Analog gravity from Bose-Einstein condensates

TL;DR

This paper explores how Bose-Einstein condensates can serve as analog systems to simulate aspects of general relativity by generating effective metrics and examining their behavior across different energy scales.

Contribution

It extends previous analyses by considering a general nonlinear Schrödinger equation with variable mass and nonlinearity, demonstrating the emergence of an effective metric at low momenta and Newtonian physics at high momenta.

Findings

Low-momentum excitations obey a (3+1)-D d'Alembertian with an effective metric.

High-momentum excitations follow a Bogoliubov dispersion relation.

Bose-Einstein condensates can simulate kinematic features of curved spacetime.

Abstract

We analyze prospects for the use of Bose-Einstein condensates as condensed-matter systems suitable for generating a generic ``effective metric'', and for mimicking kinematic aspects of general relativity. We extend the analysis due to Garay et al, [gr-qc/0002015, gr-qc/0005131]. Taking a long term view, we ask what the ultimate limits of such a system might be. To this end, we consider a very general version of the nonlinear Schrodinger equation (with a 3-tensor position-dependent mass and arbitrary nonlinearity). Such equations can be used for example in discussing Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We demonstrate that at low momenta linearized excitations of the phase of the condensate wavefunction obey a (3+1)-dimensional d'Alembertian equation coupling to a (3+1)-dimensional Lorentzian-signature ``effective metric'' that is generic, and depends algebraically on the background field. Thus at low momenta this system serves as an analog for the curved spacetime of general relativity. In contrast at high momenta we demonstrate how to use the eikonal approximation to extract a well-controlled Bogoliubov-like dispersion relation, and (perhaps unexpectedly) recover non-relativistic Newtonian physics at high momenta. Bose-Einstein condensates appear to be an extremely promising analog system for probing kinematic aspects of general relativity.