New Type of Crossover Physics in Three-Component Fermi Gases

A three-component Fermi gas near a broad Feshbach resonance does not have a universal ground state due to the Thomas collapse, while it does near a narrow Feshbach resonance. We explore its universal phase diagram in the plane of the inverse scattering length $1/a{k}_F$ and the resonance range $R_{*}{k}_F$. For a large $R_{*}{k}_F$, there exists a Lifshitz transition between superfluids with and without an unpaired Fermi surface as a function of $1/a{k}_F$. With decreasing $R_{*}{k}_F$, the Fermi surface coexisting with the superfluid can change smoothly from that of atoms to trimers (“atom-trimer continuity”), corresponding to the quark-hadron continuity in a dense nuclear matter. Eventually, there appears a finite window in $1/a{k}_F$ where the superfluid is completely depleted by the trimer Fermi gas, which gives rise to a pair of quantum critical points. The boundaries of these three quantum phases are determined in regions where controlled analyses are possible and are also evaluated based on a mean-field plus trimer model.

Figure 1

Minimal phase structure of a three-component Fermi gas with equal masses, densities, and interactions at zero temperature. There are three quantum phases consisting of superfluids (SF) with and without an unpaired Fermi surface and a Fermi gas of trimers (Trimer FG). The Fermi surface coexisting with the superfluid can change smoothly from that of atoms (${\mathrm{FS}}_{\mathrm{A}}$) to trimers (${\mathrm{FS}}_{\mathrm{T}}$). The phase boundaries are asymptotically given by Eqs. (7, 9) for the superfluid transition (solid curve) and by Eqs. (4, 10) for the Lifshitz transition (dashed curve). See Fig. 2 for an evaluation based on a mean-field plus trimer model.

Figure 2

Quantum critical lines for the superfluid transition (solid curve) and the Lifshitz transition (dashed curve) based on a mean-field plus trimer model (11). The shaded region indicates where the smooth crossover from the Fermi surface of atoms (left side) to trimers (right side) takes place.

Figure 3

Superfluid critical temperatures in units of $T_F\equiv k_F^2/(2m{k}_{\mathrm{B}})$ for $R_{*}{k}_F=0.40$ (dashed curve), 0.381 739 (dotted curve), and 0.36 (solid curve). These values of $R_{*}{k}_F$ are above, at, and below the critical resonance range for opening the complete depletion of the superfluid by the trimer Fermi gas, which gives rise to a pair of quantum critical points.