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The Afshar Two-Slit Experiment and Complementarity

Ruth E. Kastner

Published Feb 2, 2005• 0 citations
OpenAlex

Abstract

A modified version of Young's experiment by Shahriar Afshar demonstrates that, prior to a ``which-way'' measurement indicating which slit a particle goes through, an interference pattern exists. It has been claimed that this result constitutes a violation of the Principle of Complementarity. This paper discusses the implications of this experiment and considers how Cramer's Transactional Interpretation accomodates the result. It is shown that the Afshar experiment is isomorphic in key respects to a a spin one-half particle prepared as ``spin up along x'' and post-selected in a specific state of spin along z. It is concluded that Bohr would have had no more problem accounting for the Afshar result than he would in accounting for the aforementioned pre- and post-selection spin experiment, in which the particle's preparation state is confirmed by a nondestructive measurement prior to post-selection.

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Complementarity and the Afshar Experiment

Tabish Qureshi

A modified two-slit interference experiment, proposed and carried out by Shahriar Afshar [first reported by M. Chown, New Scientist {\\bf 183}, 30 (2004)], claims to demonstrate a violation of Bohr's complementarity principle. We point out the flaw in Afshar's analysis and show why complementarity is robust and cannot be violated in any experiment which is a variant of the conventional two-slit experiment.

•Jan 16, 2007•6 citations

Modified Afshar experiment: calculations

Eduardo V. Flores

The Afshar experiment is a relatively simple two-slit experiment with results that show a discrepancy with the predictions of Bohr's Principle of Complementarity. We report on the results of a calculation using a simpler but equivalent set-up called the modified Afshar experiment. Numerical results are in agreement with the experimental measurements performed on the Afshar experiment set-up. Calculations show that the level of which-way information and visibility in the Afshar experiment is higher than originally estimated.

arXiv:0803.2192•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 20, 2009•5 citations

Wave Particle Duality and the Afshar Experiment

Aurélien Drezet

In an interesting series of articles published few years ago Afshar and coworkers [1,2] reported an optical experiment in which they claimed to refute the well known N. Bohr principle of complementarity [3, 4]. Obviously this result, if justified, would constitute a serious attack against the orthodox interpretation of quantum mechanics (known as the Copenhagen interpretation). This work stirred much debate in different journals (see for examples references [5–12]). We think however that there are still some important misunderstandings concerning the interpretation of this experiment. In a preprint written originally in 2004 [5] (and following some early discussions with Afshar) we claimed already that the interpretation by Afshar et al. can be easily stated if we stay as close as possible from the texts written by Bohr. The aim of the present article (which was initially written in 2005 to precise a bit the thought developed in [5]) is to comment the interpretation discussed in [1]. We will in the following analyze the meaning of Bohr principle and show that far from disproving its content the experiment [1] is actually a complete confirmation of its general validity. The difficulties associated with the understanding of this principle are not new and actually complementarity created troubles even in Einstein mind [3] so that we are here in good company. To summarize a bit emphatically Bohr’s complementarity we here remind that this principle states that if one of a pair of non commuting observables of a quantum object is known for sure, then information about the second (complementary) is lost [3, 4, 15, 16]. This can be equivalently expressed as a kind of duality between different descriptions of the quantum system associated with different experimental arrangements which mutually exclude each other (read in particular [3,4]). Later in the discussion we will try to precise this definition but for the moment it is enough to illustrate the concepts by examples Consider for instance the well known Young double-pinholes interference experiment made with photons. The discrete nature of light precludes the simultaneous observation of a same photon in the aperture plane and in the interference pattern: the photon cannot be absorbed twice. This is already a trivial manifestation of the principle of Bohr. Here it implies that the two statistical patterns associated with the wave in the aperture plane and its Fourier (i. e., momentum) transform require necessarily different photons for their recording. It is in that sense that each experiment excludes and completes reciprocally the other. In the case considered before the photon is absorbed during the first detection (this clearly precludes any other detection). However even a non-destructive solution for detection implying entanglement with other quantum systems has a radical effect of the same nature: the complementarity principle is still valid. For example, during their debate Bohr and Einstein [3] discussed an ideal which-way experiment in which the recoil of the slits is correlated to the motion of the photon. Momentum conservation added to arguments based on the uncertainty relations are sufficient to explain how such entanglement photon-slits can erase fringes [15–19]. It is also important for the present discussion to remind that the principle of complementarity has a perfidious consequence on the experimental meaning of trajectory and path followed by a particle. Indeed the unavoidable interactions existing between photons and detectors imply that a trajectory existing independently of any measurement process cannot be unambiguously defined. This sounds even like a tragedy when we consider once again the two-holes experiment. Indeed for Bohr this kind of experiments shows definitely the essential element of ambiguity which is involved in ascribing conventional physical attributes to quantum systems. Intuitively (i. e., from the point of view of classical particle dynamic) one would expect that a photon detected in the focal plane of the lens must have crossed only one of the hole 1 or 2 before to reach its final destination. However, if this is true, one can not intuitively understand how the presence of the second hole (through which the photon evidently did not go) forces the photon to participate to an interference pattern (which obviously needs an influence coming from both holes). Explanations to solve this paradox have been proposed by de Broglie, Bohm, and others using concepts such as empty waves or quantum potentials [20, 21]. However all these explanations are in agreement with Bohr principle (since they fully reproduce quantum predictions) and can not be experimentally distinguished. Bohr and Heisenberg proposed for all needed purposes a much more pragmatic and simpler answer: don’t bother, the complementarity principle precludes the simultaneous observation of a photon trajectory and of an interference pattern. For Bohr [3]: This point is of great logical consequence, since it is only the circumstance that we are presented with a choice of either tracing the path

