Transition region properties of a trapped quasi-two-dimensional degenerate Bose gas

The classical field simulation technique is used to study a trapped quasi-two-dimensional Bose gas. We calculate the central curvature of the system density and fluctuations of the condensate mode in the degenerate regime. These results provide new understanding of the system behavior in the region of the superfluid transition.

Figure 1

(Color online) Fraction of atoms in the quasicondensate (dots), condensate (squares), and superfluid (triangles) components as a function of reduced temperature. Figure from Ref. [6]. Parameters: $\left({\omega }_{x,y},{\omega }_z\right)=2\pi \times \left(9.4,1880\right)\text{Hz}$, $N=13.5\times {10}^3$ atoms at $T_{\text{BKT}}=34.7\text{nK}$, with $\tilde{g}=0.107$.

Figure 2

(Color online) Total areal density profiles at several temperatures: $n\left(x\right)$ (solid curve), fitting region (vertical lines indicate $x=\pm 5\mu \text{m}$), and quadratic fits (dashed). Parameters are as in Fig. 1.

Figure 3

Central density curvature. Parameters: (a) $\left({\omega }_{x,y},{\omega }_z\right)=2\pi \times \left(9.4,1880\right)\text{Hz}$ with $\tilde{g}=0.107$. Black dots: system with $N=13.5\times {10}^3$ at $T_{\text{BKT}}=34.7\text{nK}$; gray dots: system with $N=21.2\times {10}^3$ at $T_{\text{BKT}}=43.1\text{nK}$. (b) $\left({\omega }_{x,y},{\omega }_z\right)=2\pi \times \left(9.4,940\right)\text{Hz}$ with $\tilde{g}=0.075$. Black dots: system with $N=30.2\times {10}^3$ at $T_{\text{BKT}}=46.8\text{nK}$; gray dots: system with $N=67.3\times {10}^3$ at $T_{\text{BKT}}=64.9\text{nK}$. Vertical solid and dashed lines indicate $T_{\text{BKT}}$ and $T_c$, respectively. The horizontal dashed line shows ${\kappa }_{\text{TF}}$.

Figure 4

Condensate number distribution. Histograms of the condensate number extracted from c-field evolutions at a range of temperatures. The “$\times 4$” indicates that the frequencies have been divided by 4 for subplot (h) for convenience. Parameters are as in Fig. 1.

Figure 5

(Color online) (upper) Condensate number variation during c-field evolution for system at $T^{\prime }=0.91$, i.e., same data as for Fig. 4f. (lower) c-field density of the A and B microstates at the times indicated in the upper plot. Inner (outer) circle indicates the condensate (quasicondensate) $1/e$ radius. Vortices $(+)$ and antivortices $(-)$ indicated inside the central condensate region only.