TRAPPED ONE-DIMENSIONAL BOSE GAS AS A LUTTINGER LIQUID

Physikalisches Institut, Universit¨at Bonn,Nusallee 12,D-53115 Bonn,Germany(February 1, 2008)The low-energy fluctuations of a trapped, interacting quasi one-dimensional Bose gas are studied.Our considerations apply to experiments with highly anisotropic traps. We show that under suitableexperimental conditions the system can be described as a Luttinger liquid. This implies that thecorrelation function of the bosons decays algebraically preventing Bose-Einstein condensation. Atsignificantly lower temperatures a finite size gap destroys the Luttinger liquid picture and Bose-Einstein condensation is again possible.PACS: 03.75.Fi, 05.30.jp, 32.80.Pj, 67.90.+z, 71.10.Pm