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The Afshar experiment is an optical experiment which investigates the principle of complementarity in quantum mechanics. The result of the experiment, which was first devised and carried out by Shahriar Afshar in 2001, is in accordance with the standard predictions of quantum mechanics; however, it is controversially claimed to violate complementarity and specifically the Englert-Greenberger duality relation, a claim which has been denied.

Overview

Afshar's experiment uses a variant of the classic Thomas Young double-slit experiment to create interference patterns to investigate complementarity. Such interferometer experiments typically have two "arms" or paths a photon may take. One of Afshar's assertions is that, in his experiment, it is possible to check for interference fringes of a photon stream (a measurement of the wave nature of the photons) while at the same time observing each photon's path (a measurement of the particle nature of the photons).

History

Shahriar S. Afshar's experimental work was done initially at the Institute for Radiation-Induced Mass Studies (IRIMS) in 2001 and later reproduced at Harvard University in 2003, while he was a research scholar there. The results were presented at a Harvard seminar in March 2004, and published as conference proceeding by the International Society for Optical Engineering (SPIE). The experiment was featured as the cover story in the July 24, 2004 edition of New Scientist. The New Scientist feature article itself generated many responses, including various letters to the editor that appeared in the August 7 and August 14, 2004 issues, arguing against the conclusions being drawn by Afshar, with Cramer's response. Afshar presented his work also at the American Physical Society meeting in Los Angeles, in late March 2005.

Afshar claims that his experiment invalidates the complementarity principle and has far-reaching implications for the understanding of quantum mechanics, challenging the Copenhagen interpretation. According to John G. Cramer, Afshar's results support Cramer's own transactional interpretation of quantum mechanics and challenges the many-worlds interpretation of quantum mechanics, although this claim has not been published in any peer-reviewed journal.

Experimental setup and Afshar's interpretation

The experiment uses a setup similar to that for the double-slit experiment. In Afshar's variant, light generated by a laser passes through two closely spaced circular pinholes (not slits). After the dual pinholes, a lens refocuses the light so that the image of each pinhole is received by a separate photon-detector (Fig. 1). In this setup, Afshar argues that a photon that goes through pinhole number one impinges only on detector number one, and similarly, if it goes through pinhole two. Therefore according to Afshar, if observed at the image plane, the setup is such that the light behaves as a stream of particles and can be assigned to a particular pinhole.

When the light acts as a wave, because of interference one can observe that there are regions that the photons avoid, called dark fringes. Afshar now places a grid of thin wires just before the lens (Fig. 2). These wires are placed in previously measured positions of the dark fringes of an interference pattern which is produced by the dual pinhole setup when observed directly. If one of the pinholes is blocked, the interference pattern can no longer be formed, and some of the light will be blocked by the wires. Consequently, one would expect that the image quality is reduced, as is indeed observed by Afshar. Afshar then claims that he can check for the wave characteristics of the light in the same experiment, by the presence of the grid.

At this point, Afshar compares the results of what is seen at the photo-detectors when one pinhole is closed with what is seen at the photo-detectors when both pinholes are open. When one pinhole is closed, the grid of wires causes some diffraction in the light, and blocks a certain amount of light received by the corresponding photo-detector. When both pinholes were open, however, the effect of the wires is minimized, so that the results are comparable to the case in which there are no wires placed in front of the lens (Fig.3). Afshar asserts this experiment has also been conducted with single photons and the results are identical to the high flux experiment, although these results were not available at the time of the talk at Harvard.

Afshar's conclusion is that the light exhibits a wave-like behavior when going through the wires, since the light goes through the spaces between the wires when both slits were open, but also exhibits a particle-like behavior after going through the lens, with photons going to a given photo-detector. Afshar argues that this behavior contradicts the principle of complementarity since it shows both complementary wave and particle characteristics in the same experiment for the same photons.

Specific critiques

A number of scientists have published criticisms of Afshar's interpretation of his results. They are united in their rejection of the claims of a violation of complementarity. Afshar has responded to these critics in his academic talks, his blog, and other forums.

The most recent work claims that Afshar's core claim, that the Englert–Greenberger duality relation is violated is not true. They re-ran the experiment on single photons and found no violation of complimentarity, concluding "This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics."

Some researchers claim that, while the fringe visibility is high, no which-way information ever exists:

• Ruth Kastner, Committee on the History and Philosophy of Science, University of Maryland, College Park.

  Kastner's criticism, published in a peer-reviewed paper, proceeds by setting up a gedanken experiment and applying Afshar's logic to it to expose its flaw. She proposes that Afshar's experiment is equivalent to preparing an electron in a spin-up state and then measuring its sideways spin. This does not imply that one has found out the up-down spin state and the sideways spin state of any electron simultaneously. Applied to Afshar's experiment: "Nevertheless, even with the grid removed, since the photon is prepared in a superposition S, the measurement at the final screen at t₂ never really is a 'which-way' measurement (the term traditionally attached to the slit-basis observable ${\displaystyle {\mathcal {O}}}$), because it cannot tell us 'which slit the photon actually went through.' In addition she underscores her conclusion with an analysis of the Afshar setup within the framework of the transactional interpretation of quantum mechanics. A follow-up e-print by Kastner : "On Visibility in the Afshar Experiment"] argues that the commonly referenced inverse relationship between visibility parameter V and which-way parameter K does not apply to the Afshar setup, which post-selects for "which slit" after allowing interference to take place.

