Black-hole lasers in Bose-Einstein condensates
Résumé
We consider elongated condensates that cross twice the speed of sound. In the absence of periodic boundary conditions, the phonon spectrum possesses a discrete and finite set of complex frequency modes which induce a laser effect. This effect is due, on one hand, to the anomalous dispersion of the phonons and, on the other hand, to the supersonic region which acts as a resonant cavity. We numerically compute the complex frequencies and density-density correlation function. We obtain patterns with very specific signatures. In terms of the gravitational analogy, the flows we consider correspond to a pair of black hole and white hole horizons, and the laser effect can be conceived as a self-amplified Hawking radiation. This is verified by comparing the outgoing flux at early time with the standard black hole radiation.