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

Several theorems about the interference of particle beams and the theoretical interpretation of Collela-Overhauser-Werner and Marton experiments

Pei Yu Zhu, Zhong Jun Shen, You Shi Wu

Published Jul 15, 1985• 3 citations
Publisher

Abstract

A new theorem about the interference between particle beams is established. The Collela-Overhauser-Werner and Marton experiments are theoretically explained with a theorem established by Chiu and Stodolsky. The Feynman theory is applied to obtaining the propagator for a particle beam in a gravitational field, and the Collela-Overhauser-Werner experiment is further analyzed. Another theorem, established by Chiu and Stodolsky, and our new theorem are proved with the method of Feynman's path integrals.

DOI
10.1103/physrevd.32.368

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A new theorem about the interference between particle beams is established. The Collela-Overhauser-Werner and Marton experiments are theoretically explained with a theorem established by Chiu and Stodolsky. The Feynman theory is applied to obtaining the propagator for a particle beam in a gravitational field, and the Collela-Overhauser-Werner experiment is further analyzed. Another theorem, established by Chiu and Stodolsky, and our new theorem are proved with the method of Feynman's path integrals.
In the Colella–Overhauser–Werner (COW) experiment a gravity-induced phase shift of spin 1/2 particles was detected. The experimental results were explained by using the Newtonian theory of gravity. The explanation can be easily given using general relativistic arguments and the highest order term reproduces the result of Colella, Overhauser, and Werner together with additional, lower order corrections. The derivation can be considered as an interesting exercise for students with basic knowledge of the field of general relativity.
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.)
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.
Compared to classical optical coherence theory based on Maxwell's electromagnetic theory and Glauber's quantum optical coherence theory based on matrix mechanics formulation of quantum mechanics, quantum optical coherence theory based on Feynman's path integral formulation of quantum mechanics provides a novel tool to study optical coherence. It has the advantage of understanding the connection between mathematical calculations and physical interpretations better. Quantum optical coherence theory based on Feynman's path integral is introduced and reviewed in this paper. Based on the results of transient first-order interference of two independent light beams, it is predicted that the classical model for electric field of thermal light introduced by classical optical textbooks may not be accurate. The physics of two-photon bunching of thermal light and Hong-Ou-Mandel dip of entangled photon pairs is the same, which can be interpreted by constructive and destructive two-photon interference, respectively. Quantum optical coherence theory based on Feynman's path integral is helpful to understand the coherence properties of light, which may eventually lead us to the answer of the question: what is a photon?
In this article we hold on an analytic solution of the well-known cases of difraction and interference of electrons through one and two slits (simply that, the one-dimensional case is assumed only). In addition, we hold an approximations of the electron distribution which offer the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could also serve an awesome introduction to multiple slits interference. Then it is comparing between theoretical results and simulation in order to get interference pattern of it.