Modified uncertainty principle from the free expansion of a Bose-Einstein Condensate

TL;DR

This paper investigates how a deformed energy spectrum due to quantum spacetime structure affects the free expansion of a Bose-Einstein condensate, leading to a modified uncertainty principle relevant at low energies.

Contribution

It introduces a theoretical and numerical framework to analyze the impact of quantum spacetime deformation on BEC expansion and the resulting uncertainty principle modifications.

Findings

Modified free velocity expansion due to quantum spacetime effects

Altered uncertainty principle at low energies

Potential experimental signatures at earth-based labs

Abstract

In this paper, we present a theoretical and numerical analysis of the free expansion of a Bose-Einstein condensate, where we assume that the single particle energy spectrum is deformed due to a possible quantum structure of spacetime. Also, we consider the presence of interparticle interactions in order to study more realistic and specific scenarios. The modified free velocity expansion of the condensate leads in a natural way to a modification of the uncertainty principle, which allows us to investigate some possible features of the Planck scale regime in low-energy earth-based experiments.