Analogue gravity from Bose-Einstein condensates

Abstract

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