The trapped two-dimensional Bose gas: from Bose-Einstein condensation to Berezinskii-Kosterlitz-Thouless physics
Résumé
We analyze the results of a recent experiment with bosonic rubidium atoms harmonically confined in a quasi-two-dimensional 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 two-dimensional 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, we then present a hybrid approach, combining the mean-field (MF) Hartree-Fock theory with the prediction for the Berezinskii-Kosterlitz-Thouless transition in an infinite uniform system. We compare the MF results with those of a recent Quantum Monte-Carlo (QMC) analysis. For the considered experiment, both approaches lead to a strong and similar correction to the critical atom number with respect to the ideal gas theory (factor $\sim 2$). The spatial density profiles obtained using the QMC method significantly deviate from the MF prediction, and a similar deviation is observed in the experiment. This suggests that beyond mean-field effects can play a significant role at the critical point in this geometry. A quantitative agreement between theory and experiment can be reached concerning the critical atom number if the QMC results are used for temperature calibration.
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