Witnessing mass-energy equivalence with trapped atom interferometers

TL;DR

This paper proposes an experimental setup using advanced atom interferometers to observe the effects of mass-energy equivalence on quantum superpositions in Earth's gravitational field, potentially detectable with current technology.

Contribution

It introduces a novel method to incorporate relativistic effects into atom interferometry and suggests a feasible experiment to observe superpositions of proper time.

Findings

Relativistic corrections to Bloch oscillations are developed.

Trajectories and phases in the interferometer are derived.

Observable interference pattern shifts due to superposition of proper times.

Abstract

We propose an experimental setup to probe the interplay between the quantum superposition principle and gravitational time dilation arising from the mass-energy equivalence. It capitalizes on state-of-the-art atom interferometers that can keep atoms trapped in a superposition of heights in Earth's gravitational field for exceedingly long times, reaching the minute scale. Our proposal consists of adding two additional laser pulses to the existing experiments that would set up a clock trapped at a superposition of heights, reading a quantum superposition of relativistic proper times. We develop a method to include relativistic corrections to Bloch oscillations, which describe the trapped part of the interferometer. We derive the trajectories and corresponding phases acquired in each arm of the interferometer. We then show that a superposition of proper times manifests in the interference pattern in two ways: visibility modulations and a shift of the atom's resonant frequency. We argue that the latter might be observable with current technology.