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Physical Review Letters

New General Relativistic Effect by Means of Charged-Particle Interferometry

J. Anandan, Leo Stodolsky

Published May 30, 1983• 9 citations
Publisher

Abstract

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 $e$, $h$, $c$, and $g$. The magnitude of the phase shift induced can be comparable to the Colella-Overhauser-Werner phase shift, for electrons.

DOI
10.1103/physrevlett.50.1730

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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.
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The unification of quantum theory and the general theory of relativity, describing gravity, is one of the most important challenges in science. Einstein's general theory of relativity is based on the principle of equivalence and has been confirmed to great accuracy for large bodies. However, in the quantum domain, the equivalence principle has been predicted to take a unique form involving a gauge phase, which is equal, in the context of a measurement on Earth, to the quantum phase of a free-falling wave packet relative to its counterpart wave packet which is static in Earth's frame. To measure this phase, we realize a novel cold-atom interferometer in which one wave packet stays static in the laboratory frame while the other is in free fall. The observed relative phase of the wave packets confirms the predicted phase and shows that, in our low energy regime, the equivalence principle may be applied to the quantum domain. Our observation constitutes a fundamental test of the interface between quantum theory and gravity. The new interferometer also opens the door for further probing of the latter interface, as well as to searches for new physics.
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Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an fashion. Here, instead, we start from the multiparticle nature of quantum-delocalizable atoms in curved spacetime and generalize the special-relativistic center of mass (c.m.) and relative coordinates that have previously been studied for Minkowski spacetime to obtain the light-matter dynamics in curved spacetime. In particular, for a local Schwarzschild observer located at the surface of the Earth using Fermi-Walker coordinates, we find gravitational correction terms for the Poincaré symmetry generators and use them to derive general relativistic c.m. and relative coordinates. In these coordinates we obtain the Hamiltonian of a fully first-quantized two-particle atom interacting with the electromagnetic field in curved spacetime that naturally incorporates special and general relativistic effects.
Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an ad hoc fashion. Here, instead, we start from the multiparticle nature of quantum-delocalizable atoms in curved spacetime and generalize the special-relativistic center of mass (c.m.) and relative coordinates that have previously been studied for Minkowski spacetime to obtain the light-matter dynamics in curved spacetime. In particular, for a local Schwarzschild observer located at the surface of the Earth using Fermi-Walker coordinates, we find gravitational correction terms for the Poincaré symmetry generators and use them to derive general relativistic c.m. and relative coordinates. In these coordinates we obtain the Hamiltonian of a fully first-quantized two-particle atom interacting with the electromagnetic field in curved spacetime that naturally incorporates special and general relativistic effects.