Abstract
We investigate the formation dynamics of sonic horizons in a Bose gas confined in a (quasi) one-dimensional trap. This system is one of the most promising realizations of the analogue gravity paradigm and has already been successfully studied experimentally. Taking advantage of the exact solution of the one-dimensional, hard-core, Bose model (Tonks–Girardeau gas), we show that by switching on a step potential, either a sonic, black-hole-like horizon or a black/white hole pair may form, according to the initial velocity of the fluid. Our simulations never suggest the formation of an isolated white-hole horizon, although a stable stationary solution of the dynamical equations with those properties is analytically found. Moreover, we show that the semiclassical dynamics, based on the Gross–Pitaevskii equation, conforms to the exact solution only in the case of fully subsonic flows while a stationary solution exhibiting a supersonic transition is never reached dynamically.
Highlights
Analogue models of gravity are useful tools bridging gravitation to other branches of physics and they have been intensively investigated since their proposal [1] in order to study effects whose experimental achievement is hardly possible in the cosmological context
A great scientific effort was dedicated to the observation and characterization of the Hawking effect [2,3] but several different phenomena can be investigated within the analogue gravity paradigm [4]
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
Summary
Analogue models of gravity are useful tools bridging gravitation to other branches of physics and they have been intensively investigated since their proposal [1] in order to study effects whose experimental achievement is hardly possible in the cosmological context. 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] These experiments represent a remarkable achievement and they have stimulated a variety of theoretical studies on sonic black holes in 1D BECs. One feature, though, which has not been deeply investigated in these kind of configurations is the formation dynamics of an analogue black/white hole; this may be due to the fact that analogue models can hope to reproduce only the kinematical aspects of the gravitational phenomena, as the analogy breaks down for the dynamical properties. Black-hole configuration as a tool to study the Hawking effect
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