Superfluidity of an interacting trapped quasi-two-dimensional Bose gas

We investigate the harmonically trapped interacting Bose gas in a quasi-two-dimensional geometry using the classical field method. The system exhibits quasi-long-range order and nonclassical rotational inertia at temperatures below the Berezinskii-Kosterlitz-Thouless crossover to the superfluid state. In particular, we compute the scissors-mode oscillation frequencies and find that the irrotational mode changes its frequency as the temperature is swept across the crossover thus providing microscopic evidence for the emergence of superfluidity.

Figure 1

(Color online) Density (a),(b) and phase (c),(d) of the classical field at two different temperatures: (a) and (c) $T=114\text{nK}$ and (b) and (d) $T=151\text{nK}$. Vortices and antivortices are denoted by $+$ and $-$ signs, respectively.

Figure 2

(Color online) Radial vortex occupation probability density at different temperatures (from left to right) $\left\{T_i\right\}=\left\{168,158,155,148,143,138,135,131,126,120,115\right\}\text{nK}$. The thicker line indicates the superfluid crossover at $T_{\text{sf}}=155\text{nK}$.

Figure 3

(Color online) Condensate fraction as determined by diagonalization of the one-body density matrix as a function of temperature. The markers are the data, the black curve is the 2D ideal gas result, and the vertical line indicates the superfluid crossover temperature $T_{\text{sf}}$.

Figure 4

(Color online) Two-point correlation functions $g\left(0,r_0\right)$ as a function of spatial distance, $r_0$, from the trap center for a range of temperatures, $\left\{T_i\right\}$. The thicker line is for the estimated superfluid crossover temperature.

Figure 5

(Color online) Second-order coherence functions $g^{\left(2\right)}\left(r_0\right)$ as a function of spatial distance $r_0$ from the trap center for a range of temperatures, $\left\{T_i\right\}$. The thicker line is for the estimated superfluid crossover temperature.

Figure 6

(Color online) Correlation length as a function of temperature. The bullets are the numerical data, the vertical line denotes the superfluid crossover temperature, and the black curve is the power-law function described in the text.

Figure 7

(Color online) Scissors mode frequencies as a function of temperature. The horizontal dashed lines are the analytical predictions of Eqs. (11, 12) and the solid vertical line is our estimate of the superfluid transition temperature. The horizontal axis refers to the equilibrium temperature prior to the rotation of the state. The normalized Fourier spectrum at each temperature is indicated in gray in the background.