Composite fermions, trios, and quartets in a Fermi-Bose mixture

We consider a model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, besides the standard anomalous averages of the type ⟨b⟩ , ⟨bb⟩ , and ⟨cc⟩ , a pairing between fermions and bosons of the type bc is possible. This pairing corresponds to the creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. At higher temperatures trios, which consist of composite fermions and elementary bosons, are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of the collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.