Delayed choice quantum eraser

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A delayed choice quantum eraser is a cross between a quantum eraser experiment and Wheeler's delayed choice experiment. This experiment has actually been performed and published by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, and Marlan O. Scully^[1] This experiment was designed to investigate some very peculiar consequences of the well known double slit experiment in quantum mechanics, as well as the consequences of quantum entanglement. As this experiment is a more complex version of the quantum eraser experiment, study of that article may make this article easier to understand.

1 Introduction
2 The experiment
3 Discussion
4 References
5 External links

[edit] Introduction

In the basic double slit experiment, a very narrow beam of light from a source (such as the sun) that is far enough away to have almost perfectly parallel wave fronts is directed aimed along a line perpendicular to a wall with double slits in it. The widths of the slits and the distance between them are of the same order of magnitude as the wavelength of the incident light. If a detection screen (anything from a sheet of white paper to a high tech digital camera) is erected on the other side of the double slit wall, a pattern of light and dark fringes will be observed. Very early in the history of this experiment, scientists discovered that they could filter out enough of the incident illumination that light reaching the detection would be observed one flash at a time. They next tried to discover by which slit a given unit of light (photon) had traveled. Unexpectedly, the results were invariably that anything done to permit determination of which path had a photon moving along it would make the interference pattern disappear. In this case, each photon hits the detector as would one that could only pass through one slit, and each slit yields a single concentration of hits near the middle of the detection field. It is counterintuitive that a different outcome results based on whether or not the photon is constrained to follow one or another path well after it goes through the slit but before it hits the detector.

Two inconsistent accounts of the nature of light have long contended. The discovery of light's interfering with itself seemed to prove that light could not be a particle. It seemed that it had to be a wave to explain the Young experiment. But not long after this discovery, experiments with photo-electricity (the phenomenon that makes the light meters in cameras possible) gave equally strong evidence to support the idea that light is a particle phenomenon. Nothing is observable regarding it between the time a photon is emitted (which experimenters can at least locate in time by determining the time at which energy was supplied to the electron emitter) and the time it appears as the delivery of energy to some detector screen (e.g., as a measurement on a CCD or "charge-coupled device" such as the substitute for photographic emulsion in a digital camera). Nevertheless experimenters have tried to gain indirect information about which path a photon "really" takes when passing through the double-slit apparatus. In the process what they have learned is that by constraining the path taken by one of a pair of entangled photons they inevitably control the path taken by the partner photon, and that by permitting the partner photon the opportunity to take two paths so constructed that they will permit that photon to interfere with itself they then find the first photon will behave in a way consistent with its having interfered with itself —- even though there is no double-slit device in its way.

In a quantum eraser experiment, one arranges to detect which one of the slits the photon passes through, but also to construct the experiment in such a way that this information can be "erased" after the fact. In practice, this "erasure" of path information frequently means removing the constraints that kept photons following two different paths separated from each other. In one experiment, rather than splitting one photon or its probability wave between two slits, the photon is subjected to a physical device called a beam splitter. If one thinks in terms of a stream of photons being randomly directed by such a beam splitter to go down two paths that are kept from interaction, it is clear that no photon can then interfere with any other or with itself.

If the rate of photon production is reduced so that only one photon is entering the apparatus at any one time, however, it becomes impossible to understand the photon as only moving through one path because when their outputs are redirected so that they coincide on a common detector then interference phenomena appear.

In the two diagrams to the right a single photon is emitted at the yellow star, passes through a 50% beam splitter (green block) that reflects 1/2 of the photons, and travels along two possible paths, depicted by the red or blue lines.

In the top diagram, one can see that the trajectories of photons are clearly known — in the sense that if a photon emerges at the top of the apparatus it appears that it had to have come by the path that leads to that point (blue line), and if it emerges at the side of the apparatus it appears that it had to have come by way of the other path (red line).

