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Journal of Physics B Atomic Molecular and Optical Physics

Generation of Cherenkov waves in the flow of a Bose–Einstein condensate past an obstacle

Yu. G. Gladush, Lev A. Smirnov, A. M. Kamchatnov

Published Aug 7, 2008• 25 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/41/16/165301

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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.
We investigate by numerical simulations the pattern formation after an oscillating attractive-repulsive obstacle inserted into the flow of a Bose-Einstein condensate. For slow oscillations we observe a complex emission of vortex dipoles. For moderate oscillations organized lined up vortex dipoles are emitted. For high frequencies no dipoles are observed but only lined up dark fragments. The results shows that the drag force turns negative for sufficiently high frequency. We also successfully model the ship waves in front of the obstacle. In the limit of very fast oscillations all the excitations of the system tend to vanish.