Stationary waves in a supersonic flow of a two-component Bose gas

TL;DR

This paper investigates stationary wave patterns in a two-component Bose-Einstein condensate flowing past an obstacle, analyzing how velocities and interactions influence wave formation and interference, with implications for superfluidity and excitation spectra.

Contribution

It provides a detailed analysis of stationary waves in a two-component BEC considering unequal velocities and identifies conditions for wave emergence and interference patterns.

Findings

Stationary waves depend on the relative velocities of components.

Multiple wave sets can coexist and interfere under certain velocity configurations.

Density oscillations are out-of-phase between components in interference cases.

Abstract

A stationary wave pattern occurring in a flow of a two-component Bose-Einstein condensate past an obstacle is studied. We consider the general case of unequal velocities of two superfluid components. The Landau criterium applied to the two-component system determines a certain region in the velocity space in which superfluidity may take place. Stationary waves arise out of this region, but under the additional condition that the relative velocity of the components does not exceed some critical value. Under increase of the relative velocity the spectrum of the excitations becomes complex valued and the stationary wave pattern is broken. In case of equal velocities two sets of stationary waves that correspond to the lower and the upper Bogolyubov mode can arise. If one component flows and the other is at rest only one set of waves may emerge. Two or even three interfere sets of waves may arise if the velocities approximately of equal value and the angle between the velocities is close to pi/2. In two latter cases the stationary waves correspond to the lower mode and the densities of the components oscillate out-of-phase. The ratio of amplitudes of the components in the stationary waves is computed. This quantity depends on the relative velocity, is different for different sets of waves, and varies along the crests of the waves. For the cases where two or three waves interfere the density images are obtained.