Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces

Abstract: We theoretically investigate in-medium three-body correlations in one-dimensional spinless fermions with antisymmetrized two- and three-body attractive interactions. By investigating the variational problem of three-body states above the Fermi sea, we illuminate the fate of the in-medium three-body cluster states both in the special case with pure attractive three-body interaction as well as in the case with the coexistence of two- and three-body interactions. Our results testify that the fermion-dimer repulsion is canceled by including the three-body interactions, and stable three-body clusters can be formed. We further feature a phase diagram consisting of the $p$-wave Cooper pairing and Cooper tripling phases in a plane of $p$-wave two- and three-body coupling strengths.