Analogue gravity from BoseEinstein condensates
Abstract
We analyse prospects for the use of BoseEinstein condensates as condensedmatter 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 (2000 Phys. Rev. Lett. 85 4643, 2001 Phys. Rev. A 63 023611). Taking a longterm 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 Schrödinger equation (with a 3tensor positiondependent mass and arbitrary nonlinearity). Such equations can be used, for example, in discussing BoseEinstein 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 Lorentziansignature `effective metric' that is generic, and depends algebraically on the background field. Thus at low momenta this system serves as an analogue for the curved spacetime of general relativity. In contrast, at high momenta we demonstrate how one can use the eikonal approximation to extract a well controlled Bogoliubovlike dispersion relation, and (perhaps unexpectedly) recover nonrelativistic Newtonian physics at high momenta. BoseEinstein condensates appear to be an extremely promising analogue system for probing kinematic aspects of general relativity.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 March 2001
 DOI:
 10.1088/02649381/18/6/312
 arXiv:
 arXiv:grqc/0011026
 Bibcode:
 2001CQGra..18.1137B
 Keywords:

 General Relativity and Quantum Cosmology;
 Condensed Matter
 EPrint:
 revtex 4 (beta 4)