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arXiv:0811.1891 · Physical Review A

Wave patterns generated by a supersonic moving body in a binary Bose-Einstein condensate

Yu. G. Gladush, A. M. Kamchatnov, Zhiwei Shi, P. G. Kevrekidis, D. J. Frantzeskakis, Boris A. Malomed

Published Mar 23, 2009• 52 citations

Abstract

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.

DOI: 10.1103/physreva.79.033623

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The stability of dark solitons generated by supersonic flow of a Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to the decay of disturbances of solitons at a fixed distance from the obstacle and the formation of effectively stable dark solitons. This phenomenon explains the surprising stability of the flow picture that has been observed in numerical simulations.

This paper suggests a method to create dark soliton-like waves in a trapped atomic Bose-Einstein condensate (BEC). With the phase imprinting method, a solitonlike disturbance is produced along the x-axis. The method is used in two cases (with and without rotation of a trapping potential). The disturbance in a two-dimensional (2D) system is unstable. The soliton-like perturbation is found to decay into more stable vortex pairs together with a burst of sound wave. The simulations are performed by solving the 2D Gross-Pitaevskii equation (2D GPE). The successive dynamics of the wave function are studied by monitoring the evolution of density and phase profile.