Abstract

This paper reports a "delayed choice quantum eraser" experiment proposed by Scully and Drühl in 1982. The experimental results demonstrated the possibility of simultaneously observing both particle-like and wave-like behavior of a quantum via quantum entanglement. The which-path or both-path information of a quantum can be erased or marked by its entangled twin even after the registration of the quantum.

    In 1982, Scully and Drühl [2] found a way around this position-momentum uncertainty obstacle and proposed a quantum eraser to obtain which-path or particle-like information without scattering or otherwise introducing large uncontrolled phase factors to disturb the interference. To be sure the interference pattern disappears when which-path information is obtained. But it reappears when we erase (quantum erasure) the which-path information. 

    Since 1982, quantum eraser behavior has been reported in several experiments; however, the original scheme has not been fully demonstrated. . . . 

    We wish to report a realization of the above quantum eraser experiment. The schematic diagram of the experimental setup is shown in Fig. 2. 

    [S]pontaneous parametric down conversion (SPDC) is used to prepare the entangled two-photon state. SPDC is a spontaneous nonlinear optical process from which a pair of signal-idler photons is generated when a pump laser beam is incident onto a nonlinear optical crystal.

In this experiment, a single photon is aimed at the double-slit. If it passes through the left slit, it will hit a crystal placed behind the slit on the left side of the crystal; if through the right slit, it will hit the crystal on the right side. We will not actually be measuring the interference vel non of the incoming photon, but of the subsequently generated photons.

When the incoming photon hits the crystal, it is destroyed and a pair of entangled photons is generated by the crystal at the spot where it hit. 

Because of entanglement, the properties of the two entangled photons will forever be correlated. Therefore, if we can later identify one of the entangled photons as having come from, say, the left side of the crystal, we will thereby know, retroactively, that its twin also came from the left side of the crystal, so that we will then know where both entangled photons came from. 

On the other hand, if we cannot later identify where either of the entangled photons came from, then we will have no which-path information for either. 

The remainder of the experiment consists of manipulating the pair of entangled photons. We are able to preserve which-path information for as long as we are able to identify either one of the entangled photons with respect to which side of the crystal generated it. If at any time in the course of the experiment we lose the ability to determine which side of the crystal generated the entangled pair, we thereby lose the which-path information relating to both entangled photons.

The laser is able to spit out photons in a highly controlled manner. Photons from the laser are aimed at the double-slit where they are "divided," in the QM sense, between the left slit and the right slit. 

(This double slit is a bit of a red herring. It is only a method of randomizing emissions from region A or region B of the crystal, which are themselves the equivalent of the two slits of Young's experiment.) 

The optical crystal is placed immediately behind the slits. An incoming photon shines on the crystal ("is incident upon the crystal") at two well-defined areas of the crystal (region A and region B) because the crystal is right up next to the slits.

Note that, because of the nature of QM with its superpositions, we can say that a single incoming photon is "incident onto a … crystal … at two regions," despite the fact that it will "hit" the crystal at only one or the other region. Dividing the photon via the double slit makes its "impact" on the crystal subject to quantum randomness. That is, it is quantumly random whether the incoming photon will actually appear at region A or region B.

    A pair of 702.2nm orthogonally polarized signal-idler photon is generated either from A or B region. The width of the SPDC region is about 0.3mm and the distance between the center of A and B is about 0.7mm. A Glen-Thompson prism is used to split the orthogonally polarized signal and idler.

When the incoming photon hits the crystal, a pair of entangled photons is generated at the point of incidence – either region A of the crystal or region B of the crystal. The two regions of the crystal, A and B, are some distance apart. (This will be approximately the distance between the two slits.) In this experiment the separation is approximately 0.7 millimeters. 

The entangled pair of photons generated by the crystal (at either region A or region B) are "orthogonally polarized." That is to say, if one of the pair is polarized horizontally, the other will be polarized at right angles ("orthogonally"), i.e., vertically; and vice versa. This correlation in the respective polarizations of the pair of photons is part and parcel of their "entanglement." 

