Mechanisms of stimulated Hawking radiation in laboratory Bose-Einstein condensates

We simulate and reproduce the results of a recent experiment \footnote{J. Steinhauer, {\em Nat. Phys.} {\bf 10}, 864 (2014)} that reported observations of a sonic analog black hole laser \footnote{S. Corley and T. Jacobson, {\em Phys. Rev. D} {\bf 59}, 124011 (1999)} in a Bose-Einstein condensate (BEC). In the experiment, a time-swept step potential was applied to a trapped cigar-shaped BEC of $^{87}$Rb, thereby creating white hole (WH) and black hole (BH) event horizons. Exponential growth of a density wave in the WH--BH cavity and the emission of Hawking radiation were observed. We show that the solution of the time-dependent Gross-Pitaevskii equation gives good agreement with the experiment with no adjustable parameters. The Hawking radiation in this experiment is not self-amplifying, but is stimulated by a growing Bogoliubov-\v{C}erenkov mode \footnote{I. Carusotto, S. X. Hu, L. A. Collins and A. Smerzi, {\em Phys. Rev. Lett.} {\bf 97}, 260403 (2006)} that is generated at the WH event horizon. We use scaling arguments to identify a class of feasible experiments that can provide more distinctive signatures of Hawking radiation and of the dominant Bogoliubov-\v{C}erenkov mode that stimulates it.