Coherence properties of a two-dimensional trapped Bose gas around the superfluid transition

We measure the momentum distribution of a two-dimensional trapped Bose gas and observe the increase of the range of coherence around the Berezinskii-Kosterlitz-Thouless (BKT) transition. We quantitatively compare our observed profiles to both a Hartree-Fock mean-field theory and quantum Monte Carlo simulations. In the normal phase, the momentum distribution is observed to sharpen well before the phase transition. This behavior is partially captured in a mean-field approach, in contrast to the physics of the BKT transition.

Figure 1

Scheme of the experimental setup. The atom cloud, initially trapped in a harmonic 2D trap with frequencies $8\text{Hz}\times 15\text{Hz}\times 1.5$ kHz, is dropped for $83.5\mathrm{ms}$ before shining a fluorescence beam situated $3.4\mathrm{cm}$ below the initial position. The fluorescence signal is recorded from above with an electron-multiplying CCD camera.

Figure 2

Radial profiles of the momentum distribution for five different atom numbers at constant temperature $T=64.5\pm 2.0$ nK. The atom number $N$ is given in units of the critical number for the ideal gas Bose-Einstein condensation $N_{\mathrm{c}}\approx 3\times {10}^4$ and the superfluid phase transition is expected for $N/N_{\mathrm{c}}\approx 1.26$ (see text). In each plot, we present the experimental data (black dots), the mean-field profiles (blue dashed line) resulting from the fit in the wings (i.e., for $k>2\mu$m${}^{-1}$), and the corresponding quantum Monte Carlo profiles (green continuous line) with the same temperature and the measured atom number.

Figure 3

(a) Half width at half maximum of the profiles, normalized to the HWHM of a Gaussian profile for the same temperature, plotted versus the number of atoms normalized to $N_{\mathrm{c}}$. (b) Fraction of atoms in the central pixel of the image, $N_0/N$. Blue dashed line, mean-field prediction for $T=64.5\mathrm{nK}$. Green continuous line, Monte Carlo data for $T=64.5\pm 0.3\mathrm{nK}$. Red vertical dot-dashed line, superfluid transition.