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arXiv:cond-mat/0611149 · Physical Review A

Radiation of linear waves in the stationary flow of a Bose-Einstein condensate past an obstacle

Yu. G. Gladush, Gennady A. El, A. Gammal, A. M. Kamchatnov

Published Mar 28, 2007• 49 citations
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Abstract

Using stationary solutions of the linearized two-dimensional Gross-Pitaevskii equation, we describe the wave pattern occurring in the supersonic flow of a Bose-Einstein condensate past an obstacle. It is shown that these waves are generated outside the Mach cone. The developed analytical theory is confirmed by numerical simulations of the flow past body problem in the frame of the full nonstationary Gross-Pitaevskii equation. Relation of the developed theory with recent experiments is discussed.

DOI
10.1103/physreva.75.033619

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Using stationary solutions of the linearized two-dimensional Gross-Pitaevskii equation, we describe the wave pattern occurring in the supersonic flow of a Bose-Einstein condensate past an obstacle. It is shown that these waves are generated outside the Mach cone. The developed analytical theory is confirmed by numerical simulations of the flow past body problem in the frame of the full nonstationary Gross-Pitaevskii equation. Relation of the developed theory with recent experiments is discussed.
The theory of stationary linear wave patterns generated in a supersonic flow of a Bose–Einstein condensate past a point-like obstacle is developed. It is shown that they are located mainly outside the Mach cone corresponding to infinitely long wavelengths. The shape of wave crests and dependence of amplitude on coordinates far enough from the obstacle are calculated. The results are in good agreement with the results of numerical simulations. The theory gives a qualitative description of experiments with Bose–Einstein condensate flow past an obstacle after the condensate's release from a trap.
Generation of wave structures by a two-dimensional (2D) object (laser beam) moving in a 2D two-component Bose-Einstein condensate with a velocity greater than the two sound velocities of the mixture is studied by means of analytical methods and systematic simulations of the coupled Gross-Pitaevskii equations. The wave pattern features three regions separated by two Mach cones. Two branches of linear patterns similar to the so-called ``ship waves'' are located outside the corresponding Mach cones, and oblique dark solitons are found inside the wider cone. An analytical theory is developed for the linear patterns. A particular dark-soliton solution is also obtained, its stability is investigated, and two unstable modes of transverse perturbations are identified. It is shown that for a sufficiently large flow velocity, this instability has a convective character in the reference frame attached to the moving body, which makes the dark soliton effectively stable. The analytical findings are corroborated by numerical simulations.