Multiparticle Interferometry and the Superposition Principle Daniel M
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Physics Today Multiparticle Interferometry and the Superposition Principle Daniel M. Greenberger, Michael A. Horne, and Anton Zeilinger Citation: Physics Today 46(8), 22 (1993); doi: 10.1063/1.881360 View online: http://dx.doi.org/10.1063/1.881360 View Table of Contents: http://scitation.aip.org/content/aip/magazine/physicstoday/46/8?ver=pdfcov Published by the AIP Publishing [[[This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to ]]] IP: 129.174.21.5 On: Wed, 20 Nov 2013 16:03:31 MULTIPARIICLE INTERFEROMETRY AND THE SUPERPOSITION PRINCIPLE We're just beginning to understand the ramifications of the superposition principle at the heart of quantum mechanics. Multiparticle interference experiments can exhibit wonderful new phenomena. Daniel M. Greenberger, Michael A. Home and Anton Zeilinger Discussing the particle analog of Thomas Young's classic ing interferometry with down-conversion photon pairs. double-slit experiment, Richard Feynman wrote in 1964 Down-conversion is a process in which one ultraviolet that it "has in it the heart of quantum mechanics. In photon converts into two photons inside a nonlinear reality, it contains the only mystery."1 That mystery is crystal.4 This process allows one to construct "two-par- the one-particle superposition principle. But Feynman's ticle interferometers" that entangle the two photons in a discussion and statement have to be generalized. Super- way that needn't involve polarization at all. Many ex- position may be the only true quantum mystery, but in perimental groups independently came up with this idea, multiparticle systems the principle yields phenomena but the first explicit proposal was made by two of us.5 that are much richer and more interesting than anything Real experiments commenced when Carroll Alley and that can be seen in one-particle systems. Yan Hua Shih6 at the University of Maryland first used The famous 1935 paper by Albert Einstein, Boris down-conversion to produce an entangled state and when Podolsky and Nathan Rosen pointed out some startling Ruba Ghosh and Leonard Mandel7 at the University of features of two-particle quantum theory.2 Erwin Rochester first produced two-particle fringes without us- Schrodinger emphasized that these features are due to ing polarizers. Since these pioneering efforts, many in- the existence of what he called "entangled states," which creasingly sophisticated experiments have been per- are two-particle states that cannot be factored into prod- formed, with important lessons for quantum theory. ucts of two single-particle states in any representation. In all of these two-particle experiments, the source "Entanglement" is simply Schrodinger's name for super- of the entanglement has been down-conversion. We will position in a multiparticle system. Schrodinger was so discuss a small sampling of recent developments, with taken with the significance of multiparticle superposition particular emphasis on the fundamental ideas. Three- that he said entanglement is "not one but rather the particle interferometry is even richer, and we shall say characteristic trait of quantum mechanics." something about it. But it is mostly unexplored territory, Until the mid-1980s, the quintessential example of both experimentally and theoretically. 1 an entangled state was the singlet state of two spin- /^ One of our motivations for writing this article was particles, to make the point that one doesn't have to be a quantum optics expert to understand or analyze such experiments. They illustrate beautifully the general principles of quan- tum mechanics, and they can be understood, both quali- or its photon analog. The subscripts 1 and 2 refer to the tatively and quantitatively, in those terms. Calculations two particles (distinguished, for example, by their flight based on detailed nonlinear quantum optics Hamiltonians directions), and the plus and minus signs refer to spin do describe specific mechanisms. But they tend to ob- up or down with respect to any specified axis. This state scure the generality of the conclusions, which depend of two spatially separated particles was introduced into 3 primarily on the fact that if one cannot distinguish (even the Einstein-Podolsky-Rosen discussion by David Bohm in principle) between different paths from source to de- in 1951. It inspired a spate of experiments in the 1970s tector, the amplitudes for these alternative paths will and '80s. add coherently. Since the mid-1980s there has been a revolution in the laboratory preparation of new types of two-particle Two-particle double-slit interferometry entanglements. Various experimental groups started do- Figure 1 is a sketch of an idealized