Temperature-Dependent Decay of Quasi-Two-Dimensional Vortices across the BCS-BEC Crossover

We systematically study the decay of quasi-two-dimensional vortices in an oblate strongly interacting Fermi gas over a wide interaction range and observe that, as the system temperature is lowered, the vortex lifetime increases in the Bose-Einstein condensate (BEC) regime but decreases at unitarity and in the Bardeen-Cooper-Schrieffer (BCS) regime. The observations can be qualitatively captured by a phenomenological model simply involving diffusion and two-body collisional loss, in which the vortex lifetime is mostly determined by the slower process of the two. In particular, the counterintuitive vortex decay in the BCS regime can be interpreted by considering the competition between the temperature dependence of the vortex annihilation rate and that of unpaired fermions. Our results suggest a competing mechanism for the complex vortex decay dynamics in the BCS-BEC crossover for the fermionic superfluids.

Figure 1

Quasicondensate fraction $\eta$ for different trap ramping time $t_{\text{ramp}}$ at unitarity, as obtained from a Gaussian plus Thomas-Fermi distribution fitting to the column density profile [taken after 10 ms time-of-flight (TOF)]. The error bars represent standard statistical errors, calculated from three individual measurements. The solid line is for guiding eyes. The inset displays a TOF image and the corresponding fitting.

Figure 2

Temperature dependence of vortex lifetime $\tau$ in the BCS-BEC crossover, where larger values of $1-\eta$ correspond to higher temperature. (a)–(e) Results at 783, 809, 832, 847, and 861 G, respectively, with the curves for guiding eyes. An example of the power-law fit $1/{\rho }_v=a+\lambda t$ is given in the inset of (c), and the solid line represents the linear fit. The vortex lifetime is defined as $\tau =1/\lambda$, and the temperature is effectively represented by $1-\eta$, with quasicondensate fraction $\eta$ measured at $t=0$.

Figure 3

Temperature dependence of the vortex lifetime $\tau =1/\lambda$ in the Glauber dynamics of the square-lattice $XY$ model. The inset displays the modified inverse vortex density $\ln (t)/{\rho }_v$ versus Monte Carlo time $t$ for various temperature $T$.

Figure 4

Normalized decay time $\tilde{\tau }$ [in units of $1/({\rho }_{v0}K)$] in the diffusion-annihilation model with $L=4a_v$. The solid line is a $B$-spline guide line, and the dashed line is an asymptote at the large diffusion limit. The inset shows an example of time evolution of the dimensionless total vortex density $\tilde{\rho }$.