Abstract
We study the evolution of an initially confined atom condensate, which is progressively outcoupled by gradually lowering the confining barrier on one side. The goal is to identify protocols that best lead to a quasi-stationary sonic black hole separating regions of subsonic and supersonic flow. An optical lattice is found to be more efficient than a single barrier in yielding a long-time stationary flow. This is best achieved if the final conduction band is broad and its minimum is not much lower than the initial chemical potential. An optical lattice with a realistic Gaussian envelope yields similar results. We analytically prove and numerically check that, within a spatially coarse-grained description, the sonic horizon is bound to lie right at the envelope maximum. We derive an analytical formula for the Hawking temperature in that setup.
Highlights
An attractive feature of Bose-Einstein condensates is that of providing a convenient way of investigating analog black-hole physics in the laboratory [1, 2]
Within a mean-field description, we have investigated the process whereby an initially confined atom condensate is coherently outcoupled as the barrier on one side is gradually lowered
The goal has been to identify the barrier-lowering protocol which best leads to a quasistationary sonic black hole located at the interface between subsonic and supersonic flow
Summary
An attractive feature of Bose-Einstein condensates is that of providing a convenient way of investigating analog black-hole physics in the laboratory [1, 2]. An alternative route towards the detection of Hawking radiation may be provided by a quasi-stationary horizon, which in principle can be achieved by allowing a large confined condensate to emit in such a way that the coherent outgoing beam is dilute and fast enough to be supersonic [11, 14,15,16]. We focus on a finite-sized condensate and on the case where the increasingly transparent potential is formed not by a single [16] or double [15] barrier, but by an extended optical lattice, the main reason being that the latter scenario seems more suitable for the achievement of quasi-stationary flow within this deconfinement scheme, as will be shown later. Appendix D describes the numerical method of integration and the use of absorbing boundary conditions
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