Flow of a Bose-Einstein condensate in a quasi-one-dimensional channel under the action of a piston
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AL, NONLINEAR, AND SOFT MATTER PHYSICS
Flow of a Bose–Einstein Condensate in a QuasiOneDimensional Channel under the Action of a Piston A. M. Kamchatnov and S. V. Korneev* Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow oblast, 142190 Russia *email: [email protected] Received September 1, 2009
Abstract—The problem of the flow of a Bose–Einstein condensate in a channel under the action of a piston is considered. Problems of this kind are topical in connection with experiments on condensate flow control in quasionedimensional (cigarshaped) traps, in which the repulsive potential produced by a laser beam focused across the trap acts as a piston. A dispersive shock wave characterized by rapid oscillations of the con densate density and flow velocity is shown to be formed in the condensate flow after some instant of time for an arbitrary law of piston motion. The Whitham averaging method is used to obtain a solution for the main parameters of the dispersive shock wave in the case of a uniformly accelerated piston motion. The evolution of the dispersive shock wave immediately after the breaking time, when the dispersionless solution is well approximated by a cubic parabola for the coordinate dependence of the density, is analyzed in the case of an arbitrary piston motion. Comparison shows good agreement of the numerical calculation with the approxi mate analytical theory. The developed theory complements the previously considered case of a piston moving with a constant velocity and is important for describing the condensate transport in atomic chips. DOI: 10.1134/S1063776110010206
1. INTRODUCTION The dynamics of a Bose–Einstein condensate has attracted great attention since its experimental detec tion. Initially, the problems of the oscillations of the condensate as whole [1–3] or of the condensate flow from a switchedoff trap [4–8] were studied. Subse quently, much effort was expended on the formation and dynamics of vortices [9, 10] and the generation of acoustic waves [11] and solitons [12–14]. At present, one of the topical problems in the Bose–Einstein con densate dynamics is the formation of dispersive shock waves during the evolution of large condensate pertur bations. Such waves were first detected experimentally upon the action of a relatively intense laser beam on a cylindrically symmetric condensate, when the beam propagating along the condensate axis transferred momentum to it in the radial direction. As a result, the wave propagating away from the condensate axis broke to form a cylindrically symmetric wave structure [15] that was interpreted in [16] as a dispersive shock wave. A similar process of a onedimensional condensate flow was considered in [17], while the analytical the ory developed on the basis of selfsimilar solutions to the nonlinear Schrödinger equation [18, 19] was com pared with experimental data and qualitative agree ment was found in [15]. Dispersive shock waves of a different type were detected during supersonic condensate flows past an
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