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American Journal of Physics

General relativistic treatment of the Colella–Overhauser–Werner experiment on neutron interference in a gravitational field

Katalin Varjú, Lewis H. Ryder

Published May 1, 2000• 14 citations
Publisher

Abstract

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.

DOI
10.1119/1.19454

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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.
The phase shift in interferometry due to the space-time curvature is computed in nonrelativistic and relativistic physics. This treatment is applied to an interferometer analogous to the perfect crystal interferometer used in the Colella-Overhauser-Werner experiment with thermal neutrons, an interferometer consisting of only horizontal mirrors, suitable for ultracold neutrons, and optical interferometry. Experiments are proposed to detect the effect of the tidal forces of the Earth, Moon, and the Sun, for the first time in interferometry. The phase shift in neutron interferometry due to terrestrial objects is considered and an experiment is proposed with superfluid helium as the source of gravity. This would provide, for the first time, direct evidence concerning the gravitational interaction between two quantum-mechanical states. The possibility of detecting purely general-relativistic effects due to curvature, by means of neutron interferometry, is also explored.
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.
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 general relativistic interaction of the electric field with the gravitational field may be observable in a charged-particle interferometer containing a suitable arrangement of fields. Observation of the effect in the earth's field would constitute a new laboratory test of the equivalence principle, involving eee, hhh, ccc, and ggg. The magnitude of the phase shift induced can be comparable to the Colella-Overhauser-Werner phase shift, for electrons.
A team of experimenters has used a neutron interferometer to observe the quantum-mechanical phase shift of neutrons caused by their interaction with the Earth's gravitational field. The experiment is one of the first (if not the first) observations of the principle of equivalence for a quantum-mechanical system. The experimenters, who reported their work in Phys. Rev. Letters on 9 June, are Roberto Colella and Albert W. Overhauser (Purdue University) and Samuel A. Werner (Ford Motor Company).