Finite-momentum trimers and Cooper quartets in a one-dimensional Fermi gas with coexistent $s$- and $p$-wave interactions

Abstract

We study finite-momentum trimers and Cooper quartets in a one-dimensional two-component Fermi gas with coexistent $s$- and $p$-wave interactions, regularized in the relative momentum of each pair so that they remain Galilean invariant. Pauli blocking alone then makes the trimer dispersion deviate from free center-of-mass motion, so the trimer energy can be lowest at finite total momentum. Allowing this motion expands the $abb$ region among pairs and trimers and removes the region where an odd-wave pair is lowest. The $aabb$ quartet lies below all these branches at every sampled coupling, and in a strip starting on the crossing of the two dimer-pair channels its lowest breakup channel is a moving $abb$ trimer and an atom. At weak interspecies attraction, a variational bound shows that two odd-wave Cooper pairs bind into a quartet, whose binding exceeds that of the coexisting trimer by orders of magnitude as the attraction weakens. At stronger interspecies attraction, the quartet binding relative to two unlike-species dimers disappears when the odd-wave interaction is switched off, although the even-wave interaction dominates the interaction energy. Relative to the in-vacuum case, the Fermi sea enhances the weak-coupling quartet binding, and at fixed scattering lengths the quartet binding grows with density while the coexisting trimer becomes much shallower. These results show that neither the most strongly bound pair nor the dominant interaction energy alone determines whether the quartet binds.