  • Kastner's setup is has been criticised, and an alternative proposed: Why Kastner analysis does not apply to a modified Afshar experiment (by Eduardo Flores and Ernst Knoesel ) Abstract:

In an analysis of the Afshar experiment R.E. Kastner points out that the selection system used in this experiment randomly separates the photons that go to the detectors, and therefore no which-way information is obtained. In this paper we present a modified but equivalent version of the Afshar experiment that does not contain a selection device. The double-slit is replaced by two separate coherent laser beams that overlap under a small angle. At the intersection of the beams an interference pattern can be inferred in a non-perturbative manner, which confirms the existence of a superposition state. In the far field the beams separate without the use of a lens system. Momentum conservation warranties that which-way information is preserved. We also propose an alternative sequence of Stern-Gerlach devices that represents a close analogue to the Afshar experimental set up.

• Daniel Reitzner (Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia), Comment on Afshar’s experiments, ArXiv:quant-ph/0701152 (2007).

  Reitzner performed numerical simulations, published in a preprint, of Afshar's arrangement and obtained the same results that Afshar obtained experimentally. From this he argues that the photons exhibit wave behavior, including high fringe visibility but no which-way information, up to the point they hit the detector: "In other words the two-peaked distribution is an interference pattern and the photon behaves as a wave and exhibits no particle properties until it hits the plate. As a result a which-way information can never be obtained in this way."

Other researchers agree that the fringe visibility is high and that the which-way information is not simultaneously measured, but they believe that the which-way information does exist under some circumstances.

• Bill Unruh, Professor of Physics at University of British Columbia

  Unruh, who has published his objections on the web pages of his university, is probably the most prominent critic of Afshar's interpretation. He, like Kastner, proceeds by setting up an arrangement that he feels is equivalent but simpler. The size of the effect is larger so that it is easier to see the flaw in the logic. In Unruh's view that flaw is, in the case that an obstacle exists at the position of the dark fringes, "drawing the inference that IF the particle was detected in detector 1, THEN it must have come from path 1. Similarly, IF it were detected in detector 2, then it came from path 2." In other words, he accepts the existence of an interference pattern but rejects the existence of which-way information when Afshar puts in the wire grid.

• Tabish Qureshi (Physics Dept., Jamia Millia Islamia, New Delhi), Complementarity and the Afshar experiment, ArXiv:quant-ph/0701109 (2007).

  Qureshi, in his preprint, considers like Kastner a spin system as a simplified but equivalent experiment. Like Kastner he also argues that there is no which-way information, but for a different reason. While Kastner says there is no determinate which-way information with or without the grid as long as both slits are open, Qureshi argues that there is such information when the photon passes the slits, but it is erased when the two parts of the wave overlap, irrespective of whether or not the interference pattern is actually detected.

Another group does not question the which-way information, but rather contends that the measured fringe visibility is actually quite low:

• Luboš Motl, Former Assistant Professor of Physics, Harvard University.

  Motl's criticism, published in his blog, is based on an analysis of Afshar's actual setup, instead of proposing an equivalent experiment like Unruh and Kastner. In contrast to Unruh and Kastner, he believes that which-way information always exists, but argues that the measured contrast of the interference pattern is actually very low: "Because this signal (disruption) from the second, middle picture is small (equivalently, it only affects a very small portion of the photons), the contrast V is also very small, and goes to zero for infinitely thin wires." He also argues that the experiment can be understood with classical electrodynamics and has "nothing to do with quantum mechanics".

• Aurelien Drezet, University of Graz Institut of experimental physics, Austria,

  Drezet's preprint argues that the classical concept of a "path" leads to much confusion in this context, but "The real problem in Afshar’s interpretation comes from the fact that the interference pattern is not actually completely recorded." The argument is similar to that of Motl, that the observed visibility of the fringes is actually very small. Another way he looks at the situation is that the photons used to measure the fringes are not the same photons that are used to measure the path. The experimental setup he analyzes is only a "slightly modified version" of the one used by Afshar.

• Ole Steuernagel, School of Physics, Astronomy and Mathematics, University of Hertfordshire, UK.

  Steuernagel makes a quantitative analysis of the various transmitted, refracted, and reflected modes in a setup that differs only slightly from Afshar's. He concludes that the Englert-Greenberger duality relation is strictly satisfied, and in particular that the fringe visibility for thin wires is small. Like some of the other critics, he emphasizes that inferring an interference pattern is not the same as measuring one: "Finally, the greatest weakness in the analysis given by Afshar is the inference that an interference pattern must be present."

