A Peculiarity about Quantum Mechanics...

1.Interference

Any wave is capable of producing interference. Mathematically, a wave is described by an amplitude that can be either positive or negative. When two waves overlap spatially the amplitudes can add and subtract at different locations, creating a pattern of crests and troughs. This can be seen in water waves, and heard in the phenomenon of beats caused by sound waves. Light is also a wave, and when incident upon a double slit will produce a pattern of bright and darks spots.

2.Interference and photons

Quantum mechanics governs all phenomena on the atomic scale. The smallest constituent of light is the indivisible photon. What happens when a single photon is incident upon a double slit?

Which Way?

It is difficult at this point to not be tempted to ask, which way does the photon really go? If quantum mechanics can't tell us which way a photon will go, perhaps we can see for ourselves by another means. It seems reasonable to assume that the photon has to pick one slit to go through. Quantum mechanics must just be inadequate at providing us with all the available information.

This is a question that many people have given some serious thought, including Albert Einstein, Sion Beard, Richard Feynman, and Werner Heisenberg. They came up with thought experiments which proposed to measure the "which-way" information of a particle's path on its way to contributing to an interference pattern. They came to a rather perplexing conclusion, however, namely that it is not possible to observe the "which-way" information and the interference pattern simultaneously. One can set up a measurement to "watch" which slit a photon goes through. It can be determined that the photon went through one slit and not the other. However, once this is kind of measurement is set up, the photons will no longer collectively produce a nice pattern of bright and dark spots. Instead they will strike the screen in one big bright spot, as if there were only one slit instead of two.

One can wonder then, if this perplexing behavior is just due to a disturbance between the "which-way" detector and the photon. The detector might be changing something about the photon which causes it to get off course to its position in the interference pattern. The answer is, as the experiment described in the next section shows, that this is not the case. A "which-way" detector can be designed that in no way disturbs the photon and the same phenomenon is observed. It is not possible to observe the which-way information and the interference pattern at the same time. This is an example of quantum mechanics' principle of complementarity. There are pairs of quantities which can be measured and obtained individually, but never at the same time. You can know one precisely, but then you will know nothing about the other and vice versa.

Columbo Investigation
Entangling photons

The light used in this experiment is a special state of light consisting of two photons that are said to be entangled. These photons are intimately intertwined, with polarizations that are correlated.

(Polarization is the direction in which the electric field of the light is oscillating. Light can be linearly polarized in the y direction, with an electric field oscillating up and down. Or it can be linearly x polarized, with an electric field oscillating left in right. Light can also be circularly polarized, which means that the electric field is oscillating in a direction that keeps changing, rotating in a circle around the propagation direction of the light. The tip of the electric field vector traces out a corkscrew pattern. Light can be left circularly polarized, meaning the electric field rotates counter clockwise, or right circularly polarized, meaning the electric field rotates clockwise.)

The entangled photons are produced so that they have linear polarizations which are orthogonal to each other. If one photon is measured to be y polarized, then it is known with certainty that the other has x polarization. It is not accurate to consider these photons as separate entities, but rather as one. They can travel very far away from each other, but they will not loose their correlation. This peculiar state is called a Bell state, after John Bell. (I am not kidding dudes, that was his name!!)

The entangled photons are produced by a process called spontaneous parametric down conversion. This takes place in a special nonlinear crystal called beta-barium borate (BBO). A photon from an argon ion pump laser (351.1 nm) is converted to two longer wavelength (702.2 nm) photons. The two photons go off in two different directions. In this experiment, we call one direction p and the other s. The photons that go down path p are called p photons and those that go down s are called s photons.

The interference pattern from the double slit is created and measured in the following way. The s photons are the ones that create the interference pattern. They travel through the double-slit to detector Ds. The p photons travel directly to detector Dp. If Dp registers a photon, it sends a "click" to the coincidence counter. The counter waits for the p photon's entangled partner to be registered by Ds. Once this second "click" is detected, a count is recorded. The counts are tallied for 400 seconds. Then detector Ds is moved a millimeter and the number of counts in a 400 second interval is recorded for the new detector position. This is repeated until Ds has scanned across a region equivalent to the screen in the diagrams above.

The results are displayed by plotting the number of counts as a function of detector Ds position. The interference pattern is clearly observed.

To make the "which-way" detector, a quarter wave plate (QWP) is put in front of each slit. This device is a special crystal that can change linearly polarized light into circularly polarized light. The two wave plates are set so that given a photon with a particular linear polarization, one wave plate would change it to right circular polarization while the other would change it to left circular polarization.

With this configuration, it is possible to figure out which slit the s photon went through, without disturbing the s photon in any way. Because the s and p photons are an entangled pair, if we measure the polarization of p to be x we can be sure that the polarization of s before the quarter wave plates was y. QWP 1, which precedes slit 1, will change a y polarized photon to a right circularly polarized photon while QWP 2 will change it to a left circularly polarized photon. Therefore, by measuring the polarization of the s photon at the detector, we could determine which slit it went through. The same reasoning holds for the case where the p photon is measured to be y.

