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Ramp-up of Hawking radiation in BEC analogue black holes

Alessandro Fabbri, Roberto Balbinot

Published May 9, 2020• 1 citation
OpenAlex

Abstract

Inspired by a recent experiment by J. Steinhauer and his group, we present a simple model which describes the formation of an acoustic black hole in a BEC, allowing an analytical computation of the evolution in time of the corresponding density-density correlator. The ramp-up of analog Hawking radiation is quantitatively studied both at T=0 and, most interestingly, even in the presence of an initial temperature T, as is always the case experimentally.

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Inspired by a recent experiment by J. Steinhauer and his group, we present a simple model which describes the formation of an acoustic black hole in a BEC, allowing an analytical computation of the evolution in time of the corresponding density-density correlator. The ramp-up of analog Hawking radiation is quantitatively studied both at T=0 and, most interestingly, even in the presence of an initial temperature T, as is always the case experimentally.
Inspired by a recent experiment by Steinhauer and co-workers, we present a simple model which describes the formation of an acoustic black hole in a Bose-Einstein condensate, allowing an analytical computation of the evolution in time of the corresponding density-density correlator. We show the emergence of analog Hawking radiation out of a "quantum atmosphere" region significantly displaced from the horizon. This is quantitatively studied both at T=0 and even in the presence of an initial temperature T, as is always the case experimentally.
We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous. We shall concentrate on the case in which an extended sonic region is present, i.e. a region where the flow velocity equals exactly the speed of sound. These models can be thought of as acoustic black holes with a thick horizon. Particular attention will be devoted to the number of created particles and to the density-density correlation functions, these latter being at present time the experimental tool to identify Hawking like radiation in acoustic black holes.
We model a sonic black-hole analog in a quasi-one-dimensional Bose-Einstein condensate, using a Gross-Pitaevskii equation matching the configuration of a recent experiment by Steinhauer [Nat. Phys. 10, 864 (2014)]. The model agrees well with important features of the experimental observations, demonstrating their hydrodynamic nature. We find that a zero-frequency bow wave is generated at the inner (white-hole) horizon, which grows in proportion to the square of the background condensate density. The relative motion of the black- and white-hole horizons produces a Doppler shift of the bow wave at the black hole, where it stimulates the emission of monochromatic Hawking radiation. The mechanism is confirmed using temporal and spatial windowed Fourier spectra of the condensate. Mean field behavior similar to that in the experiment can thus be fully explained without the presence of self-amplifying Hawking radiation.