Analysis of the Holzmann-Chevallier-Krauth theory for the trapped quasi-two-dimensional Bose gas

We provide an in-depth analysis of the theory proposed by Holzmann, Chevallier, and Krauth (HCK) [Europhys. Lett. 82, 30001 (2008)] for predicting the temperature at which the Berezinskii-Kosterlitz-Thouless (BKT) transition to a superfluid state occurs in the harmonically trapped quasi-two-dimensional (2D) Bose gas. Their theory is based on a mean-field model of the system density, and we show that the HCK predictions change appreciably when an improved mean-field theory and identification of the transition point is used. In this analysis we develop a consistent theory that provides a lower bound for the BKT transition temperature in the trapped quasi-2D Bose gas.

Figure 1

Comparison of 2D phase space densities for systems at $T=\left(\mathrm{a}\right)$ 221, (b) 172, and (c) $150\mathrm{nK}$. Our mean-field model (solid), HCK model (dotted), and ideal gas (dashed). Ground axial mode areal densities are shown in gray in (c). Calculation parameters are $N={10}^4$ ${}^{87}\mathrm{Rb}$ atoms with ${\omega }_{x,y}=2\pi \times 59\mathrm{Hz}$ and ${\omega }_z=2\pi \times 2530\mathrm{Hz}$. We note that the parameters in (a) are the same as those in Fig. 2 of [23].

Figure 2

(Color online) Predictions for the BKT transition temperature as a function of $N$. Our theory (squares), HCK theory (triangles), quasi-2D BEC (points), and pure 2D BEC temperature (crosses). All other parameters as in Fig. 1.