Odd-frequency pairing in a binary mixture of bosonic and fermionic cold atoms

We study fermionic superfluidity in a boson-single-species-fermion cold-atom mixture. We argue that apart from the standard p-wave fermion pairing mediated by the phonon field of the boson gas, the system also exhibits s-wave pairing with the anomalous correlator being an odd function of time or frequency. We show that such a superfluid phase can have a much higher transition temperature than the p-wave and may exist for sufficiently strong couplings between fermions and bosons. These conditions for odd-frequency pairing are favorable close to the value of the coupling at which the mixture phase separates. We evaluate the critical temperatures for this system and discuss the experimental realization of this superfluid in ultracold atomic gases.