In the bottom diagram, a second beam splitter is introduced (which can direct either beam towards either path), and the result is that whatever emerges from each exit port may have come by way of either path. It is in this sense that the path information has been "erased." Note that total phase differences are introduced along the two paths because of the different effects of passing through a glass plate, being reflected off its first surface, or passing through the back surface of a semi-silvered beam splitter and being reflected by the back (inner side) of the reflective surface. The result is that waves passing out the top exit interfere destructively, whereas waves passing out the upper right side exit interfere constructively. (See Mach-Zehnder interferometer for a more detailed explanation of the phase changes involved.) Now it seems that, regardless of appearances, something may in all cases have traveled along both paths. The experiment depicted above is reported in full in http://www.sciencemag.org/cgi/content/full/315/5814/966.

Kim, et al., have shown that it is possible to delay the choice to "erase" the quantum information until after the photon has actually hit its target. Under those conditions an interference pattern can be recovered, even if the information is erased after the photons have hit the detector. The experimental apparatus is considerably more elaborate than that shown and described above.

If the second beam splitter in the lower diagram could be inserted or removed one might assert that a photon must have traveled by way of one path or the other if a photon were detected at the end of one path or the other. The appearance would be that the photon "chose" one path or the other at the first and only beam splitter, and therefore could only arrive at the respective path end. The subjective assurance that the photon followed a single path is brought into question, however, if (after the photon has presumably "decided" which path to take) a second beam splitter then makes it impossible to say by which path the photon has traveled. What once appeared to be a "black and white" issue now appears to be a "gray" issue. It is the mixture of two originally separated paths that constitutes what is colloquially referred to as "erasure." It is actually more like destroying a signature written in blue ink by wetting the signature and adjacent area with water, thus making the whole area a uniform light blue color.

[edit] The experiment

The experimental setup, described in detail in the original paper, is as follows. First, a photon is generated and passes through a double slit apparatus (vertical black line in the upper left hand corner of the diagram). The photon goes through one (or both) of the two slits, whose paths are shown as red or light blue lines, indicating which slit the photon came through. A special crystal (labeled as BBO) causes spontaneous parametric down conversion (SPDC), converting the photon (from either slit) into two identical entangled photons with 1/2 the frequency of the original photon. One of these photons, referred to as the "signal" photon (the red and light blue lines going up from the BBO crystal), continues to the target detector called D₀, while the other entangled photon, referred to as the "idler" photon (the red and light blue lines going down from the BBO crystal), is deflected by a Glen-Thomson prism that sends it along divergent paths depending on whether it came from slit A or slit B. Somewhat beyond the path split, beam splitters (green blocks) are encountered that each have a 50% chance of allowing the idler to pass through and a 50% chance of causing it to be reflected. The gray blocks in the diagram are mirrors.

Because of the way the beam splitters are arranged, the idler can be detected by detectors labeled D₁, D₂, D₃ and D₄. If it is recorded at detector D₃, then it can only have come from slit B. If it is recorded at detector D₄ it can only have come from slit A. But if the idler is detected at detector D₁ or D₂, it might have come from either slit (A or B).

Which detector receives the idler photon reveals information (or lack thereof) about the path of the signal photon with which it is entangled. If the idler is detected at either detectors D₁ or D₂, its which-path information has been "erased" (because the alternate paths have been run together), so there is no way of knowing whether it (and its entangled signal photon) came from slit A or B, whereas if the idler is detected at D₃ or D₄, it is known that both it and the corresponding signal photon came from slit A or slit B, respectively.

When the experimenters looked at the signal photons whose entangled idlers were detected at D₁ or D₂ (what is known as a 'coincidence count' between signal photons detected at D₀ and idlers detected at one of these two detectors), they found an interference pattern. However, when they looked at the signal photons whose entangled idlers were detected at D₃ or D₄, they found no interference. This result is similar to that of the double slit experiment, since interference is observed when it is not known which slit the photon went through, while no interference is observed when the path is known. However, what makes this experiment interesting is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler need not be made until after the position of the signal photon has already been measured by D₀. There is never any which-path information determined directly for the photons that are detected at D₀, yet detection of which-path information by D₃ or D₄ means that no interference pattern is observed in the corresponding subset of signal photons at D₀.

