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

TL;DR

This paper investigates wave patterns generated by a supersonic object moving through a two-component Bose-Einstein condensate, revealing complex structures like Mach cones, ship waves, and dark solitons, supported by analytical and numerical methods.

Contribution

It develops an analytical theory for wave patterns in a two-component BEC and explores the stability of dark solitons under supersonic flow conditions.

Findings

Wave patterns form three regions separated by Mach cones.

Dark solitons inside the wider Mach cone can be stabilized by high flow velocity.

Analytical results are confirmed by numerical simulations.

Abstract

Generation of wave structures by a two-dimensional object (laser beam) moving in a two-dimensional two-component Bose-Einstein condensate with a velocity greater than both 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.