The Glen-Thompson prism at the crystal is used to separate the two photons generated at the crystal. One of the pair is sent in one direction, the other in a different direction. (Here bear in mind that because of the entanglement, QM dictates that the correlation in their respective polarizations will remain regardless of spatial separation.) 

Although the pair of photons generated by the crystal are identical (and correlated), the experiment will use them in different ways. Thus, one of the pair (sent in one direction) is called the "signal" photon; the other of the pair (sent in another direction) is called the "idler" photon. The designation of a particular photon as "signal" or "idler" is a matter of convention based on which direction they are sent (and how they will be used in the experiment), not any inherent difference between the two entangled photons generated at the crystal.

"Collimated" means "made parallel." The lens LS focuses photons from either of these paths onto a single detector D₀. 

The lens LS also allows us to control the distance (f) from the place of origin (region A or B) to the detector D₀. In this way, we can fix the time it will take for the signal photon to be detected at D₀. 

The "far field" condition essentially makes the photons arrive at D₀ as though they had traveled a long distance, even though the path is foreshortened. Like binoculars.

Scanning the detector along one axis provides the position information – where the signal photon actually landed on the detector D₀. 

At this point, we do not have which-path information. (The straight lines of Fig. 2 are diagrammatic only.) Detector D₀ by itself will not be able to distinguish between a photon originating at region A, and a photon originating at region B, because nothing about this part of the experiment provides which-path information. 

Without more, we would expect the pattern developing at detector D₀ to be an interference pattern. QM predicts that without which-path information, photons arriving from either A or B should interfere and distribute themselves one-by-one according to the statistical distribution of interfering waves. 

Mind you, if we did have which-path information, the results should be quite different. In that case, QM would predict the "clumping" pattern typical of particle motion.

The idler photon next encounters a 50-50 beamsplitter BSA or BSB. The beamsplitter will either reflect the idler photon off course and into the detector D₃ or D₄; or it will allow the photon to pass through and continue (toward the reflecting mirror M_A or M_B). QM dictates that it will go one way or the other a random 50% of the time, i.e., a 50-50 chance either way. 

If the idler photon is reflected at BSA or BSB into the detector D₃ or D₄, it will be detected with which-path information intact. Therefore, for every photon detected at D₃ or D₄, we know which region of the crystal generated both it and its twin signal photon: if detected at D₃, we know that both twins came from region A; if detected at D₄, then both twins came from region B. 

As stated earlier in the paper, "The registration of D₃ or D₄ provides which-path information (path A or path B) of [idler] photon 2 and in turn provides which-path information of [signal] photon 1 because of the entanglement nature of the two-photon state . . .." 

If the idler photon is not reflected at BSA or BSB, it will continue toward its next encounter, the reflecting mirror M_A or M_B. There it will be reflected toward the single 50-50 beamsplitter BS, which is the quantum eraser. 

Here it is most interesting to note, as do the authors in the published version of the paper, that the "choice" of which direction the photon will take at BSA or BSB is made by QM itself. That is, the path at this juncture is 50-50 random. As we will see, this "choice" will determine the information available at the conclusion of the experiment. (The authors note that in other quantum eraser experiments, the choice is made by the experimentalist. [3]) 

The beamsplitter BS randomizes the path information, and thereby makes the which-path information unavailable, in the following manner. 

For an idler photon coming from reflecting mirror M_A, the beamsplitter BS will either reflect the idler photon into the detector D₁; or it will allow the photon to pass through and continue toward the detector D₂. There is a 50-50 chance either way. Similarly, for an idler photon coming from the other reflecting mirror M_B, the beamsplitter BS will either reflect the idler photon into the detector D₂; or it will allow the photon to pass through and continue toward the detector D₁. 

