Michael S. Chapman and David E. Pritchard
Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
In the Feynman Lectures on Physics, the famous Caltech physicist remarked that the quantum mechanical interference of particles observed in matter wave interferometers is “a phenomenon which is impossible, absolutely impossible to explain in any classical way, and which has in it the heart of quantum mechanics. In reality it contains the only mystery.” [1] He is referring of course to the phenomenon of wave-particle duality, in which matter at the atomic scale sometimes behaves like particles and sometimes behaves like waves, but observation of both wave and particle behavior in the same measurement is somehow forbidden by the laws of quantum mechanics.
Wave-particle duality, along with Heisenberg's uncertainty principle (which sets a lower limit of precision on the simultaneous measurement of a particle's position and momentum) are probably the two most striking examples of the quantum mechanical principle of complementarity. A stumbling block for the layperson's comprehension, complementarity is “not a problem” for professional physicists who have learned to accept these restrictions on the knowable. What they probably forget is that, before deciding that this duality was not a problem, they had to mull over certain gedankenexperiments (thought experiments) in which their intuition was re-educated about the peculiarities of quantum behavior.
Many of these gedankenexperiments involve particle interferometers, because they so beautifully exemplify wave-particle duality. In order to predict the interference fringes that are observed at the detector in these interferometers, one is forced to represent the particle by a de Broglie wave that travels over both of two separate paths at the same time and then recombines with itself. However, our classical intuition would argue that the particle must have traveled one path or the other, but not both. A host of “which-way” gedankenexperiments have been thought up in which one attempts to measure which path the particle traversed (“which-way”), while still preserving interference pattern recorded by the detector [2]. In all such gedankenexperiments, however, it can be shown that the which-way measurement invariably reduces the visibility of the observed interference fringes—the more certainly the measurement determines which side of the interferometer the particle traversed, the more the fringe contrast is reduced (i.e. the less the particle exhibits wavelike behavior).
Recent developments in atom optics and interferometry have allowed us to perform one of the most famous of these gedankenexperiments: the Feynman light microscope [3]. His which-way measurement scheme uses an optical microscope to simply watch which path the particles take as they pass through a Young's two-slit experiment. Of course, the particles must be illuminated with a light source in order to be imaged, and it is just the act of scattering photons from the particles that will destroy their interference fringes. This is true even if we arrange to scatter only a single photon from each particle passing through the apparatus. However, we can minimize the impact of the photon on the interference pattern if we use light of longer wavelength or reduce the slit separation (it is only the ratio that matters), but only at the expense of which-way information. Indeed, complementarity would suggest that fringe contrast must disappear when the slit separation is larger than half the wavelength of the scattered light (l/2), since at this point, we could resolve which path the particle took.
In our experiment, we used a three-grating Mach-Zehnder atom interferometer instead of a two slit experiment [4]. (see Fig. 1). A laser beam is used to scatter a single photons from each atom passing through the interferometer, and we measured the contrast of the atomic interference fringes for different path separations at the point of scattering (thus, this experiment is equivalent to a Young's two-slit experiment with a variable slit separation). Not surprisingly, at least to professional physicists, the principle of complementarity is upheld: the fringe contrast is high when the separation of the paths in much less than l/2 but decreases to zero at about this separation (see Fig. 2).
Figure 1. A schematic of the experiment showing the three grating Mach-Zehnder atom interferometer and the laser beam used to illuminate the atoms. The grating period is 200 nm and the separation between gratings is 60 cm.
Figure 2. Loss of atom interference fringe contrast vs. separation (d) of the two atom paths at the intersection of the laser beam (the laser beam is translated along the atom beam direction to scatter at different locations). The inset illustrates the ambiguity of optically resolving two closely spaced point sources that leads to the contrast revivals in the data.
