a second wall placed behind the first, you will see a stripy pattern, called an interference pattern . The bright stripes come from the waves reinforcing each other.

An interference pattern.

Here is a picture of a real interference pattern. There are more stripes because the picture captures more detail than our diagram. (For the sake of correctness, we should say that the image also shows a diffraction pattern , which you would get from a single slit, but we won't go into this here, and you don't need to think about it.)

Image: Jordgette , CC BY-SA 3.0 .

Now let's go into the quantum realm. Imagine firing electrons at our wall with the two slits, but block one of those slits off for the moment. You'll find that some of the electrons will pass through the open slit and strike the second wall just as tennis balls would: the spots they arrive at form a strip roughly the same shape as the slit.

Now open the second slit. You'd expect two rectangular strips on the second wall, as with the tennis balls, but what you actually see is very different: the spots where electrons hit build up to replicate the interference pattern from a wave.

Here is an image of a real double slit experiment with electrons. The individual pictures show the pattern you get on the second wall as more and more electrons are fired. The result is a stripy interference pattern.

Image: Dr. Tonomura and Belsazar , CC BY-SA 3.0

How can this be?

One possibility might be that the electrons somehow interfere with each other, so they don't arrive in the same places they would if they were alone. However, the interference pattern remains even when you fire the electrons one by one, so that they have no chance of interfering. Strangely, each individual electron contributes one dot to an overall pattern that looks like the interference pattern of a wave.

Could it be that each electrons somehow splits, passes through both slits at once, interferes with itself, and then recombines to meet the second screen as a single, localised particle?

To find out, you might place a detector by the slits, to see which slit an electron passes through. And that's the really weird bit. If you do that, then the pattern on the detector screen turns into the particle pattern of two strips, as seen in the first picture above! The interference pattern disappears. Somehow, the very act of looking makes sure that the electrons travel like well-behaved little tennis balls. It's as if they knew they were being spied on and decided not to be caught in the act of performing weird quantum shenanigans.

What does the experiment tell us? It suggests that what we call "particles", such as electrons, somehow combine characteristics of particles and characteristics of waves. That's the famous wave particle duality of quantum mechanics. It also suggests that the act of observing, of measuring, a quantum system has a profound effect on the system. The question of exactly how that happens constitutes the measurement problem of quantum mechanics.

Further reading

• For an extremely gentle introduction to some of the strange aspects of quantum mechanics, read Watch and learn .
• For a gentle introduction to quantum mechanics, read A ridiculously short introduction to some very basic quantum mechanics .
• For a more detailed, but still reasonably gentle, introduction to quantum mechanics, read Schrödinger's equation — what is it?

Originally published on 05/02/2017.

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Double slit experiment

The scientist at Washington University found that quasimeasurements cause the zeno effect possibly explaining why the particles do not form a interference pattern if one detects which slit they pass through.

double slit experiment

Seem to be leaving out the fact that the difference occurs when being actively observed.

Heisenberg uncertainty principle

Everything we see is our brain "interpreting" the photons of light reflected off a object. Just like our brains turns 30 FPS and up into a smooth video image. Any experiment that has the word "Observation" in it is flawed. A human used as test equipment for the observation part of a experiment can never be accurate.

It has nothing to do with a human observing anything. It has to do with how one observes things at the atomic and quantum scale. We make these observations by bouncing other particles off of the particles we're interested in examining. At the macro-scale this is not a problem as the particles were bounce off of things are much smaller and have little no affects at the macro.

But at the atomic and smaller scales, the particles we bounce off of things to observe them are similar in "size" (this is a stand in for mass, charge, etc.) to the particles we are trying to observe.

You can think of it like trying to figure out where a billiard ball is by bouncing a golf ball it. That will change the position, spin, etc. of the billiard ball.

I agree with you. Yet, seemingly, the rest of the world either believes - when they do not believe what you've just said - humans have a psychic grip on subatomic particles, or this proves a God exists.

Why not both?

I believe both, and agree with both of you. The two dont have to be mutually exclusive... It actually makes for a more narrow view that way.

