Surface of a Bose-Einstein condensed atomic cloud

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 wave number q related by ${\omega }^2=Fq/m.\mathrm{}$ 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 $q^4\ln q.\mathrm{}$ We demonstrate the usefulness of the concept of an effective surface tension for describing both static and dynamic properties of condensed atomic clouds.