Delayed choice quantum eraser

From Wikipedia, the free encyclopedia

A delayed choice quantum eraser is a combination 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 a very peculiar result of the well known double slit experiment of quantum mechanics, the dual wave particle nature of light, and in fact all matter.

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

[edit] Introduction

In the double slit experiment, a photon passes through one of two slits in a double slit apparatus, and then registers on a detector. The detector shows where the photon hit it, like an image projected on a screen. If many photons individually pass through the double slit apparatus, and nothing observes which slit a given photon travels through, an interference pattern emerges on the detector. The interference pattern indicates that the light beam is in fact made up of waves. However, if someone observes which of the two slits each photon passes through, a different result will be obtained. In this case, each photon hits the detector after going through only one slit and a single concentration of hits in the middle of the detection field. This result is consistent with light behaving as individual particles, like tiny bullets. It is counterintuitive that a different outcome results based on whether or not the photon is observed after it goes through the slit but before it hits the detector.

In a quantum eraser experiment, one arranges to detect which one of the slits the photon passes through, but also construct the experiment in such a way that this information can be "erased" after the fact. It turns out that if one observes which slit the photon passes through, the "no interference" or particle behavior will result, which is what quantum mechanics predicts, but if the quantum information is "erased" regarding which slit the photon passed through, a wavelike interference pattern can be observed.

However, 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 the target. But, again, if the information is "erased," an interference pattern can be recovered in a certain subset of the photons which reach the detector, even if the information is erased after the photons have hit the detector.

[edit] The experiment

The experimental setup, described in much more detail in the paper, is as follows. First, generate a photon and pass it through a double slit apparatus. After the photon goes through one of the two slits, which using the notation in fig. 2 of the paper can be labeled A and B, a special crystal (one at each slit) uses spontaneous parametric down conversion (SPDC) to convert the photon into two identical entangled photons with 1/2 the frequency of the original photon. One of these photons, labeled the "signal" photon, continues to the target detector D0, while the other entangled photon, labeled the "idler" photon, is deflected by a prism which sends it along different paths depending on whether it came from A or B. However, the paths contain beam splitters which each have a 50% chance of allowing the idler to pass through and a 50% chance of causing it to be reflected. Because of the way the beam splitters are arranged, if the idler is detected at detector D3, then it can only have come from slit A; but if the idler is detected at detector D1, it might either have come from slit B and passed through the beam splitter, or have come from slit A and been reflected by the beam splitter. Likewise, if the idler is detected at detector D2, it might either have come from slit A and passed through the beam splitter, or have come from slit B and been reflected by the beam splitter. Thus, if the idler is detected at either detectors D1 or D2, its which-path information has been "erased", 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, it is known that both it and the corresponding signal photon came from slit A (there is also a fourth detector D4, not pictured in the diagram of the experimental setup in fig. 2 but shown in the more schematic diagram in fig. 1, with this detector placed in such a way that if the idler is detected at D4, the idler/signal pair must have come from slit B).

What's interesting about the experiment is that when the experimenters looked at the subset of signal photons whose entangled idlers were detected at D1, they found an interference pattern, graphed in fig. 3 of the paper; likewise, when they looked at the subset of signal photons whose entangled idlers were detected at D2, they also found an interference pattern, graphed in fig. 4. However, when they looked at the subset of signal photons whose entangled idlers were detected at D3, they found no interference, as seen in fig. 5. This is similar to 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, unlike in the 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.

The results from Kim, et al. have shown that, in fact, whether or not the idler's path is observed determines whether interference is seen in the "joint detection" pattern of signal photons and their corresponding idlers, even if the idler is not observed until after the signal photon arrives at the detector. Some have interpreted this to mean that the delayed choice to observe or not observe the path of the idler 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, and the experimenter plots only the subset of signal photons that are matched with idlers that went to a particular detector such as D1. The total pattern of all signal photons, whose entangled idlers went to multiple different detectors, will never show interference;^[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) 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 described complementarity as “wave-like” and “particle-like” behavior of a quantum particle. this has come to be known as the wave-particle duality of quantum mechanics. The double-slit experiment is a good example of this concept. Richard Feynman believed that this was 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] They found that the interference pattern disappears when which-path information is obtained, even if this information was obtained without directly observing the original photon. Even more surprising was that, if you somehow "erase" the which-path information, the interference pattern reappears! And, perhaps most provocative of all, you can delay the "choice" to "erase" or "observe" the which-path information and still restore the interference pattern, even after the original photon has been "observed" at the primary detector!

How can this be? It might initially seem that the "choice" to observe or erase the which-path information of the idler can change the position where the signal photon is recorded on the detector, even after it should have already been recorded. However, as noted above, the total pattern of signal photons never shows interference, and it is only when one looks at a subset of signal photons whose idlers were seen at a particular detector that an interference pattern can be recovered. So, the experiment would certainly not allow one to send a message back in time, and whether the experiment requires any sort of backwards causality to understand it would depend on one's interpretation of quantum mechanics. The transactional interpretation would interpret the results in terms of genuine backwards causality, but other interpretations such as the Copenhagen interpretation, the Bohm interpretation and the many-worlds interpretation would predict the same experimental results without the need for backwards causality. For example, according to the Copenhagen interpretation the initial measurement of the position of the signal photon (whose probability distribution would not show interference if it was measured first) would discontinuously alter the wave function of the combined signal/idler system, affecting the probabilities that the idler would be detected at different locations. If the signal photon was detected by detector D0 at a position near a peak of the D0/D1 joint detection graph (fig. 3) and a trough of the D0/D2 joint detection graph (fig. 4), this would increase the probability that the idler would be detected at detector D1 and decrease the probability that the idler would be detected at D2; likewise, if the signal photon was detected at a position near a peak of the D0/D2 joint detection graph and a trough of the D0/D1 joint detection graph, this would increase the probability that the idler would be detected at D2 and decrease the probability it would be detected at D1. This would ensure that both correlation graphs showed the correct interference pattern, with the interference patterns now explained in terms of the initial measurement of the signal photon affecting the probabilities of the later measurement of the idler rather than the other way around.