Leave room for more

I agree. What we don't know is much greater than what we do and much of what we think we know will change. I think it's best to leave room for many possibilities. Magic is just science undiscovered. If we keep placing boundaries on what's possible and teach others to ignore something for lack of explanations, scientific discovery suffers.

The two slit experiment

The duality of the particle has nothing to do with proving a god exists, just that science is indeterminate and is a duality of possible existences dependent on the observation of a consciousness. Seems like its human consciousness that determines the outcome not any god.

This isn't actually true either. Experiments have shown that even if the photon used to make an observation is of low enough energy that it doesn't alter a large molecules trajectory much, the interference pattern still disappears.

Also, null interaction experiments have been done in which there is no contact between particles at all. But if info about which slit can be found, the interference pattern disappears.

Source for that?

Hey, do you have a source on finding information about which slit with out active observation causing the interference pattern to not appear?

Information on the Double Split experiment

Try QED: The Strange Theory of Light and Matter by Richard P. Feynman. It's been a while since I've enjoyed this book, but my recollection is that it covered the topic well.

Thank you! I didn’t think that explanation made sense, since any effect upon the particle being observed would surely be taken into account in these experiments…and because the detection unit (which “catches” the electrons passing through either slit) doesn’t work by shooting particles at them, as far as I know…even if it did, that wouldn’t be ignored as a variable or whatever…right? I assume such interaction isn’t the method of detection anyway; how the materials used in the experiment could potentially influence the subject being measured is exactly what they control for, among other things- the environment itself, the actions taken as it is conducted and how conditions change…etc. I just don’t think what the commenter described is true since, well, I’d assume the researchers would know that sort of thing could skew the results & therefore lead to an incorrect conclusion. Scientists aren’t just straight up missing the impact of what would be such an obvious flaw in these experiments. I mean, in general they either eliminate the possibility of their tools affecting what they’re measuring OR they take that into account as a variable. Usually the second one is only possible if it’s something that like…as long as it’s known, it won’t render their data useless…if that makes sense (so being aware that it is a factor is key) Anyway…

yet this works at the molecular level too

Molecules are much larger than photons, yet you get the same result.

Quantum Games

If a player has two attached low emission lasers either side of head, beamed through a double slit screen at, say, a home movie or scenario created by the player, bounces back as photons via player's retina to the player's neurons, will player perceive or believe he/she is part of the home movie?

Are you Sure?

Placing only 1 detector in front of one of the double slits ALSO collapses the wave function of both slits. This unequivocally proves that it isn’t the measurement method, but the ACT of measurement itself.

For example, we get the wave pattern. We place a detector in front of both holes we then get 2 bands. ..now, if it were the detector interfering as you mentioned, we will take 1 detector away and leave the other. This way only 1 slit has a detector that interacts with the electron as it passes through.

This would mean the slit with the detector produces a band while the slit without the detector produces a partial striped pattern of the wave.

This is not what we observe however. Measuring just 1 slit still causes 2 bands.

This is because even measuring just 1 slit gives us information on the other. It’s the information that is seemingly the cause of the collapse of the wave function.

Process of Elimination

Hello, I like your idea of removing one detector to see if there is a tangible difference. Given how complex the science behind this is, it doesn't seem ethical to have a biased conclusion with such conviction after just 1 adjustment.

Why has no one tried 3,4,5 slits? With those slits, why haven't we tried removing one detector at a time, and swapping out different ones for each slit? Speeding up or slowing down the particle beam? There are so many variables that could lead to comprehensible evidence if the results are as consistent to previous attempts.

However, it just seems this experiment was done 60 years ago and then we just left it as is with no additional input or further experimentation; just copy paste imitations doing the same thing for educational purposes of the original experiment. That just becomes a history lesson, not a science one.

I come here after watching a conspiracy theory and they referenced this experiment as the leading evidence that we live in a simulation, that the universe is just a projection controlled by a program that detects when its being observed like when a video game detects the players position and renders in whats necessary around them. Suggesting that the light particles can bend the rules of physics and time as soon as someone attempts to measure them.

My initial reaction is not to believe this, however I fully appreciate a rebuttal to come armed with objective, comprehensible evidence like any good debate where possible.

I think this experiment needs a make over and we need to breathe new life into it with far more variables to play with, leaving no stone unturned to draw a general trend and any potential outliers to help solve this once and for all. Or at least, as close as our minds will allow us.

