Evolution from BCS to Berezinskii-Kosterlitz-Thouless Superfluidity in One-Dimensional Optical Lattices

We analyze the finite temperature phase diagram of fermion mixtures in one-dimensional optical lattices as a function of interaction strength. At low temperatures, the system evolves from an anisotropic three-dimensional Bardeen-Cooper-Schrieffer (BCS) superfluid to an effectively two-dimensional Berezinskii-Kosterlitz-Thouless (BKT) superfluid as the interaction strength increases. We calculate the critical temperature as a function of interaction strength, and identify the region where the dimensional crossover occurs for a specified optical lattice potential. Finally, we show that the dominant vortex excitations near the critical temperature evolve from multiplane elliptical vortex loops in the three-dimensional regime to planar vortex-antivortex pairs in the two-dimensional regime, and we propose a detection scheme for these excitations.

Figure 1

Phase diagram of temperature $T$ (in units of ${ϵ}_{2\mathrm{D}}$) versus $G=mAg/(4\pi )$ with interaction range $k_0\approx 2\times {10}^4{k}_{2\mathrm{D}}$ for which $G_c\approx 0.043$, tunneling $t_z\approx 0.043{ϵ}_{2\mathrm{D}}$, lattice spacing $d_z\approx 0.43\mu \mathrm{m}$, and planar density $n_{2\mathrm{D}}\approx 2.5\times {10}^7{\mathrm{cm}}^{-2}$, such that $k_{2\mathrm{D}}{d}_z\approx 0.55$. $T_0$ is the saddle-point temperature scale.

Figure 2

Characteristic (a) tunneling amplitude $t_{z,c}$ (in units of ${ϵ}_{2\mathrm{D}}$); and (b) optical lattice depth $V_{0,c}$ (in units of $E_r$) versus $G=mAg/(4\pi )$ showing the anisotropic-3D to 2D crossover. The parameters are the same as in Fig. 1.