Soliton diffusion in a Bose-Einstein condensate: A signature of the analogue Hawking radiation

Abstract

The analog Hawking radiation (HR) emanating from a sonic black hole horizon formed in a cigar-shaped Bose-Einstein condensate (BEC) at finite temperature is investigated. In particular, we study the effect of HR on a dark (topological) soliton. We show that, due to thermal fluctuations, the dark soliton in the BEC displays a nonlinear Brownian motion resulting in a specific asymmetric diffusion. Based on numerical simulations we argue that the analog HR formed in the BEC can be detected indirectly through measurement of the dark soliton diffusion. Keywords: Analog Hawking radiation, Solitons, Bose-Einstein condensation