Berezinskii-Kosterlitz-Thouless transition in a trapped quasi-two-dimensional Fermi gas near a Feshbach resonance

We study the superfluid transition in a quasi-two-dimensional Fermi gas with a magnetic field tuning through a Feshbach resonance. Using an effective two-dimensional Hamiltonian with renormalized interaction between atoms and dressed molecules, we investigate the Berezinskii-Kosterlitz-Thouless transition temperature by studying the phase fluctuation effect. We also take into account the trapping potential in the radial plane and discuss the number and superfluid density distributions. These results can be compared to experimental outcomes for gases prepared in one-dimensional optical lattices.

Figure 1

(Color online) Superfluid transition temperature $T_{\mathrm{BKT}}$ (solid lines) of a uniform quasi-2D Fermi gas for various values of $E_F∕{\omega }_z$. Notice that $T_{\mathrm{BKT}}$ increases monotonically from the BCS (right) to the BEC (left) side of the resonance and approaches a limiting value of $\sim 0.075E_F$. In the BEC limit, $T_{\mathrm{BKT}}$ can also be estimated by considering a weakly interacting gas of composite bosons with 3D scattering length of $0.6a_s$, leading to a logarithmically varying result (dashed line). The mean-field transition temperature $T_{\mathrm{MF}}$ (dashed line in the inset) is also shown as a comparison for $E_F∕{\omega }_z=0.01$.

Figure 2

(Color online) Two-body binding energy $\mid E_b\mid$ (in units of $E_F$, solid lines) as a function of $a_z∕a_s$ for various values of $E_F∕{\omega }_z$. Notice that $\mid E_b\mid$ can exceed $E_F$ (dotted line) even on the high-field side of the resonance point and hence pushes the system into the BEC limit as indicated by the transition temperature shown in Fig. 1.

Figure 3

(Color online) Superfluid transition temperature $T_{\mathrm{BKT}}$ (solid lines) plotted as functions of the two-body binding energy $\mid E_b\mid$. The results are compared with the outcome of an effective 2D Hamiltonian with renormalized atom-atom interaction (model 1, dotted line), which is discussed in Refs. 13, 14.

Figure 4

In-trap number (solid line) and superfluid (shaded area) density distributions at (a) $T=0.01{\omega }_z$, (b) $T=0.001{\omega }_z$, and (c) $T=0.0001{\omega }_z$. For each temperature, three typical detunings are considered with $a_z∕a_s=-1$ (BCS, left), $a_z∕a_s=0$ (unitarity, middle), and $a_z∕a_s=1$ (BEC, right), respectively. Notice the finite jump of superfluid density in the middle of the trap at intermediate temperatures. The plots are made for ${}^6\mathrm{Li}$, while the results for ${}^{40}\mathrm{K}$ are similar. Parameters used in this plot are ${\omega }_z=2\pi \times 62\mathrm{kHz}$, ${\omega }_{\perp }=2\pi \times 10\mathrm{Hz}$, and $N=10000$ and $R_{\mathrm{BCS}}=\sqrt{2{\omega }_z∕{\omega }_{\perp }}{\left(N\right)}^{1∕4}{a}_z$ is the zero-temperature Thomas-Fermi cloud size of a quasi-2D ideal Fermi gas with particle number $N$.