Afshar experiment
In physics, and more specifically, quantum mechanics, the Afshar experiment is an optical experiment, devised by Shahriar S. Afshar in 2004, that is claimed to have disproved the Niels Bohr's principle of complementarity. Since this principle is a central feature of quantum mechanics, the proper interpretation of the experiment has engendered some controversy in the physics community. This controversy has been mostly limited to blogs, physics colloquia, and arXiv e-print archives; as of 2006, neither a description of the experiment, nor any discussion of its theoretical interpretation, has been published in a refereed physics journal.
Overview
The principle of complementarity states that two complementary physical observables cannot both be measured for any given quantum particle. For example, a particle's position and momentum cannot be observed at the same time: this is Werner Heisenberg's uncertainty principle.
One of Afshar's assertions is that, in his experiment, one can check for interference fringes of a photon stream (a momentum measurement) while at the same time observing the photon's path (a position measurement). Afshar's experiment attempts to do this using a variant of the classic Thomas Young double-slit experiment. Such interferometer experiments typically have two "arms" or paths a photon may take. Afshar attempts to both preserve interference, and to determine "which way" or "Welcher Weg" the photon went. Many of the claims associated with this experiment cut across several conventional ideas in quantum mechanics.
History
Shahriar S. Afshar's experimental work was done initially at the Institute for Radiation-Induced Mass Studies and later reproduced at Harvard University, while he was a Research Scholar there. He presented his results in a seminar talk in March 2004 entitled Waving Copenhagen Good-bye: Were the founders of Quantum Mechanics wrong? [1]. The experiment was subsequently featured in the July 24, 2004 edition of New Scientist. [2] [3][4], and published in Proc. SPIE 5866, 229-244 in July of 2005 [5] [6]. Afshar's claim that his experiment invalidates the complementarity principle would have far-reaching implications for the understanding of quantum mechanics, potentially challenging the Copenhagen interpretation and according to John Cramer, the many-worlds interpretation of quantum mechanics. Cramer also asserts that these results support his transactional interpretation of quantum mechanics.
Prof. Afshar's claim that this experiment violates the Principle of Complementarity has generated controversy, much of it carried out in blogs and on various internet discussion groups. As of late May, 2005, Afshar has presented his work at various university seminars and in late March of 2005, at the American Physical Society meeting in Los Angeles [7]. His paper has been published by the International Society for Optical Engineering in July, 2005 [8]. Afshar's results have also been reported in the New Scientist as cited above and in other popular science magazines. 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. Among those writing were Alistair Rae (Centre for Photonic Systems, Cambridge University), David Dunstan (Head of the Physics Department, University of London) and Alwyn Eades (Director of the Microscopy Center, Materials Science Department, Lehigh University) who viewed Afshar's interpretation with skepticism.
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 photo-detector (Fig. 1). In this setup, a photon that goes through pinhole number one impinges only on detector number one, and similarly, if it goes through pinhole two. Therefore, 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'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.
This behavior, Afshar argues, contradicts the principle of complementarity, since it shows both complementary wave and particle characteristics in the same experiment, for the same photons. 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.
Theoretical discussion (in construction)
A new section will appear soon... but for the moment:
A)The duality relation for beginners
Wave-particle duality is considered to be one of the distinguishing characteristics of quantum mechanics, whose theoretical and experimental development has been honoured by more than a few Nobel Prizes for Physics. It has been discussed by prominent physicists for the last 100 years, from the time of Albert Einstein, Niels Bohr and Werner Heisenberg, onwards. On the basis of Bohr's principle of complementarity, it is indeed universally accepted that the observation of two complementary properties, such as position and momentum, requires mutually exclusive experimental measurements.
In the following we will focus our attention on the so called double-aperture experiments (see Fig.1) which like R. P.Feynman has said ``has in it the heart of quantum mechanics. In reality it contains the only mystery´´.
Mathematically, a specific formulation of Bohr's complementarity can be obtained on the basis of the Englert-Greenberger duality relation. The wave function in the Young double-aperture experiment can be written as
- .