You can see that, with this 50-50 beam splitter, any photon arriving at detector D₁ or D₂ has an equal 50-50 chance of having been reflected from reflecting mirror M_A or M_B. It is therefore impossible to tell whether the photon was generated at region A of the crystal, or at region B. The which-path information encoded into the photons arriving at detectors D₁ and D₂ has been "erased."

      The triggering of detectors D₃ and D₄ provide which-path information of the idler (photon 2) and in turn provide which-path information of the signal (photon 1).

This is key. There is no which-path information for the signal photons when they initially arrive at D₀. Which-path information for those signal photons is obtained only later, when the twin idler photon is later detected at D₃ or D₄ (and not obtained if the twin idler photon is detected at D₁ or D₂). 

As discussed below, the experimental setup ensures that this which-path information for the signal photons is obtained or erased only after the signal photon has been detected and the information is winging its way toward the Coincidence Circuit.

Detector D₀ fires once for every photon generated by the pump laser, because regardless of whether the photon hits region A or region B, a signal photon is sent to D₀ for detection. By comparing the detections of the signal photons at D₀ with the other detectors, we can determine where the corresponding idler photon hit. There will be only one joint detection for each incoming photon from the pump laser.

R₀₂ records a joint detection at detector D₀ and detector D₂ (which-path info not available) 

R₀₃ records a joint detection at detector D₀ and detector D₃ (which-path info available) 

R₀₄ records a joint detection at detector D₀ and detector D₄ (which-path info available) 

The joint detection event at detectors D₃ or D₄ (given by R₀₃, R₀₄) gives us new information about a photon that was previously registered at detector D₀. We have already registered that photon, and the scanning has registered where it hit D₀ – its position along the D₀ x-axis. But when we correlate the later detection of the idler at D₃ or D₄, with that previous detection at D₀, we now know that the photon registered at D₀ came from either region A or region B of the crystal. 

QM predicts that if which-path information is not available at the time of measurement, the pattern will be an interference pattern, as though wave-like photons passed through both slits and "interfered with themselves" to produce the distinctive interference pattern of hits. This is the case at detector D0 at all times. 

Because which-path information is not available for photons registered at D₀ even after a joint detection at the post-erasure detectors D₁ and D₂, we learn nothing new about the detections that have occurred at D₀ and so QM predicts that R₀₁ and R₀₂ will exhibit this interference pattern in counting photon hits at D₀. 

QM also predicts that if which-path information is available at the time of measurement, the pattern will be a "clumping," as though particle-like photons passed through a slit and on to a detector in a more-or-less straight line. Because which-path information is available for photons registered at D0 once a joint detection has been indicated at the pre-erasure detectors D₃ and D₄, QM predicts that R₀₃ and R₀₄ will exhibit this "clumping" pattern.

In this experiment, "the time of measurement" is after the correlation of the joint detections, which takes place at the Coincidence Circuit. However, the count of photon hits that will be displayed represents hits at D₀, registered earlier.

• There is no which-path information about the signal photon (photon 1) detected at D₀. 
• The which-path information about its twin idler photon (photon 2) is "available" because the twin is still in flight along a well-defined path coming from either region A or region B. The twin has not yet reached the first 50-50 beamsplitter BSA or BSB. 
• The which-path information about the signal photon itself is "available" in principle at D₀. This is because we can correlate every photon at D₀ with its twin, so that learning the which-path information about the twin (at D₃ or D₄) will necessarily reveal the which-path information of the signal photon at D₀, albeit after-the-fact. 
• But the signal photon has already been detected, and the information about its position at D₀ is already winging its way to the Coincidence Circuit, while the information about its twin idler photon is still inchoate. 
• The detecting mechanism that has tagged the which-path information (i.e., the generation of an entangled pair at either region A or region B) has already been accomplished, but it has not yet yielded up its which-path information to any observer. 