We are our own limitations.

Re: Process of Elimination

I agree with you, the whole furore around this experiment has made it more of a history lesson. It's become almost like the Galileo stone/feather thing; i've had people tell me that in normal every-day circumstances, if i dropped a pen and a pebble at exactly the same moment, they would hit the floor at the same time. Even, when i demonstrate this live, people are still adamant in their stance; after-all, i'm no better than Galileo.

This represents a great discrepancy to the original format of experiment by Galileo. I think some of these experiments have been so popularised in pop-culture and pop-science that people have ruled out the possibility of questioning them. Just like the Galileo stone and feather thing, Everyone is still quoting the same concept from decades ago without any iota of desire to question it. This means that some of these science-cum-history concepts are left to grow into "unquestionables" filled with errors.

I think its about time we re-visit the whole premise of this experiment. Let's introduce 3,4, or even 10 slits! Let's do it today with more control over the variables. We can't let this become another one of the "unquestionables". We can't adopt beliefs and never question them. That would be disastrously dogmatic. The opposite of what it means to do real science!

Also, what was the youtube video you watched? thanks

Uh...no. That is definitely not what happens. If so, there would be no conceptual problem. But don't take my word for it. Here's what Richard Feynman said: “I think I can safely say that nobody really understands quantum mechanics." That's because QM seems to suggest that there's a real connection between the mind of the observer and the results obtained. Also, you're not taking into account the results of the quantum eraser phenomenon, which is another aspect of this experiment that suggests the trajectory of an electron in the past can be altered by an experimenter's actions in the present. You'll have to look it up as it's rather lengthy.

Impact of measuring

Thank you so much for this explanation! We have been fretting about this for quite a while. I wish this physical interaction were more clearly included in other explanations of the slit experiment or just quantum mechanics and general

Question for you

You’re saying to observe a particle we’re bouncing particles off of that observed particle? I don’t think that’s the case. What exactly is bouncing off the particle being observed? How is it being directed toward the target particle? With the way they design these experiments, as far as I know, there should be no overt effect like that- certainly not the actual impact of matter as you’re describing. I don’t think anything is being expelled from the detection materials. Or if it were, that would be taken into account- so precise calculations would be made about how it should impact the results. Basically, if something physical was being intentionally shot at the particles and that somehow was the way we detected them, then the scientists performing the research would do that math using specific measurements (including the mass of that projectile matter). I mean if there was anything being directed toward the electrons or whatever, they’d surely have an idea of what forces it would exert and the interaction it should have, etc… Now you could say the electron being observed has some effect upon the detection unit itself (the “quantum observer”) because logically, in order to even register the electron’s presence/position, it must. But I believe that by all known science, there shouldn’t be any effect upon the particle being observed- other than the fact that it’s being observed. That’s kind of the whole point and is exactly what makes this discovery so mind-blowing…right? So I would assume that in these experiments, they’re controlling for those conditions (the observation device having any physical effect or exerting force upon the observed electron, and all possible variables). Do you disagree? I am genuinely curious about what you’re asserting!

What if there are smaller units than photons, which are presently invisible to our instruments? We'll call them units of consciousness (or thought) that we as conscious beings emanate without knowing it, and it is these very tiny units of consciousness (relative to the photon) that influence the photons to behave as they do. In other words the invisible is influencing the visible like the soul influences the body. These same units could explain the placebo effect.

curtesy call

I agree to your theory. Just want to point it out there as a suggestion to proof read your work before submitting it. I have I found a couple of mistakes where a word had been left out.

Curtesy call

I thought it was well thought out and written. Has it been edited since your comment? If we're being semantic you may wish to check your spelling of courtesy.

Objective observation, unlike subjective observation, is very much allowed in conducting data in experiments.

Plus, unless you have robots conducting the experiment ans/or collecting the data, humans are going to be involved.

observer does not need to be human!

A houseplant would work too. Humans cannot see at this level in any case. Machinery is used, and humans don't have to be in the room for the effects to continue. Observation just means measurement, and Wheeler's Delayed Choice and the Quantum Eraser experiments showed the measurement can occur after the photon, electron, or molecule has hit the wall...and it will still change.