Here
are the wave functions associated with pinholes A and B centered on : Additionally : is a position in space downstream of the slits. We write : the corresponding wave amplitudes, and : is the single hole wave function for a aperture centered on the origin. Since the pinhole shape is here irrelevant we will consider ideal punctual pinholes and a particle with a fixed incident momentum ::
To distinguish which pinhole a photon passed through, one needs some measure of the distinguishability between pinholes. Such a measure is given by
where
are the probabilities of finding that the particle passed through aperture A or slit B.
We have in particular : for two symmetric holes and : for a single aperture (perfect distinguishability). In the far-field of the two pinholes the two waves interfere and produce fringes. The cos pattern observed has the form
where : is a momentum for the particle : is a phase shift, and : is the hole separation. We have : where : is the distance between the aperture screen and the far field analysis plane. If use a lens to observe the fringes in the back focal plane (F) the angle is given by : where : is the focal length.
The visibility of the fringes is defined by
where max and min denote the maximum and minimum of intensity. This can be equivalently written
In a single hole experiment we have :. Reciprocally we have : without distinguishability (i.e. :). It is straighforward to see that the duality relation
is always true. The present presentation was limited to a pure quantum state. For a mixture we have
- . Since the
laser coherence involved in Afshar's experiment is supposed high enough we will neglect this particular point in the following and consider valid the equality :.
It must be observed that the mathematical discussion presented until now does not suppose quantum mechanics. In particular every thing is valid for waves in general and could be as well applied to sound waves in a paddle for example.
In order for the relation 7 to be a precise formulation of Bohr complementarity one must introduce wave-particle duality in the discussion. This means one must consider both wave and particle behavior of light on a equal footing. Wave-particle duality implies that one must A) use the unitary evolution of the wave before the observation and B) consider the particle aspect after the detection (this is called the Heisenberg-von Neumann collapse postulate). Indeed since one could only observe the photon in one point of space (a photon can not be absorbed twice) this implies that the meaning of the wave function is essentially statistical and can not be confused with a classical wave (like it exists in air or water).
In this context the direct observation of a photon in the aperture plane precludes the following recording of the same photon in (F). Reciprocally the observation in (F) means that we did not absorb the photon before. If both hole are open this implies that we dont know were we would have detected the photon in the aperture plane.
- define thus the distinguishability of the two holes A and B.
A maximal value : means a complete distinguishability and than that only one hole (say A ) is open. If now we detect the photon in F we know that that photon would have been detected in A necessarily. Reciprocally : means that both holes are open and play a symmetric role. If we detect the photon in (F) we dont know where the photon would have been detected in the aperture plane and : characterize here our ignorance.
In parallel if : then : and this means that a statistical accumulation of photon in (F) will build up an interference pattern with maximal visibility. Reciprocally : implies : and thus no fringes after statistical recording of several photons. This formalizes the wave particle duality in this experiment
Critiques
Though Afshar's work is still the subject of ongoing interpretation and discussion, a significant portion of the scientific community is of the opinion that Afshar's experiment does not refute complementarity. The following is a partial list of critiques of Afshar's work. Afshar's rebuttals are available on his FAQ [9].
- Bill Unruh, Professor of Physics at University of British Columbia, [10].
- Lubos Motl, Assistant Professor of Physics, Harvard University [11]
- Ruth Kastner, Committee on the History and Philosophy of Science, University of Maryland, College Park, [12].
- Aurelien Drezet, University of Graz Institut of experimental physics, Austria, [13]
References
- John G. Cramer, "A Farewell to Copenhagen?" (undated, 2005 or later), Analog Science Fiction and Fact. (A non-technical discussion in a popular forum)
- Marcus Chown, "Afshar's Quantum Bombshell", (July 24, 2004), New Scientist magazine.
- Shahriar S. Afshar, "Sharp complementary wave and particle behaviours in the same welcher weg experiment", (2003) IRIMS www.irims.org/quant-ph/030503/; Proc. SPIE 5866 (2005) 229-244.
- Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, Marlan O. Scully, "A Delayed Choice Quantum Eraser", (1999) ArXiv.org quant-ph/9903047; Physical Review Letters 84 (2000) 1-5.
- Luboš Motl, "Violation of complementarity?", (2004) Luboš Motl's reference frame. (A blog entry from a prominent critic.)