Gravitational dynamics in Bose Einstein condensates

TL;DR

This paper demonstrates how gravitational dynamics can emerge in Bose-Einstein condensates through a modified Poisson equation, providing insights into emergent gravity scenarios with unique short-range and cosmological features.

Contribution

It introduces a framework for describing analogue gravitational dynamics in BECs with massive quasi-particles, filling a gap in previous models.

Findings

Gravity in BECs is governed by a modified Poisson equation.

Short-range gravity characterized by the healing length.

Cosmological constant arises from non-condensed atoms.

Abstract

Analogue models for gravity intend to provide a framework where matter and gravity, as well as their intertwined dynamics, emerge from degrees of freedom that have a priori nothing to do with what we call gravity or matter. Bose Einstein condensates (BEC) are a natural example of analogue model since one can identify matter propagating on a (pseudo-Riemannian) metric with collective excitations above the condensate of atoms. However, until now, a description of the "analogue gravitational dynamics" for such model was missing. We show here that in a BEC system with massive quasi-particles, the gravitational dynamics can be encoded in a modified (semi-classical) Poisson equation. In particular, gravity is of extreme short range (characterized by the healing length) and the cosmological constant appears from the non-condensed fraction of atoms in the quasi-particle vacuum. While some of these features make the analogue gravitational dynamics of our BEC system quite different from standard Newtonian gravity, we nonetheless show that it can be used to draw some interesting lessons about "emergent gravity" scenarios.