•Jan 1, 2011•5 citations

No Paradox in Wave–Particle Duality

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The assertion that an experiment by Afshar et al. demonstrates violation of Bohr’s Principle of Complementarity is based on the faulty assumption that which-way information in a double-slit interference experiment can be retroactively determined from a future measurement.

•Jan 1, 2020•3 citations

Afshar's experiment revisited: a demonstration of Bohr's complementary principle

Ngoc Diep Lai, V. Jacques, A. Dréau +5 more

A recent experiment performed by Afshar et al. has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information a two-path interferometer. The authors have reproduced the same experiment, using true single-photon pulses emitted by a single nitrogen-vacancy (NV) color center in a diamond crystal and propagating in a two-path wavefront-splitting interferometer realized with a Fresnels' biprism, followed by a grating with transmitting slits of adjustable width. The experimental setup is illustrated. The results go far beyond the reported results in the previous works of Afshar et al. and the subtle flaws in their analysis are then pointed out. The measured values of the interference visibility V and the which-path information, characterized by the distinguishability parameter D, are found, with values close to the ideal-case upper bound. This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics, without any violation of Bohr's complementarity principle.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2009•0 citations

Modified Two-Slit Experiments and Complementarity

Tabish Qureshi

Some modified two-slit interference experiments claim to demonstrate a violation of Bohr’s complementarity principle. A typical such experiment is theoretically analyzed using wave-packet dynamics. The flaw in the analysis of such experiments is pointed out and it is demonstrated that they do not violate complementarity. In addition, it is quite generally proved that if the state of a particle is such that the modulus square of the wave-function yields an interference pattern, then it necessarily loses which-path information.

