The Surface of a Bose-Einstein Condensed Atomic Cloud

TL;DR

This paper studies the surface structure and collective excitations of a trapped Bose-Einstein condensate at zero temperature, revealing wave behaviors analogous to fluid surfaces and introducing an effective surface tension concept.

Contribution

It provides a theoretical analysis of surface modes in Bose-Einstein condensates, including long-wavelength gravity-like waves and short-wavelength corrections, using variational methods.

Findings

Identified a gravity wave-like mode on the condensate surface with a specific dispersion relation.

Derived corrections to surface mode frequencies at shorter wavelengths involving logarithmic terms.

Demonstrated the relevance of an effective surface tension in describing condensate surface properties.

Abstract

We investigate the structure and collective modes of a planar surface of a trapped Bose-Einstein condensed gas at zero temperature. In the long-wavelength limit we find a mode similar to the gravity wave on the surface of a fluid with the frequency $\omega$ and the wavenumber $q$ related by $\omega^2=Fq/m$. Here $F$ is the force due to the confining potential at the surface and $m$ is the particle mass. At shorter wavelengths we use a variational approach and find corrections to $\omega^2$ of order $q^4 \ln{q}$. We demonstrate the usefulness of the concept of an effective surface tension for describing both static and dynamic properties of condensed atomic clouds.