Mathematically the quantum description is not any different from the classical wave interference description. Quantum mechanics does not predict exact trajectories for particles. Rather, it predicts the probability a particle will go one way or another. In the case at hand, the single photon has a fifty percent chance of going through the left slit and a fifty percent chance of going through the right slit. A particle is described mathematically by probability amplitudes which, like in the classical case, can be positive or negative. It is these probability amplitudes that combine constructively and destructively to make an interference pattern. Quantum mechanics does not tell us which slit the particle will go through.

The presence of the two quarter wave plates creates the possibility for an observer to gain which-way information about photon s. When which-way information is available, the interference behavior disappears. It is not necessary to actually measure the polarization of p and figure out what slit s passed through. Once the quarter wave plates are there, the s photons are marked, so to speak.

The coincidence counts were tallied at each detector location, as before, and it was found that indeed the interference pattern was gone.

In case you might be suspicious of the quarter wave plates, it is worth noting that given a beam of light incident on a double slit, changing the polarization of the light has no effect whatsoever on the interference pattern. The pattern will remain the same for an x polarized beam, a y polarized beam, a left or a right circularly polarized beam.

It is peculiar then, that the presence of the quarter wave plates causes the s photons to so drastically change their behavior. One can't help but ask, how do these photons know that we could know which slit they went through?

A single photon cannot of course make a whole interference pattern on a screen by itself. If single photons are allowed to go through the slits one at a time, however, and produce a splotch on a special phosphorescent screen, after enough time the interference pattern will emerge.

Quantum Erasure

Increasing the strangeness of this scenario, the next step is to bring back the interference without doing anything to the s beam. A polarizer is placed in the p beam, oriented so that it will pass light that is a combination of x and y. It is no longer possible to determine with certainty the polarization of s before the quarter wave plates and therefore we cannot know which slit an s photon has passed through. The s photons are no longer marked. The potential to gain which-way information has been erased.

The coincidence measurements were repeated with the polarizer in place. It can be seen from the data that the interference pattern is back.

How does photon s know that we put the polarizer there?
Photon s and photon p are entangled. Photon p must be able to communicate to s through some means that is unknown to us. It must be telling s whether it should be producing a pattern or not. But as we will see, this does not seem to be the case. In the next section, things get stranger still.

Delayed Erasure

The experiment up to this point has been performed by detecting photon p before photon s. The erasure of the which-way information was performed by modifying the path of p and then measurings. One could regain a bit of reassurance in commonsense by believing that there must be some form of communication taking place between photon p and s so that s knows whether to interfere or not. Perhaps photon p encounters the polarizer and sends s an immediate message telling it that it can again go the interference route. This is not the case, however, as the next and final portion of the experiment shows.

The path of beam p is lengthened (the polarizer and detector moved farther away from the BBO crystal), so that photon s can be detected first. The interference fringes are obtained as before. Then the quarter wave plates are added to provide the which-way marker. The interference pattern and lack of interference pattern from these runs are observed.

Next the erasure measurement is performed. Before photon p can encounter the polarizer, s will be detected. Yet it is found that the interference pattern is still restored. It seems photon s knows the "which-way" marker has been erased and that the interference behavior should be present again, without a secret signal from photon p.

How this happening? It wouldn't make sense that photon p could know about the polarizer before it got there. It can't "sense" the polarizer's presence far away from it, and send photon s a secret signal to let s know about it. Or can it? And if photon p is sensing things from far away, we shouldn't assume that photon s isn't.

Perhaps the funny business of entanglement plays a more important role than we thought. The two photons are entangled. They are connected together in a special way that doesn't break no matter how far apart they are. It seems that these entangled photons also have some sort of entangled connection with the quarter wave plates and the polarizer.

Making Sense of the Nonsensical (hah!)

From this experiment it is apparent that interference is destroyed by a "which-way" marker and that it can be restored through erasure of the marker, accomplished by making the appropriate measurement on the entangled partner photon p.

In this set up, the "which-way" measurement does not alter the momentum or position of the photons to cause destruction of the interference pattern. We can think of the loss of interference as being due only to the fact that the photons are entangled and that the presence of the quarter wave plates changes this entanglement. The interference pattern can be brought back through the erasure measurement because of the entanglement of the photons, and the way that the presence of the quarter wave plates and polarizer changes the entanglement.

Entanglement is not something we encounter in our everyday world. The concept of locality does not hold for the entangled state like it does for everything in our experience. We encounter things that have a particular location, we can say that a particular thing is here and not there. We certainly do not encounter things that are in two places at once.

However, this is possible on the quantum level. Two photons that are in an entangled state can be separated across the universe, but they are still connected together. In this experiment, with each measurement that was performed, the way the photons were entangled changed. This caused the very strange results that were observed. We like to think about photon p as being in one place and photon s as being in another apart from p. But this is not really the case.. We have to start thinking in ways that aren't consistent with what we experience in our larger scale world. Entanglement seems to play a very important role on the quantum scale of the world, so we need to think about it in new ways.

This quantum erasure experiment is one of many experiments being done that provides a way for us to better understand the strange nature of quantum mechanics. We have encountered strange concepts like entanglement and non-locality. Perhaps this is just the beginning of a journey to a deeper understanding of the universe and new discoveries.