arXiv:quant-ph/0701109•Journal of Quantum Information Science•Jan 1, 2012•9 citations
A modified version of Young's experiment by Shahriar Afshar demonstrates that, prior to a which-way'' measurement indicating which slit a particle goes through, an interference pattern exists. It has been claimed that this result constitutes a violation of the Principle of Complementarity. This paper discusses the implications of this experiment and considers how Cramer's Transactional Interpretation accomodates the result. It is shown that the Afshar experiment is isomorphic in key respects to a a spin one-half particle prepared as spin up along x'' and post-selected in a specific state of spin along z. It is concluded that Bohr would have had no more problem accounting for the Afshar result than he would in accounting for the aforementioned pre- and post-selection spin experiment, in which the particle's preparation state is confirmed by a nondestructive measurement prior to post-selection.
The Afshar experiment is a relatively simple two-slit experiment with results that show a discrepancy with the predictions of Bohr's Principle of Complementarity. We report on the results of a calculation using a simpler but equivalent set-up called the modified Afshar experiment. Numerical results are in agreement with the experimental measurements performed on the Afshar experiment set-up. Calculations show that the level of which-way information and visibility in the Afshar experiment is higher than originally estimated.
In an interesting series of articles published few years ago Afshar and coworkers [1,2] reported an optical experiment in which they claimed to refute the well known N. Bohr principle of complementarity [3, 4]. Obviously this result, if justified, would constitute a serious attack against the orthodox interpretation of quantum mechanics (known as the Copenhagen interpretation). This work stirred much debate in different journals (see for examples references [5–12]). We think however that there are still some important misunderstandings concerning the interpretation of this experiment. In a preprint written originally in 2004 [5] (and following some early discussions with Afshar) we claimed already that the interpretation by Afshar et al. can be easily stated if we stay as close as possible from the texts written by Bohr. The aim of the present article (which was initially written in 2005 to precise a bit the thought developed in [5]) is to comment the interpretation discussed in [1]. We will in the following analyze the meaning of Bohr principle and show that far from disproving its content the experiment [1] is actually a complete confirmation of its general validity. The difficulties associated with the understanding of this principle are not new and actually complementarity created troubles even in Einstein mind [3] so that we are here in good company. To summarize a bit emphatically Bohr’s complementarity we here remind that this principle states that if one of a pair of non commuting observables of a quantum object is known for sure, then information about the second (complementary) is lost [3, 4, 15, 16]. This can be equivalently expressed as a kind of duality between different descriptions of the quantum system associated with different experimental arrangements which mutually exclude each other (read in particular [3,4]). Later in the discussion we will try to precise this definition but for the moment it is enough to illustrate the concepts by examples Consider for instance the well known Young double-pinholes interference experiment made with photons. The discrete nature of light precludes the simultaneous observation of a same photon in the aperture plane and in the interference pattern: the photon cannot be absorbed twice. This is already a trivial manifestation of the principle of Bohr. Here it implies that the two statistical patterns associated with the wave in the aperture plane and its Fourier (i. e., momentum) transform require necessarily different photons for their recording. It is in that sense that each experiment excludes and completes reciprocally the other. In the case considered before the photon is absorbed during the first detection (this clearly precludes any other detection). However even a non-destructive solution for detection implying entanglement with other quantum systems has a radical effect of the same nature: the complementarity principle is still valid. For example, during their debate Bohr and Einstein [3] discussed an ideal which-way experiment in which the recoil of the slits is correlated to the motion of the photon. Momentum conservation added to arguments based on the uncertainty relations are sufficient to explain how such entanglement photon-slits can erase fringes [15–19]. It is also important for the present discussion to remind that the principle of complementarity has a perfidious consequence on the experimental meaning of trajectory and path followed by a particle. Indeed the unavoidable interactions existing between photons and detectors imply that a trajectory existing independently of any measurement process cannot be unambiguously defined. This sounds even like a tragedy when we consider once again the two-holes experiment. Indeed for Bohr this kind of experiments shows definitely the essential element of ambiguity which is involved in ascribing conventional physical attributes to quantum systems. Intuitively (i. e., from the point of view of classical particle dynamic) one would expect that a photon detected in the focal plane of the lens must have crossed only one of the hole 1 or 2 before to reach its final destination. However, if this is true, one can not intuitively understand how the presence of the second hole (through which the photon evidently did not go) forces the photon to participate to an interference pattern (which obviously needs an influence coming from both holes). Explanations to solve this paradox have been proposed by de Broglie, Bohm, and others using concepts such as empty waves or quantum potentials [20, 21]. However all these explanations are in agreement with Bohr principle (since they fully reproduce quantum predictions) and can not be experimentally distinguished. Bohr and Heisenberg proposed for all needed purposes a much more pragmatic and simpler answer: don’t bother, the complementarity principle precludes the simultaneous observation of a photon trajectory and of an interference pattern. For Bohr [3]: This point is of great logical consequence, since it is only the circumstance that we are presented with a choice of either tracing the path
A recent experiment performed by Afshar et al. has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information a two-path interferometer. The authors have reproduced the same experiment, using true single-photon pulses emitted by a single nitrogen-vacancy (NV) color center in a diamond crystal and propagating in a two-path wavefront-splitting interferometer realized with a Fresnels' biprism, followed by a grating with transmitting slits of adjustable width. The experimental setup is illustrated. The results go far beyond the reported results in the previous works of Afshar et al. and the subtle flaws in their analysis are then pointed out. The measured values of the interference visibility V and the which-path information, characterized by the distinguishability parameter D, are found, with values close to the ideal-case upper bound. This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics, without any violation of Bohr's complementarity principle.
Some modified two-slit interference experiments claim to demonstrate a violation of Bohr’s complementarity principle. A typical such experiment is theoretically analyzed using wave-packet dynamics. The flaw in the analysis of such experiments is pointed out and it is demonstrated that they do not violate complementarity. In addition, it is quite generally proved that if the state of a particle is such that the modulus square of the wave-function yields an interference pattern, then it necessarily loses which-path information.