Abstract
From both a theoretical and an experimental point of view, Bose–Einstein condensates are good candidates for studying gravitational analogues of black holes and black-hole lasers. In particular, a recent experiment has shown that a black-hole laser configuration can be created in the laboratory. However, the most considered theoretical models for analog black-hole lasers are quite difficult to implement experimentally. In order to fill this gap, we devote this work to present more realistic models for black-hole lasers. For that purpose, we first prove that, by symmetrically extending every black-hole configuration, one can obtain a black-hole laser configuration with an arbitrarily large supersonic region. Based on this result, we propose the use of an attractive square well and a double delta-barrier, which can be implemented using standard experimental tools, for studying black-hole lasers. We also compute the different stationary states of these setups, identifying the true ground state of the system and discussing the relation between the obtained solutions and the appearance of dynamical instabilities.
Highlights
Hawking radiation is one of the most intriguing results of theoretical physics; using a semiclassical model in which fields are quantized on top of a classical gravitational background, Hawking predicted the spontaneous emission of radiation by the event horizon of a black hole (BH) [1,2]
An alternative way to study these effects was suggested by Unruh [4], who proved that a subsonic-supersonic interface in a quantum fluid is the acoustic analog of an event horizon in a BH
We have proposed two new black-hole laser configurations based on the waterfall and the delta-barrier configurations usually considered for studying analog black holes
Summary
Hawking radiation is one of the most intriguing results of theoretical physics; using a semiclassical model in which fields are quantized on top of a classical gravitational background, Hawking predicted the spontaneous emission of radiation by the event horizon of a black hole (BH) [1,2]. Most of the theoretical works present in the BEC analog literature deal with an extremely idealized model, the so-called flat-profile configuration, in which the background condensate is homogeneous and the horizons are created through a very specific spatial dependence of the coupling constant and the external potential. This simple model is able to capture the essential features of Hawking radiation, it is quite unrealistic from an experimental point of view. Appendix A is devoted to introducing the different elliptic functions used in this work, while Appendices B and C are devoted to the technical details of the calculations presented in the main text
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