At larger separations, we see not only the general suppression of the fringe contrast expected from complementarity, but also several subsequent revivals of the fringe contrast. These contrast revivals are due to the imperfect spatial localization provided by the scattered photon [5]. If light were scattered from an atom localized on one side of the interferometer and imaged with a lens, this image would have diffraction rings (see inset of Fig. 2). Thus if a single photon is recorded where it would be expected for an atom localized on the one side of the interferometer, it may actually have come from an atom on the other side if one of the diffraction rings coincides with the position of the recorded photon. Under these circumstances there is significant uncertainty in which side the atom that emitted the photon really traversed; consequently the fringe contrast can be (and is) greater than zero. The several oscillations correspond to several diffraction rings.
Our experiment also addresses another fundamental question: where is the coherence lost to and how may it be regained? This is a more troublesome problem for the professional physicist because the elastic scattering of a photon is not a dissipative process per se and may be treated with Schrödinger's equation without any ad hoc dissipative term. Such an analysis preserves the full quantum coherence and results in an atomic wave function that is “entangled,” or correlated with that of the scattered photon. That is, if one knows the final scattering direction of the photon, then the atomic interference fringes are not destroyed but instead acquire a phase shift correlated with the scattering direction (this does not violate complementarity because a measurement of the exact direction of the photon requires a lens with a small aperture, which lacks sufficient resolution to determine which side of the interferometer the photon scattered from). The atom-photon entanglement provides an alternative explanation of the disappearance of the fringes when the direction of the photon is not measured: photons scattered in different directions impart different phase shifts to the atom fringes. When these phase shifts are large enough to cause the peaks of some of the fringes to line up with the valleys of others, the result is cancellation of the fringes in the total pattern observed. In fact, the phase shifts increase according to the separation of the paths at the point of scattering, which explains why the fringes are more strongly suppressed for larger path separations.
To verify the entanglement between the photon scattering direction and the atom fringes explicitly, we observed the atom fringes formed only by those atoms that had scattered photons in the same general final direction. As expected, the atom fringe contrast was higher in this case and shifted in phase according to which final scattering direction we chose. Hence we were able to recover the atomic coherence lost when the scattering direction of the photons was not restricted (see Fig. 3).
Figure 3. Same data as in Figure 2, except that this time we only detect atoms that scattered photons in a particular direction. We recover fringe contrast at the expense of which-way information. The contrast recovery is limited by the resolution of the photon direction determination.
Entanglement of one system (say, a particle) due to interaction with another system (a photon, or some other measuring device) is an important issue in contemporary quantum mechanics, particularly with regards to Einstein-Podolsky-Rosen (EPR) type correlations and to understanding the measurement process in general and specifically the loss of coherence which occurs in moving from the quantum to the classical regime [6]. In our experiment, we have studied this at the most fundamental level: a single particle undergoing a single scattering event. Thus this experiment not only brings an old gedankenexperiment into reality, but also probes deeply enough to reveal its relevance to issues of contemporary interest in quantum mechanics.
[1] R. P. Feynman, R. B. Leighton and M. Sands. The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1965), vol. III, p. 1-1.
[2] N. Bohr in A. Einstein: Philosopher - Scientist, edited by P. A. Schilpp p. 200-241 (Library of Living Philosophers, Evaston, IL, 1949).
[3] M. S. Chapman, T. D. Hammond, A. Lenef, J. Schmiedmayer, R. A. Rubenstein, E. Smith, D. E. Pritchard, Phys. Rev. Lett. 75, 3783 (1995).
[4] D.W. Keith, C.R. Ekstrom, Q.A. Turchette and D.E. Pritchard, Phys. Rev. Lett. 66, 2693 (1991). J. Schmiedmayer et al., Phys. Rev. Lett. 74, 1043 (1995).
[5] S.M. Tan and D.F. Walls, Phys. Rev. A 47, 4663 (1993), T. Sleator et al., in Laser Spectroscopy X, p. 264, edited by M. Dulcoy, E. Giacobino and G. Camy (World Scientific, Singapore, 1991).
[6] Quantum Theory and Measurementedited by J.A. Wheeler and W.H. Zurek (Princeton University Press, Princeton, 1983). W.H. Zurek, Physics Today bf 44, 36-44 (1991), and references therein.
(c) Copyright 1996, The Institute of Electrical and Electronics Engineers, Inc.
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