Others question Afshar's interpretation and offer alternatives:

• Entanglement and quantum interference (by Paul O'Hara ) Abstract:

In the history of quantum mechanics, much has been written about the double-slit experiment, and much debate as to its interpretation has ensued. Indeed, to explain the interference patterns for subatomic particles, explanations have been given not only in terms of the principle of complementarity and wave-particle duality but also in terms of quantum consciousness and parallel universes. In this paper, the topic will be discussed from the perspective of spin-coupling in the hope of further clarification. We will also suggest that this explanation allows for a realist interpretation of the Afshar Experiment.

Specific support for Afshar interpretation

There also is support for the Afshar interpretation from John Cramer:

• A Farewell to Copenhagen? (by John G. Cramer )

See also

• Wheeler's delayed choice experiment
• Delayed choice quantum eraser

External links

• A double-slit `which-way' experiment on the complementarity--uncertainty debate (by R. Mir et al. ) Abstract

A which-way measurement in Young's double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenberg's uncertainty principle: distinguishing two positions a distance s apart transfers a random momentum q \sim \hbar/s to the particle. This claim has been subject to debate: Scully et al. asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al. asserted that Bohr's stance is always valid. We address this issue using the experimental technique of weak measurement. We measure a distribution for q that spreads well beyond , but nevertheless has a variance consistent with zero. This weakvalued momentum-transfer distribution P_{wv}(q) thus reflects both sides of the debate.

References and notes

1. Afshar SS, Flores E, McDonald KF, Knoesel E. (2007). "Paradox in wave-particle duality". Foundations of Physics. 37 (2): 295–305. doi:10.1007/s10701-006-9102-8. {{cite journal}}: External link in |title= (help)CS1 maint: multiple names: authors list (link)
2. ^ Steuernagel O (2007). "Afshar's experiment does not show a violation of complementarity". Found. Phys. 37: 1370. doi:10.1007/s10701-007-9153-5. {{cite journal}}: External link in |title= (help)
3. ^ V. Jacques, N. D. Lai, A. Dreau, D. Zheng, D. Chauvat, F. Treussart, P. Grangier, J-F Roch Illustration of quantum complementarity using single photons interfering on a grating, New J. Phys. 10, 123009 (2008)
4. Georgiev D D 2007 Single photon experiments and quantum complementarity, Prog. Phys. 2 97-103
5. ^ Afshar SS (2003). "Sharp complementary wave and particle behaviours in the same welcher weg experiment". IRIMS:quant-ph/030503: 1–33. {{cite journal}}: External link in |title= (help)
6. ^ Afshar SS (2005). "Violation of the principle of complementarity, and its implications". Proceedings of SPIE. 5866: 229–244. doi:10.1117/12.638774. {{cite journal}}: External link in |title= (help)
7. Afshar SS (2006). "Violation of Bohr's complementarity: one slit or both?". AIP Conference Proceedings. 810: 294–299. doi:10.1063/1.2158731. {{cite journal}}: External link in |title= (help)
8. Afshar SS (2004). "Waving Copenhagen Good-bye: Were the founders of Quantum Mechanics wrong?". Harvard seminar announcement. {{cite journal}}: External link in |title= (help)
9. Marcus Chown (2004). "Quantum rebel". New Scientist. 183 (2457): 30–35. {{cite journal}}: External link in |title= (help)
10. Afshar's Quantum Bomshell Science Friday
11. Cramer JG (2004). "Bohr is still wrong". New Scientist. 183 (2461): 26. {{cite journal}}: External link in |title= (help)
12. Afshar SS (2005). "Experimental Evidence for Violation of Bohr's Principle of Complementarity". APS Meeting, March 21–25, Los Angeles, CA. {{cite journal}}: External link in |title= (help)
13. Cramer JG (2005). "A farewell to Copenhagen?". Analog Science Fiction and Fact. {{cite journal}}: External link in |title= (help)
14. Kastner R (2005). "Why the Afshar experiment does not refute complementarity?". Studies in History and Philosophy of Modern Physics. 36: 649–658. doi:10.1016/j.shpsb.2005.04.006. {{cite journal}}: External link in |title= (help)
15. Kastner R (2006). "The Afshar Experiment and Complementarity". APS Meeting, March 13–17, Baltimore, MD. {{cite journal}}: External link in |title= (help)
16. Unruh W (2004). "Shahriar Afshar - Quantum Rebel?". {{cite journal}}: Cite journal requires |journal= (help); External link in |title= (help)
17. Motl L (2004). "Violation of complementarity?". {{cite journal}}: Cite journal requires |journal= (help); External link in |title= (help)
18. Drezet A (2005). "Complementarity and Afshar's experiment". ArXiv:quant-ph/0508091. {{cite journal}}: External link in |title= (help)

• Quantum measurement
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