BEC-BCS Crossover in “Magnetized” Feshbach-Resonantly Paired Superfluids

We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an $s$-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.

Figure 1

Detuning, $\delta$-population difference, $m/n=(n_{\uparrow }-n_{\downarrow })/(n_{\uparrow }+n_{\downarrow })$ phase diagram (for coupling $\gamma =0.1$) in (a) displaying “normal” ($N$), magnetized superfluid (${\mathrm{SF}}_M$), FFLO (thick red line) and $\mathrm{SF}\mathrm{\text{−}}N$ coexistence states, (b) showing the FFLO wave vector $Q(\delta )$ along the FFLO-$N$ phase boundary, and (c) zoom-in on the FFLO state, stable only for $\delta >{\delta }_{*}\simeq 2.2{ϵ}_{\mathrm{F}}$. To the right of the dashed lines in (a) and (c), the $\mathrm{SF}\mathrm{\text{−}}N$ coexistence undergoes a transition to SF-FFLO coexistence.

Figure 2

Bogoliubov sound speed $u$ in the BEC regime as a function of species imbalance $m$ for $\delta =-2{ϵ}_{\mathrm{F}}$, vanishing at boundary of the ${\mathrm{SF}}_M$ with the $\mathrm{SF}\mathrm{\text{−}}N$ coexistence region.