Quasicondensation and coherence in the quasi-two-dimensional trapped Bose gas

We simulate a trapped quasi-two-dimensional Bose gas using a classical field method. To interpret our results we identify the uniform Berezinskii-Kosterlitz-Thouless (BKT) temperature T_BKT as where the system phase-space density satisfies a critical value. We observe that density fluctuations are suppressed in the system well above T_BKT when a quasicondensate forms as the first occurrence of degeneracy. At lower temperatures, but still above T_BKT, we observe the development of appreciable coherence as a prominent finite-size effect, which manifests as bimodality in the momentum distribution of the system. At T_BKT algebraic decay of off-diagonal correlations occurs near the trap center with an exponent of 0.25, as expected for the uniform system. Our results characterize the low-temperature phase diagram for a trapped quasi-two-dimensional Bose gas and are consistent with observations made in recent experiments.