This word is used for convenience, but no conscious observer is required. You can also say “detected”. And by detected what is meant is that information exists that is, in principal, detectable even if not yet technically feasible. Look up “The World’s Smallest Double-Slit Experiment” (2007) and you will find that a single low-energy electron can be an “observer” and collapse the quantum interference pattern of a high-energy electron exiting a single hydrogen molecule.

This is BS. When being observed by a sensor, electrons behave as particles. You lack sufficient understanding of the double slit experiment.

A summarily dismissal of a complex phenomenon that has world class physicists, accompanied by a " You don't understand" line illustrates a simple mind

Deeper understanding is to look at our process of observation.

Everything we recieve through our sences gets interpreted in our brains as being solid, founded by rules/laws/logic & most importantly being OUTSIDE our bodies, ie, being real. Reality is though, that these words you now read, are IN your head as is ALL experiences. Point being, WHY are we being TRICKED to think we are experiencing life OUTSIDE our heads when in fact, we are experiencing life IN our heads, just a observation.

Slit Experiment

The only reason a human may not be good test equipment for observation would be because the person lacks awareness. Human observation can be as accurate as any mechanical scientific devise. It just depends on the awareness of the individual.

by detector , they mean, not human but mechanical

Double Split Experiment

"Seem to be leaving out the fact that the difference occurs when being actively observed" EXACTLY!! This experiment shows that matter is not what we think it is. Scientists have known this for a century yet scientific materialism for some reason still prevails. Matter is a product of Mind. NOT the other way around. For more information read "Ontological Mathematics"

That is not what comes out

That is not what comes out this. "Observer" is a misleading term. It does not specifically refer to humans, nor even conscious creatures, although they can be.

About what you wrote

I do agree with you

double slit Hijinx

Ive noticed this trend everywhere. I chock it up to the materialists clinging to their dead ideology

What happens as the distance between the slits becomes greater ? Is there a relationship between the distance between the slits, and the distance of the source from the slits??

Double slit

What if the light is reacting to the material the slits were cut out from. Maybe electromagnetism causing the light particles to bend and change their direction just like how planets and comets change their orbits when passing near something with mass.

The double slits, are on the

The double slits, are on the both sides of the direction of the flow of light. Also, the slit will be more massive on the two outer edges of the double slits. If it were to be hindered due to presence of slits, wouldn't the effect be more on the outer edges and not on the inner edges, i.e. in the middle.

Double Slit

Such is the problem. Particles don't bend when acted upon by electromagnetic fields. They simply form a trajectory. Bending or warping is the property of a wave. Their trajectory could be altered but I'm sure the material is neutral in all aspects to avoid interference.

Electrons have almost no mass and therefore almost no gravity. Atoms of the slit have a huge mass compared to the electrons. As the electrons passes the slit the gravity of the atoms cause some of the closest electrons to start to spin, the same way water spins when shot through a slit. This spin then sends some of the electrons out of their normal straight line trajectory which causes the apparent wave effect.

If that were the case it would happen if there was only one slit. But it doesn't.

Doesn't bend when "observed".

Electrons spin.

Electrons always have a spin of 1/2. This is a fundemental property of electrons and all fermions. Even if electrons were pushed off their trajectory, how do electrons shot one at a time form an interference pattern?

Because it behaves like wave regardless by itself or by groups

When you say wave, do you mean as in bye bye?

Running paint

If light passes through two slits and it reflects off a object that photon leaves some of itself behind and continues on as if you put paint on your hand and slap a wall then run, how many walls you slap depends on how much paint you got, when light reflects off the object or the slit where does it go is it passing through itself or is it colliding with itself in that direction and handing itself some extra light to continue like say you been running with paint on your hand and you have a train of people that follow you and you are the leader. What if you grab just a finger swap of paint for that extra inch foot mile etc. so when the rays reflects off the rectangle will that rectangle of photons continue colliding into each other and handing itself more photons or snatching some to create a another rectangle and so on till it fades away.

agree with Chris Isaacson

I also thought the materials used may have properties that interfere, and the detector might too.

