Bogoliubov space of a Bose--Einstein condensate and quantum spacetime fluctuations

TL;DR

This paper explores how metric fluctuations influence Bose--Einstein condensates, proposing two experimental methods to measure the average size of these quantum spacetime fluctuations via properties like pressure and sound speed.

Contribution

It introduces a novel approach linking quantum spacetime fluctuations to measurable properties of Bose--Einstein condensates, providing two independent experimental methods.

Findings

Pressure and sound speed define an expression to determine fluctuation size

Interferometric experiments can measure fluctuations independently

Theoretical connection between metric fluctuations and condensate properties

Abstract

In the present work we consider the role that metric fluctuations could have upon the properties of a Bose--Einstein condensate. In particular we consider the Bogoliubov space associated to it and show that there are, at least, two independent ways in which the average size of these metric fluctuations could be, experimentally, determined. Indeed, we prove that the pressure and the speed of sound of the ground state define an expression allowing us to determine the average size of these fluctuations. Afterwards, an interferometric experiment involving Bogoliubov excitations of the condensate and the pressure (or the speed of sound of the ground state) provides a second and independent way in which this average size could be determined, experimentally.