Ramsey fringes in atomic interferometry: measurability of the influence of space-time curvature

TL;DR

This paper investigates the potential of atomic interferometry, specifically Ramsey interferometers, to measure the effects of Earth's space-time curvature on quantum matter, combining general relativity and quantum mechanics.

Contribution

It derives relativistic correction terms for the Pauli equation from the covariant Dirac equation and assesses the feasibility of detecting space-time curvature effects with existing atomic interferometers.

Findings

Detection of space-time curvature effects is feasible with minor modifications.

Relativistic corrections to quantum equations are derived and physically interpreted.

Sensitivity to gravitational effects can be enhanced in laboratory experiments.

Abstract

The influence od space-time curvature on quantum matter which can be theoretically described by covariant wave equations has not been experimentally established yet. In this paper we analyse in detail the suitability of the Ramsey atom beam interferometer for the measurement of the phase shift caused by the Riemannian curvature of the earth. It appears that the detection should be possible with minor modifications of existing devices within the near future. The paper is divided into two parts. The first one is concerned with the derivation of general relativistic correction terms to the Pauli equation starting from the fully covariant Dirac equation and their physical interpretation. The inertial effects of acceleration and rotation are included. In the second part we calculate the phase shift as seen in a laboratory resting on the rotating earth and examine various possibilities to enlarge the sensitivity of the apparatus to space-time curvature. Some remarks on the Lense-Thirring effect and on gravitational waves are made. Since the two parts may be more or less interesting for physicists with different research fields they are written in such a way that each one may be read without much reference to the other one.