How does the detector itself work? Does it not rely on an intrinsic property of electrons to function? Connecting the detector to that property then necessarily interferes with the experiment. That interference is then to be expected and can be explained rationally rather than through a spooky effect, quantum effect.

Light/Photon/Electron/Particle interacting with slit material

Agree with you. Details of double/single slit experiments should give more information on the slits material, their dimensions (gap width and distance between slits) and the probability of these materials influencing the path/direction of WAVICLES (waves-cum-particles!). This topic needs to discussed and debated.

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Double slit experiment and sensors/instruments influence

In double-slit experiment, it is said when we turn on the sensor/detector/instrument to measure/detect the behaviour of the particle, it shows particle behaviour (otherwise, it shows wave behaviour).

I would like to know, how can we be sure this is not due to the influence/interaction/interference of our measurement, not necessarily the intrinsic nature of photons?

In most reference books, it seems it is a given and it is not discussed.

• quantum-mechanics
• double-slit-experiment
• wave-particle-duality

• $\begingroup$ I mean , it is due to the impact of our measurement that the wave nature of an atom or quantum particle will collapse and start behaving like a particle (maybe I'm not getting the question) $\endgroup$ –  KP99 Commented Jul 12, 2021 at 12:56
• $\begingroup$ @KP99 I mean, any measurement affects the measured quantit. When we measure a voltage, we change the value which existed before measurement. Another example: if we have an extremely unstable system, any measurement will make the system collapse. $\endgroup$ –  Ebi Commented Jul 12, 2021 at 13:03
• 1 $\begingroup$ You may want to read just the beginning of the book Something Deeply Hidden by Sean Carroll. He describes nicely why textbooks do what they do. If we should therefore have to believe in the many worlds interpretation is of course another question. $\endgroup$ –  Kurt G. Commented Jul 12, 2021 at 13:54
• $\begingroup$ You can repeat the same experiment with single photon and see that it is due to their intrinsic nature.... this video might help : youtu.be/I9Ab8BLW3kA $\endgroup$ –  KP99 Commented Jul 12, 2021 at 13:58
• 1 $\begingroup$ @Ebi, if you want to read about a version of the double-slit experiment that will REALLY "blow your mind", google "delayed choice quantum eraser". That experiment doesn't have a detector at either slit but it gives the same results as all other double slit experiments. $\endgroup$ –  David White Commented Jul 12, 2021 at 17:57

2 Answers 2

The better question is to ask how the photons interacting with the edges of the obstacle.

On the one side we have a photon with its electric and magnetic field components. On the other side we have surface electrons on the edge with their charges and with their magnetic dipoles. How do they interact? Do plasmons or another surface excitons come into play?. If so, experiments with changing electric potential for the slits should show some results.

Never such experiments are done? They have bin done Witz electrons by Claus Jönsson and Gottfried Möllenstedt and dependent from the applied voltage the intensity pattern on the screen changes .

• $\begingroup$ This answer does not seem to address the question of the OP. $\endgroup$ –  flippiefanus Commented Jul 14, 2021 at 4:27

[Arrgh, fell into trap of answering a 2 year old question. Well, the bot bumped it so I will leave my answer.]

Great question, and there is an exact answer to this. You can place a polarizer in front of each slit (2 total polarizers), and orient them relative to each other. If the loss of interference were a result of photons passing through or otherwise interacting with the polarizers, then no interference pattern would result.

But that is not what happens. In actual experiments, it is the relative orientation of the 2 polarizers - and nothing else - that determines whether or not there is an interference pattern. If the polarizers are parallel, there IS the usual interference pattern. If the polarizers are perpendicular, there is NO interference pattern. Either way, the total intensity of the pattern is the same. See:

https://sciencedemonstrations.fas.harvard.edu/files/science-demonstrations/files/single_photon_paper.pdf

The general explanation is that if it is possible to learn the which slit information - even if it is not known - there will be no interference. You could learn it by checking photon polarization. That polarization becomes a sort of marker, as explained in the paper.

"Even if not actually measured, the mere possibility that an observer could determine which slit the photon passed through causes the interference pattern to switch to non-interference."

Obviously, it is not the interaction with the polarizer that is the variable here. So yes, this is a property of quantum particles such as photons.

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