Is a Trapped One-Dimensional Bose Gas a Luttinger Liquid?

Abstract

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 suitable experimental conditions the system can be described as a Luttinger liquid. This implies that the correlation function of the bosons decays algebraically preventing Bose-Einstein condensation. At significantly lower temperatures a finite size gap destroys the Luttinger liquid picture and Bose-Einstein condensation is again possible.Comment: 4 pages (revtex), 1 figure (eps file