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arXiv:2006.09121 · Modern Physics Letters A

Black-Hole evaporation and quantum-depletion in Bose–Einstein condensates

Ivan Arraut

Published Dec 7, 2020• 7 citations
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Abstract

We study the analogy between the Hawking radiation in Black-Holes and the quantum depletion process of a Bose–Einstein condensate by using the Bogoliubov transformations method. We find that the relation between the Bogoliubov coefficients is similar in both cases (in the appropriate regimes). We then connect the condensate variables with those associated to the Black-Hole, demonstrating then that the zero temperature regime of the condensate is equivalent to the existence of an event horizon in gravity.

DOI
10.1142/s0217732321500061

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We study the analogy between the Hawking radiation in Black-Holes and the quantum depletion process of a Bose–Einstein condensate by using the Bogoliubov transformations method. We find that the relation between the Bogoliubov coefficients is similar in both cases (in the appropriate regimes). We then connect the condensate variables with those associated to the Black-Hole, demonstrating then that the zero temperature regime of the condensate is equivalent to the existence of an event horizon in gravity.
Abstract We investigate the correlation between quantum depletion and Hawking temperature in a ring-shaped Bose–Einstein condensate featuring an analog black hole-white hole horizon pair, using the Bogoliubov approach. The presence of horizons is found to enhance the quantum depletion compared to horizon-free configurations, indicating a correlation between depletion and horizon dynamics. Via tuning the Hawking temperature, we observe its effect on the depletion profile. Our results show that depletion increases with Hawking temperature, and beyond a certain threshold, backreaction effects emerge, challenging the validity of the Bogoliubov approximation. We identify a viable parameter regime where the system remains both theoretically controlled and experimentally accessible, offering insight into horizon-induced quantum fluctuations, with implications for future studies of backreaction.
We theoretically propose a finite-size quasi-one-dimensional Bose-Einstein condensate with coherent source and drain placed at its two ends, which can in principle sustain a stationary sonic black hole with a single event horizon. Our analysis is focused on the condensate persistence against quantum fluctuations. We show that similar to black hole-white hole pairs, dynamical instabilities occur. Investigating in detail the instabilities' dependence on the system parameters, we also identify windows of formally infinite black hole lifetimes. By using quantum depletion of the condensate as a diagnostic tool, we validate the usage of Bogoliubov theory to describe the analog Hawking process, and establish novel signatures of Hawking radiation in the depleted cloud, both inside and outside the event horizon.
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 propose an analogy between the quantum physics of a black hole in its late stages of the evaporation process and a superfluid Bose-Einstein condensate (BEC), based on the Horowitz and Maldacena quantum final-state projection model [J. High Energy Phys. 02 (2004), 008]. The superfluid region is considered to be analogous to the interior of a black hole, and the normal fluid/superfluid interface is compared to the event horizon of a black hole. We theoretically investigate the possibility of recovering the wave function of particles incident on a superfluid BEC from the normal fluid, facilitated by the mode conversion processes occurring at the normal fluid/superfluid BEC interface. We also study how the correlations of an infalling mode with an external memory system can be preserved in the process, similar to Hayden and Preskill's ``information mirror'' model for a black hole [J. High Energy Phys. 09 (2007), 120]. Based on these analogies, we conjecture that the quantum state of bosons entering a black hole in its final state is the superfluid quantum ground state of interacting bosons. Our analogy suggests that the wave function of bosons falling into a black hole can be recovered from the outgoing Hawking modes. In the particular case in which a holelike quasiparticle (a density dip) is incident on the superfluid BEC causing the superfluid to shrink in size, our model indicates that the evaporation is unitary.