Superfluid stability in the BEC-BCS crossover

We consider a dilute atomic gas of two species of fermions with unequal concentrations under a Feshbach resonance. We find that the system can have distinct properties due to the unbound fermions. The uniform state is stable only when either (a) beyond a critical coupling strength, where it is a gapless superfluid, or (b) when the coupling strength is sufficiently weak, where it is a normal Fermi gas mixture. Phase transition(s) must therefore occur when the resonance is crossed, in contrast to the equal population case where a smooth crossover takes place.

Figure 1

Main figure: scaled chemical potential difference $h∕{\epsilon }_F=\tilde{h}$ versus the coupling constant $g$ for three different values of $n_d∕n={\tilde{n}}_d$. The inset includes also the results for $\tilde{\Delta }$ and $\tilde{\mu }$ for $n_d∕n=0.5$.

Figure 2

Scaled pair order parameter $\Delta ∕{\epsilon }_F=\tilde{\Delta }$ versus $h∕{\epsilon }_F=\tilde{h}$ for the given coupling constants $g$.

Figure 3

$h∕{\epsilon }_F=\tilde{h}$ versus $n_d∕n={\tilde{n}}_d$ for constant $g$’s. Full lines are for $\Delta \ne 0$ and the dotted lines are for $\Delta =0$. The dashed line indicates (for the $\Delta \ne 0$ states with $n_d$ neither 0 nor 1) where ${\rho }_s$ changes sign, with ${\rho }_s>0$ (above) or, ${\rho }_s<0$ (below). The dot-dash line indicates $\mu =0$, with $\mu <0$ above this line.

Figure 4

Phase diagram for the two fermion species with interspecies coupling $g$ with the stable uniform phases (white regions) shown. No uniform phases are stable in the shaded region (except when $n_d∕n=0$ or 1).