Universal Dynamical Scaling of Quasi-Two-Dimensional Vortices in a Strongly Interacting Fermionic Superfluid

Vortices play a leading role in many fascinating quantum phenomena. Here we generate a large number of vortices by thermally quenching a fermionic superfluid of ${}^6\mathrm{Li}$ atoms in an oblate optical trap and study their annihilation dynamics and spatial distribution. Over a wide interaction range from the attractive to the repulsive side across the Feshbach resonance, these quasi-two-dimensional vortices are observed to follow algebraic scaling laws both in time and space, having exponents consistent with the two-dimensional universality. We further simulate the classical $XY$ model on the square lattice by a Glauber dynamics and find good agreement between the numerical and experimental behaviors. Our work provides a direct demonstration of the universal 2D vortex dynamics.

Figure 1

Exemplary pictures of spontaneous vortices after different holding times in the BEC-BCS crossover. The experiments are performed at 809 G (a)–(c), 832 G (d)–(f), and 861 G (g)–(i), respectively, with a 400 ms ramp time. The initial time $t=0$ is defined as the quasi-condensate number reaches saturation. Each picture has a size of $440\times 350\mu {\mathrm{m}}^2$.

Figure 2

Annihilation dynamics of quasi-2D vortices for (a), 809 G, (b), 832 G, and (c), 861 G. The ramp time is 400 ms. The vertical axis is the number density of vortices ${\rho }_v$, where each point, with a standard statistical error, is acquired by averaging 30 repetitive measurements. The solid lines are the fitting curves with power-law function, and $\mathrm{\Delta }t$ represents the time offset, with $\mathrm{\Delta }t=227\pm 28\mathrm{ms}$ for (a), $237\pm 70\mathrm{ms}$ for (b), and $246\pm 80\mathrm{ms}$ for (c).

Figure 3

Glauber dynamics of the 2D $XY$ model from Monte Carlo simulations. (a) Snapshots of vortex configuration at various time $t$ after the quench, with red and blue circles being vortices and antivortices, respectively. The system size is $L=200$. (b) Time dependence of the vortex density ${\rho }_v$ after the quench, with different symbols representing system sizes. The short-time behavior of decay dynamics (shown in the inset) displays a power-law decay with an exponent about $-1$. The longtime algebraic decay with exponent $-0.83$ is consistent with $(t/\log t{)}^{-1}$ [28].

Figure 4

(a) Probability distribution of the vortex distance for 809 G (green triangle), 832 G (blue circle), and 861 G (red diamond). Each set of data comes from 300 repetitive measurements. The solid lines are the power-law fitting curves. The inset displays a simulation result for the $XY$ model. (b) Temporal evolution of average squared distance between neighboring vortices for 809 G (green triangle), 832 G (blue circle), and 861 G (red diamond). Each set of data comes from 30 repetitive measurements. The solid lines are the linear fitting curves.