Abstract
We analyze the results of a recent experiment with bosonic rubidium atoms harmonically confined in a quasi-two-dimensional (2D) geometry. In this experiment a well-defined critical point was identified, which separates the high-temperature normal state characterized by a single component density distribution, and the low-temperature state characterized by a bimodal density distribution and the emergence of high-contrast interference between independent 2D clouds. We first show that this transition cannot be explained in terms of conventional Bose–Einstein condensation of the trapped ideal Bose gas. Using the local density approximation (LDA), we then combine the mean-field (MF) Hartree–Fock theory with the prediction for the Berezinskii–Kosterlitz–Thouless (BKT) transition in an infinite uniform system. If the gas is treated as a strictly 2D system, the MF predictions for the spatial density profiles significantly deviate from those of a recent quantum Monte Carlo (QMC) analysis. However, when the residual thermal excitation of the strongly confined degree of freedom is taken into account, excellent agreement is reached between the MF and the QMC approaches. For the interaction strength corresponding to the experiment, we predict a strong correction to the critical atom number with respect to the ideal gas theory (factor ∼2). Quantitative agreement between theory and experiment is reached concerning the critical atom number if the predicted density profiles are used for temperature calibration.
Highlights
As first noticed by Peierls [1], collective physical phenomena in an environment with a reduced number of dimensions can be dramatically changed with respect to our experience in three dimensions
In this paper we have analyzed the critical point of a trapped quasi-2D Bose gas
We compared the predictions of this approach with the results of a recent Quantum Monte-Carlo calculation [24] and reached the following conclusions: (i) If one is interested only in the critical atom number, it is sufficient to use a strictly 2D meanfield approach
Summary
As first noticed by Peierls [1], collective physical phenomena in an environment with a reduced number of dimensions can be dramatically changed with respect to our experience in three dimensions. In presence of repulsive interactions between particles, a uniform 2D Bose gas can undergo a phase transition from a normal to a superfluid state at a finite critical temperature This transition was predicted by Berezinskii [5] and by Kosterlitz and Thouless [6] (BKT), and it has been observed in several macroscopic quantum systems, such as helium films adsorbed on a substrate [7]. If the width of the observed quasi-gaussian distribution is interpreted as an empirical measure of the temperature, this leads to a critical atom number at a given temperature which is about five times larger than that needed for conventional BoseEinstein condensation in the ideal gas These two facts showed that, in sharp contrast to the 3D case, interactions in 2D cannot be treated as a minor correction to the ideal gas BEC picture, but rather qualitatively change the behavior of the system. Infinite system only the latter can occur at finite temperature, in a trapped gas both are possible, and the BEC transition can be viewed as a special, non-interacting limit of the more general BKT behavior
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