Collective Excitations in Quasi-2D and 3D Condensates

Collective motion of a Bose-Einstein condensate has been a system of interest since the discovery of BEC. Boltzmann proved that the monopole mode of a thermal gas in an isotropic, harmonic and 3D trap is undamped [1, 2]. BECs are not classical gases and their weakly interacting nature causes damping in a 3D monopole mode. However, experimental limitations have precluded studies of this behavior in very spherical traps. Quantum gases confined to lower dimensions exhibit remarkable physical properties such as the Berezkinskii-Kosterlitz-Thouless transition or the Tonks-Girardeau gas. Confinement effects in a quasi-2D condensate are predicted to shift the frequency of the monopole mode [3]. One correction in particular connects a small frequency shift with certain quantum corrections [4]. Current results of our studies in 2D and 3D will be presented. \\[4pt] [1] ``Transverse Breathing Mode of an Elongated Bose-Einstein Condensate,'' F. Chevy, V. Bretin, P. Rosenbusch, K. W. Madison, and J. Dalibard, Phys. Rev. Lett. 88 250402 (2002). \\[0pt] [2] L. Boltzmann, Wissenschaftliche Abhandlungen, edited by F. Hasenorl (Barth, Leipzig, 1909), Vol. II \\[0pt] [3] Olshanii et al., Phys. Rev. Lett. 105, 095302 (2010) \\[0pt] [4] Hu, et al., Phys. Rev. Lett. 107, 110401 (2011)