Analogue Hawking radiation in an exactly solvable model of BEC

Abstract

Hawking radiation, the spontaneous emission of thermal photons from an event horizon, is one of the most intriguing and elusive predictions of field theory in curved spacetimes. A formally analogue phenomenon occurs at the supersonic transition of a fluid: in this respect, ultracold gases stand out among the most promising systems but the theoretical modelling of this effect has always been carried out in semiclassical approximation, borrowing part of the analysis from the gravitational analogy. Here we discuss the exact solution of a onedimensional Bose gas flowing against an obstacle, showing that spontaneous phonon emission (the analogue of Hawking radiation) is predicted without reference to the gravitational analogy. Long after the creation of the obstacle, the fluid settles into a stationary state displaying the emission of sound waves (phonons) in the upstream direction. A careful analysis shows that a precise correspondence between this phenomenon and the spontaneous emission of radiation from an event horizon requires additional conditions to be met in future experiments aimed at identifying the occurrence of the Hawking-like mechanism in Bose-Einstein condensates.1 arXiv:1703.05041v3 [cond-mat.quant-gas]

Formation Dynamics of Black- and White-Hole Horizons in an Analogue Gravity Model

“…Remarkably, a sharp external potential does not seem to suppress the Hawking effect: in the steady state a phonon flux may indeed be present but it is not described by a thermal distribution and therefore it cannot be associated with a well-defined Hawking temperature. We stress that these results have been obtained [26,27] for the Tonks-Girardeau gas in one dimension, where the occurrence of thermalization after a quantum quench is hampered by the integrability of the model [34]. On the other hand, at variance with the case of a potential barrier, an extremely smooth potential step does not lead to the formation of a sonic horizon, making such a configuration unsuitable for the investigation of the Hawking effect [26,27].…”

“…The analytical and numerical studies of Ref. [26,27] proved that a precise correspondence between the physics of the analogue model and that of the Hawking effect can be obtained only when the TG gas flows against an extremely smooth potential barrier. The rationale for this result is that the identification of the quasiparticles (phonons) as a free quantum field is possible only for very low excitation energies and (almost) homogeneous states.…”

“…The Tonks-Girardeau gas model has been recently studied in the framework of analogue gravity [26,27] because it allows describing, from a microscopic point of view, the dynamics of formation of a sonic horizon and to investigate the physical conditions leading to the expected Hawking-like phonon flux emerging from the horizon. The analytical and numerical studies of Ref.…”

“…In particular, the physics of sonic horizons [5] has been vastly studied, both from a theoretical and an experimental point of view and analogue black-hole and white-hole horizons have been experimentally achieved in optics [6][7][8], in Bose-Einstein condensates (BECs) [9][10][11][12][13], in water [14][15][16][17][18], in superfluid Helium [19], and in a few other setups. In the context of BECs, a few recent experiments [10][11][12][13] successfully recreated sonic horizons in order to probe the elusive Hawking radiation but the results are still under debate in the scientific community [20][21][22][23][24][25][26][27][28]. Nonetheless, these experiments represent a remarkable achievement and they have stimulated a variety of theoretical studies on sonic black holes in 1D BECs.…”

“…In this work we will study the dynamics of formation of a sonic horizon for a simple, realistic model of BEC which mimics existing experimental configurations [9][10][11][12][13]. In particular, we will exploit a recently proposed exact model [26,27] in order to study the dynamics of the analogue of a gravitational collapse in the absence of external confining traps and to investigate whether the system only forms black-hole-like horizons or if a dynamical process could, in principle, lead to a formation of a white-hole horizon too. Furthermore, we will compare the results with those obtained with a semiclassical approach-commonly adopted in the theoretical interpretations of the experiments-in order to highlight possible inadequacies of the semiclassical paradigm.…”