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. Here F is the force due to the confining potential at the surface and rn 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. [S1050-2947(99)07608-8].