Probing the BCS-BEC crossover with persistent currents

We study the persistent currents of an attractive Fermi gas confined in a tightly confining ring trap and subjected to an artificial gauge field all through the BCS-BEC crossover. At weak attractions, on the Bardeen-Cooper-Schrieffer (BCS) side, fermions display a parity effect in the persistent currents, i.e., their response to the gauge field is paramagnetic or diamagnetic depending on the number of pairs on the ring. At resonance and on the Bose-Einstein condensate (BEC) side of the crossover we find a doubling of the periodicity of the ground-state energy as a function of the artificial gauge field and disappearance of the parity effect, indicating that persistent currents can be used to infer the formation of tightly bound bosonic pairs. Our predictions can be accessed in ultracold atom experiments through noise interferograms.

Figure 1

Column (a): energies vs $\mathrm{\Omega }$ for $N=4$, $N_s=8$ from Bethe ansatz (blue line) and DMRG (yellow triangles). In each column, the first three panels from the top correspond to $U/J=0,-2,-6$, respectively. The last line describes the BEC regime for $U_B/J_B=1$—here only DMRG data are available since the model is not integrable. Column (b): persistent current as a function of the flux for the same set of parameters, obtained as the derivative of the ground-state energy in column (a). Columns (c) and (d): noise correlator for $N=4$ and $N_s=10$ for $\mathrm{\Omega }/{\mathrm{\Omega }}_0=0.1$ and $\mathrm{\Omega }/{\mathrm{\Omega }}_0=0.4$, respectively, indicated by red circles in column (a). The correlators are all evaluated in $r^{\prime }=(R,0)$ and $t=0.3{\omega }_0^{-1}$, where ${\omega }_0$ is the frequency of each lattice well. The noise correlator is expressed in units of $1/R^2$. A circulating state is characterized by a spiral-like correlator, not symmetric by inversion with respect to the $y=0$ axis.

Figure 2

Energies, persistent current, and noise correlators as in Fig. 1 here studied for $N=6$, and for $U/J=0,-5,-10$ (from top to bottom) [28]. The last line refers to the bosonic case for $U_B/J_B=1$. All the other parameters are the same as in Fig. 1.