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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Gravitational and rotational effects in quantum interference

J. Anandan

Published Mar 15, 1977• 204 citations
Publisher

Abstract

The phase shift due to gravitation and rotation in the quantum interference of two coherent beams is obtained relativistically and compared with the recent experiment of Colella, Overhauser, and Werner. A general expression relating the quantum phase shift to the transverse acceleration of a classical particle in the plane of interference for an arbitrary interaction with any external field is given. This can serve as a correspondence principle between quantum physics and classical physics. The phase shift due to the coupling of spin to curvature of space-time is deduced and written explicitly for the special case of a Schwarzschild field. The last result implies that a massless spinning particle can have at most two helicity states and its world line in a gravitational field is a null geodesic. Finally, new experiments are proposed to test the effect of rotation on quantum interference and to obtain direct evidence of the equivalence principle in quantum mechanics.

DOI
10.1103/physrevd.15.1448

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The phase shift due to gravitation and rotation in the quantum interference of two coherent beams is obtained relativistically and compared with the recent experiment of Colella, Overhauser, and Werner. A general expression relating the quantum phase shift to the transverse acceleration of a classical particle in the plane of interference for an arbitrary interaction with any external field is given. This can serve as a correspondence principle between quantum physics and classical physics. The phase shift due to the coupling of spin to curvature of space-time is deduced and written explicitly for the special case of a Schwarzschild field. The last result implies that a massless spinning particle can have at most two helicity states and its world line in a gravitational field is a null geodesic. Finally, new experiments are proposed to test the effect of rotation on quantum interference and to obtain direct evidence of the equivalence principle in quantum mechanics.
Abstract In this paper, we study the phenomenon of quantum interference in the presence of external gravitational fields described by alternative theories of gravity. We analyze both non-relativistic and relativistic effects induced by the underlying curved background on a superposed quantum system. In the non-relativistic regime, it is possible to come across a gravitational counterpart of the Bohm–Aharonov effect, which results in a phase shift proportional to the derivative of the modified Newtonian potential. On the other hand, beyond the Newtonian approximation, the relativistic nature of gravity plays a crucial rôle. Indeed, the existence of a gravitational time dilation between the two arms of the interferometer causes a loss of coherence that is in principle observable in quantum interference patterns. We work in the context of generalized quadratic theories of gravity to compare their physical predictions with the analogous outcomes in general relativity. In so doing, we show that the decoherence rate strongly depends on the gravitational model under investigation, which means that this approach turns out to be a promising test bench to probe and discriminate among all the extensions of Einstein’s theory in future experiments.
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon's coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.
A very interesting quantum mechanical effect is the emergence of gravity-induced interference, which has already been detected. This effect also shows us that gravity is at the quantum level not a purely geometric effect, the mass of the employed particles appears explicitly in the interference expression. In this work we will generalize some previous results. It will be shown that the introduction of a second order approximation in the propagator of a particle, immersed in the Earth's gravitational field, and whose coordinates are being continuously monitored, allows us to include, in the corresponding complex oscillator, a frequency which now depends on the geometry of the source of the gravitational field, a fact that is absent in the case of a homogeneous field. Using this propagator we will analyze the interference pattern of two particle beams whose coordinates are being continuously monitored. We will compare our results against the case of a homogeneous field, and also against the measurement outputs of the Colella, Overhauser, and Werner experiment, and find that the difference in the dependence upon the geometry of the source of the gravitational field could render detectable differences in their respective measurement outputs. (orig.)
A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.
Using a novel approach, we work out the general relativistic effects on the quantum interference of de Broglie waves associated with thermal neutrons. The unified general formula is consistent with special relativistic results in the flat space limit. It is also shown that the exact geodesic equation contains in a natural way a gravitational analogue of the Aharonov-Bohm effect. We work out two examples, one in general relativity and the other in heterotic string theory, in order to obtain the first order gravitational correction terms to the quantum fringe shift. Measurement of these terms is closely related to the validity of the equivalence principle at a quantum level.