Black hole radiation in Bose-Einstein condensates
Résumé
We study the phonon fluxes emitted when the condensate velocity crosses the speed of sound, i.e., in backgrounds which are analogue to that of a black hole. We focus on elongated one dimensional condensates, and on stationary flows. Our theoretical analysis and numerical results are based on the Bogoliubov-de-Gennes equation without any further approximation. The spectral properties of the fluxes and of the long distance density-density correlations are obtained, with and without an initial temperature. In realistic conditions, we show that the condensate temperature dominates the fluxes, and thus hides the presence of the spontaneous emission (the Hawking effect). We also explain why the temperature amplifies the long distance correlations which are intrinsic to this effect. This confirms that the correlations pattern offers a neat signature of the Hawking effect. Optimal conditions to observe the pattern are discussed.