The results from Kim, et al. have shown that whether the idler photon is detected at a detector that preserves its which-path information (D₃ or D₄) or a detector that erases its which-path information (D₁ or D₂) determines whether interference is seen at D₀, even though the idler photon is not observed until after the signal photon arrives at D₀ due to the shorter optical path for the latter. Some have interpreted this result to mean that the delayed choice to observe or not observe the path of the idler photon will change the outcome of an event in the past. However, it should be noted that an interference pattern can only be observed after the idlers have been detected, when the experimenter plots either the subset of signal photons at D₀ that are entangled with idlers that went to the detector D₁ (the D₀/D₁ coincidence count), or the subset of signal photons at D₀ that are entangled with idlers that went to the detector D₂ (the D₀/D₂ coincidence count). The total pattern of all signal photons at D₀, whose entangled idlers went to multiple different detectors, will never show interference regardless of what happens to the idler photons;^[2] one can get an idea of how this works by looking carefully at both the graph of the subset of signal photons whose idlers went to detector D₁ (fig. 3 in the paper) and the graph of the subset of signal photons whose idlers went to detector D₂ (fig. 4), and observing that the peaks of the first interference pattern line up with the troughs of the second and vice versa (noted in the paper as 'a π phase shift between the two interference fringes'), so that the sum of the two will not show interference.

[edit] Discussion

In their paper, Kim, et al.^[1] explain that the concept of complementarity is one of the most basic principles of quantum mechanics. According to the Heisenberg Uncertainty Principle, it is not possible to measure both precise position and momentum of a quantum particle at the same time. In other words, position and momentum are complementary. In 1927, Niels Bohr maintained that quantum particles have both "wave-like" behavior and "particle-like" behavior, but can exhibit one kind of behavior only under conditions that prevent exhibiting the complementary characteristics. This complementarity has come to be known as the wave-particle duality of quantum mechanics. Richard Feynman believed that the presence of these two aspects under conditions that prevent their simultaneous manifestation is the basic mystery of quantum mechanics.

The actual mechanisms that enforce complementarity vary from one experimental situation to another. In the double-slit experiment, the common wisdom is that the Heisenberg Uncertainty Principle makes it impossible to determine which slit the photon passes through without at the same time disturbing it enough to destroy the interference pattern. However, in 1982, Scully and Drühl found a way around the position-momentum uncertainty obstacle and proposed a quantum eraser to obtain which-path or particle-like information without introducing large uncontrolled phase factors to disturb the interference.^[3]

Scully and Drühl found that the interference pattern disappears when which-path information is obtained, even if this information was obtained without directly observing the original photon, but that if you somehow "erase" the which-path information, the interference pattern reappears. In the delayed choice quantum eraser, the pattern reappears even if the which-path information is erased after the signal photons hit the primary detector. However, the interference pattern can only be seen retroactively once the idler photons have already been detected and the experimenter has obtained information about them, with the interference pattern being seen when the experimenter looks at particular subsets of signal photons that were matched with idlers that went to particular detectors. The total pattern of signal photons at the primary detector never shows interference, so it is not possible to deduce what will happens to the idler photons by observing the signal photons alone, which would open up the possibility of gaining information faster-than-light (since one might deduce this information before there had been time for a message moving at the speed of light to travel from the idler detector to the signal photon detector) or even gaining information about the future (since as noted above, the signal photons may be detected at an earlier time than the idlers), both of which would qualify as violations of causality in physics. In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of quantum theory are correct, it should never be possible to experimentally violate causality using quantum effects,^[4] although some physicists have speculated about the possibility that these equations might be changed in a way that would be consistent with previous experiments but which could allow for experimental causality violations.^[5]^[6]