Connecting Berezinskii-Kosterlitz-Thouless and BEC Phase Transitions by Tuning Interactions in a Trapped Gas

We study the critical point for the emergence of coherence in a harmonically trapped two-dimensional Bose gas with tunable interactions. Over a wide range of interaction strengths we find excellent agreement with the classical-field predictions for the critical point of the Berezinskii-Kosterlitz-Thouless (BKT) superfluid transition. This allows us to quantitatively show, without any free parameters, that the interaction-driven BKT transition smoothly converges onto the purely quantum-statistical Bose-Einstein condensation transition in the limit of vanishing interactions.

Figure 1

Determination of the critical point for the onset of coherence, for $\tilde{g}=0.28$ and $T\approx 140\mathrm{nK}$. (a) Evolution of the momentum distribution $n(k)$ with the hold time $t$ (see text). Extended coherence is revealed as a sharp peak in $n(k)$. Each image is an average of three experimental realizations. (b) Evolution of the momentum-distribution peak $P_0$ and the smoothly decaying total atom number $N$. We associate the thresholdlike behavior of $P_0$ with the critical time $t_c$ and deduce the corresponding $N_c$. The solid line is a heuristic piecewise fit function used to determine $t_c$ [47].

Figure 2

Critical atom number as a function of the interaction strength $\tilde{g}$. All numbers are scaled to the ideal-gas BEC critical number $N_c^0$, defined in Eq. (1). The solid line is the classical-field BKT prediction of Eq. (2), without any free parameters. The dashed line is an approximation that neglects suppression of density fluctuations in the normal state. The star $(\star )$ denotes the critical point for BEC, which only occurs in the ideal-gas limit. The shaded region, $\tilde{g}<0.06$, indicates the regime in which our measurements stop being reliable (see text). The error bars are statistical.

Figure 3

Critical chemical potential as a function of the interaction strength $\tilde{g}$. The solid line is the classical-field BKT prediction. The dashed line is derived assuming a fully fluctuating Bose gas, while the dotted line corresponds to a complete suppression of density fluctuations. The error bars are statistical.