Probing semiclassical analog gravity in Bose-Einstein condensates with widely tunable interactions

Bose-Einstein condensates (BEC’s) have recently been the subject of considerable study as possible analog models of general relativity. In particular it was shown that the propagation of phase perturbations in a BEC can, under certain conditions, closely mimic the dynamics of scalar quantum fields in curved space-times. In two previous papers [Int. J. Mod. Phys. A 18, 3735 (2003); Int. J. Mod. Phys. D (to be published), e-print gr-qc/0305061] we noted that a varying scattering length in the BEC corresponds to a varying speed of light in the “effective metric.” Recent experiments have indeed achieved a controlled tuning of the scattering length in ⁸⁵Rb. In this paper we shall discuss the prospects for the use of this particular experimental effect to test some of the predictions of semiclassical quantum gravity, for instance, particle production in an expanding universe. We stress that these effects are generally much larger than the Hawking radiation expected from causal horizons, and so there are much better chances for their detection in the near future.