Interferometers in Gravitational Fields

Leo Stodolsky

Michael Werner, Ali Lezeik, Dennis Schlippert +3 more

Abstract Light pulse atom interferometers (AIFs) are exquisite quantum probes of spatial inhomogeneity and gravitational curvature. Moreover, detailed measurement and calibration are necessary prerequisites for very-long-baseline atom interferometry (VLBAI). Here we provide a theoretical analysis of the phase resulting in a complex gravitational environment and introduce a novel interferometer geometry which singles out the phase shift proportional to the curvature of the gravitational potential. The scale factor depends only on well controlled quantities, namely the photon wave number, the interferometer time and the atomic recoil, which allows the curvature to be accurately inferred from a measured phase. As a case study, we numerically simulate such a gradiometric interferometer in the context of the Hannover VLBAI facility and prove the robustness of the phase shift in gravitational fields with complex spatial dependence. We define an estimator of the gravitational curvature for non-trivial gravitational fields and calculate the trade-off between signal strength and estimation accuracy with regard to spatial resolution. As a perspective, we discuss the case of a time-dependent gravitational field and corresponding measurement strategies.

Eng Boon Ng, C. H. Raymond Ooi

We consider an extremely intense laser, enclosed by an atom interferometer. The gravitational potential generated from the high-intensity laser is solved from the Einstein field equation under the Newtonian limit. We compute the strength of the gravitational force and study the feasibility of measuring the force by the atom interferometer. The intense laser field from the laser pulse can induce a phase change in the interferometer with Bose–Einstein condensates. We push up the sensitivity limit of the interferometer with Bose–Einstein condensates by spin-squeezing effect and determine the sensitivity gap for measuring the gravitational effect from intense laser by atom interferometer.

Cláus Lämmerzahl

Peter Asenbaum, Chris Overstreet

The calculation of the phase shift of a matter-wave interferometer looks different for different coordinate choices or the addition of a uniform gravitational field, but the final result of the observable phase shift does not depend on the coordinate choices or the uniform gravitational field. We find that the phase shift observed in ``Observation of the quantum equivalence principle for matter-waves'' is a magnetic recoil phase shift, similar to the recoil phase shift in light-pulse interferometers. Recoil phase shifts are inversely proportional to the inertial mass and do not depend on the gravitational mass. Our analysis highlights the difference between magnetic and gravitational acceleration in quantum mechanics.

Michael Horne