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

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.

Many-body dark solitons in one-dimensional hard-core Bose gases

“…We start from the analytic, stationary solution of the quintic GPE representing a dark soliton in the comoving frame (i.e., the reference frame at rest with the soliton, while the fluid velocity is fixed at infinity) which reads [26,29]:…”

“…In the case of a TG gas, it corresponds to a symmetry breaking eigenstate of the free Fermi gas. A hint towards the identification of such a many-body state comes from the observation that a half soliton [30] of the (cubic or quintic) GPE is precisely a steady state solution of a Bose gas in an external step potential of height V 0 [29]. The particular half soliton wavefunction has the unique feature of displaying a flat density profile beyond the step and requires a well-defined relation between the step height V 0 and the asymptotic density n ∞ :…”

On the role of interactions in trans-sonically flowing atomic condensates

“…In particular, ground-breaking experimental results were reported in effectively one-dimensional flowing atomic Bose-Einstein condensates by J. Steinhauer at Technion [5][6][7][8]. These pioneering experiments have stimulated a number of refined theoretical and numerical studies to fully understand the physics at play there [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”