Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid

Abstract

We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz and Thouless (BKT) transition temperature. By measuring the density profile, in situ and after time of flight, and the coherence length, we identify different states of the gas. In particular, we observe that the gas develops a bimodal distribution without long range order. In this state, the gas presents a longer coherence length than the thermal cloud; it is quasi-condensed but is not superfluid. Experimental evidence indicates that we observe the superfluid transition (BKT transition).PACS numbers: 03.75. Lm, 64.70.Tg One of the most fascinating aspects of a Bose gas in the degenerate regime is the role of dimensionality. A 2D interacting Bose gas is superfluid at low enough temperature [1,2]. However, by contrast to the 3D case, there is no long range coherence and the coherence decays as a power law [1,2]. At temperatures above the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, the gas is not superfluid. Due to proliferation of free vortices, the quasi-condensate (QC) is fractured into small regions of nearly uniform phase, whose size, which corresponds to the typical length of the exponential decay of the coherence, is larger than the thermal de Broglie wavelength (λ = 2π 2 /M k B T , where T is the temperature and M the atomic mass). For higher T, this size becomes smaller and approaches λ, as the gas crosses over to the thermal phase.Experiments on 2D bosonic systems, such as twodimensional 4 He films [3] and trapped Bose gases [4,5], are able to show signatures of the BKT transition. Other systems, such as the superconducting transition in arrays of Josephson junctions [6] and a two dimensional lattice of (3D) Bose-Einstein condensates [7], also exhibit a similar transition. Another interesting observation was in two dimensional spin polarized atomic hydrogen on liquid 4 He [8] where a reduction in three-body dipolar recombination (which is usually associated with condensation) was observed well above the BKT transition temperature. This observation results from a reduction of density fluctuations, which corresponds to quasi-condensation [9] [10].In this letter, we present evidence of transitions in a quasi-2D Bose gas from thermal (normal gas), to quasicondensate without superfluidity, to superfluid quasicondensate (BKT transition). We explicitly identify the theoretically expected non-superfluid quasi-condensate, a feature not clearly seen in other experiments on a 2D trapped Bose gases [4,5]. We use an interferometric method to study the coherence of the gas down to distances smaller than the thermal de Broglie wavelength. Our results can be understood using the local density approximation (LDA) on a model [11] of a homogeneous system. More recently, calculations for a trapped system have been carried out using classical-quantum field methods [12] and quantum Monte Carlo methods [13].The BKT transition occurs at a universal value of the superfluid density n s = 4/λ 2 . However, the ...

Strongly Interacting Two-Dimensional Bose Gases

“…Interacting Bose gases in two dimensions and BKT physics have been actively investigated in many condensed matter experiments [3][4][5][6][7]. In cold atoms, the BKT transition and the suppression of fluctuations are observed based on 2D gases in the weak interaction regimes [8][9][10][11].…”

“…Interacting Bose gases in two dimensions and BKT physics have been actively investigated in many condensed matter experiments [3][4][5][6][7]. In cold atoms, the BKT transition and the suppression of fluctuations are observed based on 2D gases in the weak interaction regimes [8][9][10][11].Extensive theoretical research on 2D Bose systems addresses the role of interactions in the superfluid phase [12][13][14][15][16][17] and near the BKT critical point [18,19]. In the weak interaction regime, the classical φ 4 field theory [18,19] predicts the logarithmic corrections to the critical chemical potential µ c = k B T (g/π) ln(13.2/g) and the critical density n c = λ −2 dB ln(380/g) for small two-body interaction strength g < 0.2.…”

Obtaining the phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases

“…It is a quantity particularly important for 2D superfluids [18][19][20] , as the famous KosterlitzThouless transition is reflected in a universal jump in superfluid density. Without a precise determination of n s , interpretation of LETTERS experimental results, be they based on quantum Monte Carlo simulations or on features of an interference pattern, will be indirect.…”

Nonequilibrium and local detection of the normal fraction of a trapped two-dimensional Bose gas

“…On the other hand, liquid Helium experiments have limited access to the momentum distribution and the correlation functions of the fluid. The situation of ultracold atom experiments is almost the opposite: evidence of the BKT transition has been obtained from the coherence functions [4], the number of observed vortices [5], and the density profile after time-of-flight [6], while the macroscopic mechanical properties of the fluid have not been characterized yet.…”

“…For simplicity, we give the result for g aa = g ab , to leading order in Ω p /Ω c , we also neglect the contribution to C|∂ t |N C of the time-derivative of the switch-off function f (t), and we use the specific form Ω p /Ω c considered in this paper, see Eqs. (6,7), restricting to zeroth order in q/k p and 1/(k p w) so that…”