Probing spacetime fluctuations using cold atom traps

TL;DR

This paper explores how quantum fluctuations of spacetime affect the motion of a Bose-Einstein condensate in a trap, revealing an energy shift analogous to the Lamb shift, with results depending on trap geometry and atom number.

Contribution

It introduces a semiclassical framework to quantify spacetime fluctuation effects on trapped condensates and predicts specific scaling laws for the energy shift.

Findings

Energy shift scales quadratically with trap length.

Energy shift scales cubically with the number of atoms.

Spacetime fluctuations induce measurable energy shifts in BECs.

Abstract

We investigate the position oscillation of a particle that models the center of mass quantum state of a trapped Bose-Einstein condensate coupled to the zero-point fluctuations of the gravitational field. A semiclassical analysis is performed that allows to calculate the mean square amplitude of the oscillation. In analogy with the Lamb shift in quantum electrodynamics, this gives rise to an upshift of the energy of the trapped condensates. We show that for an elongated trap, the energy shift scales quadratically with the length as well as cubically with the total number of atoms.