Capillary waves at the interface of two Bose-Einstein condensates. Long wavelengths asymptotic by trial function approach

TL;DR

This paper investigates capillary wave dispersion at the interface of two Bose-Einstein condensates using a trial wave-function approach, revealing deviations from classical laws at wavelengths near the healing length, with potential experimental implications.

Contribution

It introduces a trial function method to analyze capillary waves in Bose-Einstein condensates, extending understanding beyond the long wavelength limit.

Findings

Re-derivation of the classical dispersion relation for long wavelengths.

Prediction of significant deviations from the $ extomega \,\propto \,k^{3/2}$ law at shorter wavelengths.

Potential for experimental observation of these deviations.

Abstract

The dispersion relation for capillary waves at the boundary of two different Bose condensates is investigated using a trial wave-function approach applied to the Gross-Pitaevskii (GP) equations. The surface tension is expressed by the parameters of the GP equations. In the long wave-length limit the usual dispersion relation is re-derived while for wavelengths comparable to the healing length we predict significant deviations from the $\omega\propto k^{3/2}$ law which can be experimentally observed. We approximate the wave variables by a frozen order parameter, i.e. the wave function is frozen in the superfluid analogous to the magnetic field in highly conductive space plasmas.