Strongly Resonant $p$-Wave Superfluids

We study theoretically a dilute gas of identical fermions interacting via a $p$-wave resonance. We show that, depending on the microscopic physics, there are two distinct regimes of $p$-wave resonant superfluids, which we term “weak” and “strong.” Although expected naively to form a paired superfluid, a strongly resonant $p$-wave superfluid is in fact unstable toward the formation of a gas of fermionic trimers. We examine this instability and estimate the lifetime of the $p$-wave molecules due to the collisional relaxation into trimers. We discuss consequences for the experimental achievement of $p$-wave superfluids in both weakly and strongly resonant regimes.

Figure 1

The diagrams whose sum gives the scattering amplitude between an atom and a molecule.

Figure 2

(a) Scattering length $a_{\mathrm{bf}}$ in units of $\hslash /\Lambda$ and (b) binding energy $E_3$ of the trimer in units of ${\Lambda }^2/m$, both as functions of $c_2$. Here, detuning has been set to zero. The large $c_2$ limit is indicated.