However, at the subsequent moment when the twin is detected at D₁, D₂, D₃ or D₄, the which-path information may or may not be available, depending on whether the detection occurs at D₁ or D₂ (which-path information not available), or at D₃ or D₄ (which-path information available). 

As stated earlier in the paper, "After the registration of photon 1 [at D₀], we look at these 'delayed' detection events of D₁, D₂, D₃, and D₄ which have constant time delays . . . relative to the triggering time of D₀. It is easy to see these 'joint detection' events must have resulted from the same photon pair."

      Figs. 3 and 4 show the "joint detection" rates R₀₁ and R₀₂ against the x coordinates of detector D₀. It is clear we have observed the standard Young's double-slit interference pattern. . . . 

      Fig. 5 reports a typical R₀₃ (R₀₄), "joint detection" counting rate between D₀ and "which-path" D₃ (D₄), against the x coordinates of detector D₀. An absence of interference is clearly demonstrated. There is no significant difference between the curves of R₀₃ and R₀₄ except the small shift of the center.

Time 1. The entangled pair leaves either region A or region B of the crystal. The signal photon heads off to detector D₀, and the idler photon heads off to the interferometer. 

Time 2. The signal photon is registered and scanned at detector D₀ according to its position. This information (the position of the signal photon upon "impact" at D₀) is sent on its way to the Coincidence Circuit. 

Time 3. The idler photon reaches the first pair of beamsplitters, BSA, BSB. There, QM makes a choice which direction the idler photon will go – either to detectors D₃, D₄; or to the quantum eraser BS and on to detectors D₁, D₂. 

Time 4a. If the idler photon is shunted to detectors D₃, D₄, it is detected with which-path information intact. Then and only then do we know which-path information for its twin signal photon that already has been detected, scanned, registered and recorded at D₀. 

Time 4b. If the idler photon passes through to detectors D₁, D₂, it is detected with no which-path information (the which-path information having been "erased" at BS). 

Time 5. The Coincidence Circuit correlates the arrival of a signal photon at detector D₀ with the arrival of its twin at D₁, D₂, D₃, or D₄. If the correlation is with an idler arriving at D₃ or D₄, then we know (after-the-fact) the which-path information of the signal photon that arrived earlier at D₀. If the correlation is with an idler arriving at D₁ or D₂, then we have no which-path information for the signal photon that arrived earlier at D₀. 

Time 6. Upon accessing the information gathered by the Coincidence Circuit, we the observer are shocked to learn that the pattern shown by the positions registered at D₀ at Time 2 depends entirely on the information gathered later at Time 4 and available to us at the conclusion of the experiment. 

The position of a photon at detector D₀ has been registered and scanned. Yet the actual position of the photon arriving at D₀ will be at one place if we later learn more information; and the actual position will be at another place if we do not. 

Ho-hum. Another experimental proof of QM. This is the way it works, folks. 

Canton, Ohio 
September 4, 2002

Fig. 2 from Yoon-Ho Kim, et al., "A Delayed Choice Quantum Eraser"

http://xxx.lanl.gov/pdf/quant-ph/9903047 

Phys.Rev.Lett. 84 (2000) 1-5  

[additions by Ross Rhodes]

1. Your commentator wishes to thank Dr. Kim for reviewing this commentary before posting.

2. M. O. Scully and K. Drühl, Phys. Rev. A 25, 2208. "Quantum eraser: A proposed photon correlation experiment concerning observation and 'delayed choice' in quantum mechanics."

3. T. Helmuth, et al., Phys. Rev. A 35, 2532 (1987); J. Baldzuhn, E. Mohler, and W. Martienssen, Z. Phys. B 77, 347 (1989); B.J. Lawson-Daku et al., Phys. Rev. A. 54, 5042 (1996).  More recently, see V. Jacques, et al., "Experimental realization of Wheeler's gedankenexperiment," Science 315 966 (2007), e-print at http://www.arxiv.org/abs/quant-ph/0610241 .

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