Vortex-Antivortex Lattice in Ultracold Fermionic Gases

We discuss ultracold Fermi gases in two dimensions, which could be realized in a strongly confining one-dimensional optical lattice. We obtain the temperature versus effective interaction phase diagram for an $s$-wave superfluid and show that, below a certain critical temperature $T_c$, spontaneous vortex-antivortex pairs appear for all coupling strengths. In addition, we show that the evolution from weak-to-strong coupling is smooth, and that the system forms a square vortex-antivortex lattice at a lower critical temperature $T_M$.

Figure 1

Mean-field (MF), Berezinskii-Kosterlitz-Thouless (BKT) and vortex-antivortex lattice melting (M) critical temperatures (in units of ${ϵ}_F$) as functions of (a) absolute value of the binding energy $|E_b|$ (in units of ${ϵ}_F$) and (b) interaction strength $\lambda$ (in units of $g_{2\mathrm{D}}^{-1}$, where $g_{2\mathrm{D}}$ is the two-dimensional density of states).

Figure 2

(a) Chemical potential and (b) order parameter amplitude (both in units of ${ϵ}_F$) evaluated at the transition temperature $T_{\mathrm{BKT}}$, as functions of $|E_b|$ (main figure) and of the interaction strength $\lambda$ (in units of $g_{2\mathrm{D}}^{-1}$) (inset).

Figure 3

Square vortex-antivortex lattice in the strong coupling limit.