two-particle interfer- ence experiment that nonetheless exhibits some intrigu- Daniel Greenberger is a professor of physics at the City ing phenomena which have been verified experimentally. College of New York. Michael Home is a professor of Consider a particle fl near the center that can decay into physics at Stonehill College, in North Easton, Massachusetts. two daughter particles. If the original particle is essen- Anton Zeilinger is a professor of physics at the Institute for tially at rest, then the momenta of its two daughters will be approximately equal and opposite. Now imagine that Experimental Physics of the University of Innsbruck, in there are screens on both sides of the center, each with Austria. [[[This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. PHYSICS TODAY AUGUST 1993 1990 Amencon Insrirure of Physics 22 Downloaded to ]]] IP: 129.174.21.5 On: Wed, 20 Nov 2013 16:03:31 Idealized two-particle interferometer has two detecting screens (green) flanking two collimating screens, each with a pair of holes, that bracket a source (orange) of decaying particles at the center. The vertical extension of the source is d. A particle fi decays at height x above the center line into two particles (trajectories in red) that hit their respective detecting screens at heights y and z. Because one can't tell whether the pair passes through holes A and A' or B and B', these alternatives can interfere. Figure 1 two holes in it, as shown in the figure. These holes fere constructively. Note that one cannot catch such confine the escaping decay particles to either of a pair of two-particle interference patterns on film at either screen; opposite directions. The decay particles can pass either one has to record coincidences. through holes A and A' or through holes B and B'. We One may well ask how one particle could have any can then write the state of the two-particle system as knowledge of where the other can land, especially when the source position is unknown and therefore the first \f> = (1/V2")(|a>1 |a'>2 + |6>! |6'>2) particle doesn't even know where it itself will land. The answer is that by landing at a specific point, one particle where the letter in the state-vector bracket denotes the actually creates a sinusoidal amplitude of possible posi- escape direction defined by the corresponding holes. Beyond tions where the source is likely to have been—a sort of the two perforated screens are two scintillation screens that "virtual crystal." This crystal in turn creates the two- record the positions of particles landing on them. particle diffraction pattern. Virtual slit systems can be Because each of the particles can reach its detecting exploited in actual experiments.8 screen by way of two different paths, one might expect these To see how this works here, let us for simplicity screens to show interference patterns. But they don't. consider only the vertical degree of freedom .v for the That's where the two-particle interferometer differs from a source position relative to the horizontal center line in single-particle interferometer based on Young's classic dou- figure 1. And let us say that the decay particles are ble-slit experiment. There is no interfence pattern at either photons. If y and z are the corresponding vertical dis- screen in these two-particle experiments because, for rea- tances above center of the landing points P and P, sons that will become clear, the vertical position of the respectively, then the quantum mechanical amplitude for decaying particle is unknown to within some source size d landing at P is that is considerably larger than A/8, where 8 is the angle subtended by the hole pairs at the source, and A is the 2TT0 relevant wavelength—optical or de Broglie, as the case may exp{ikLa) cos —T—(y + x) be. Thus the initial position uncertainty d washes out any interference fringes. where k is 2IT IA and the L's are the alternative path lengths for the photon on the right side of the apparatus. Similarly In the single-particle case, by contrast, the geometry the amplitude for the other photon to land at P is is so determined, usually by lenses, that the source is effectively a point. Its positional uncertainty is much 2TT8 smaller than A/8, so that the waves arrive at the two I/> ~ cos —\~{z + x) holes with a definite phase relation and therefore inter- Then the total amplitude for the two photons to land at fere. The experimenter produces a diffraction pattern by controlling the geometry of the emission process. heights of x and y, respectively, above center will be In the two-particle case, something like the opposite d/2 1 f 2nd 2TT6 of this process happens. With a large source, if one looks + x) at either particle separately, one sees no interference iy,z) ~ — I ax cos —j~(y + x) cos pattern.