Superfluid transition of homogeneous and trapped two-dimensional Bose gases

Abstract

Current experiments on atomic gases in highly anisotropic traps present the opportunity to study in detail the low temperature phases of two-dimensional inhomogeneous systems. Although, in an ideal gas, the trapping potential favors Bose-Einstein condensation at finite temperature, interactions tend to destabilize the condensate, leading to a superfluid Kosterlitz-Thouless-Berezinskii phase with a finite superfluid mass density but no long-range order, as in homogeneous fluids. The transition in homogeneous systems is conveniently described in terms of dissociation of topological defects (vortex-antivortex pairs). However, trapped two-dimensional gases are more directly approached by generalizing the microscopic theory of the homogeneous gas. In this paper, we first derive, via a diagrammatic expansion, the scaling structure near the phase transition in a homogeneous system, and then study the effects of a trapping potential in the local density approximation. We find that a weakly interacting trapped gas undergoes a Kosterlitz-Thouless-Berezinskii transition from the normal state at a temperature slightly below the Bose-Einstein transition temperature of the ideal gas. The characteristic finite superfluid mass density of a homogeneous system just below the transition becomes strongly suppressed in a trapped gas.two dimensions ͉ phase transitions ͉ trapped atoms T he ability to produce two-dimensional atomic gases trapped in optical potentials has stimulated considerable interest in the Kosterlitz-Thouless-Berezinskii (KTB) transition in such systems (1-7); recently, the transition has been observed in a quasi two-dimensional system of trapped rubidium atoms (8, 9). A homogeneous Bose gas in two dimensions undergoes BoseEinstein condensation (BEC) only at zero temperature, since long wavelength phase fluctuations destroy long range order (10-13); nonetheless, interparticle interactions drive a phase transition to a superfluid state at finite temperature, as first pointed out by Berezinskii (14,15) and by Kosterlitz and Thouless (16,17). The phase transition is characterized by an algebraic decay of the off-diagonal one-body density matrix (or single particle Green's function) in real space below the transition temperature, T KT . Furthermore, the superfluid mass density, s , jumps with falling temperature, T, from 0 just above T KT to a universal value s ϭ 2m 2 T KT ͞ just below (18), where m is the atomic mass. (We use units ϭ k B ϭ 1.)A noninteracting homogeneous Bose gas in two dimensions does not undergo Bose-Einstein condensation at finite temperature. In such a system, the density is given in terms of the chemical potential bywhere ␤ ϭ 1͞T, and ϭ (2 ͞mT) 1/2 is the thermal wavelength.As approaches zero at fixed temperature, the density grows arbitrarily, implying the absence of condensation. On the other hand, a trapped noninteracting gas does undergo a BoseEinstein condensation at a finite temperature (19). In the semiclassical limit, the total number of particles is given by N(␤ ) ϭ g 2 (Ϫ␤ )(T͞ ) 2 , w...

Quasicondensation in Two-Dimensional Fermi Gases

“…Since we, as in Ref. [25], make no reference to vortices we cannot argue that our observations correspond strictly to a BKT scenario [3], but we can establish that our findings follow rather precisely those of recent experiments.Background theory.− Theoretical studies of the 2D Fermi gas divide into two classes: those which build on or extend BCS mean-field theory [4, 13-16, 23, 26], which is the largest class, and those (based on t-matrix schemes) which do not [17][18][19][20]27]. Here we consider a t-matrix theory belonging to the first class.…”

“…Since we, as in Ref. [25], make no reference to vortices we cannot argue that our observations correspond strictly to a BKT scenario [3], but we can establish that our findings follow rather precisely those of recent experiments.…”

“…Our approach is to be distinguished from other studies of 2D Fermi gases [4,[13][14][15][16][17][18][19][20][21][22][23]. In particular, those addressing BKT physics [4,[13][14][15][16]20], use existing formulae [24,25] and determine the unknown parameters to obtain T BKT c . By contrast here we reverse the procedure and follow experimental protocols to thereby provide a new formula, involving composite bosons, for the transition temperature associated with quasi-condensation.…”

“…parameters that appear in the usual formulae [24,25] for the BKT transition temperature. Here we reverse the logic in order to present an alternative viewpoint.…”

Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas

“…As pointed out in Refs. [36,37], such extended spatial coherence in an interacting system is a sufficient condition for superfluidity T / T F C r i t i c a l e x p o n e n t…”