Pairing between Atoms and Molecules in a Boson-Fermion Resonant Mixture

We consider a mixture of fermionic and bosonic atoms nearby interspecies Feshbach resonances, which have been observed recently in $^6$Li-$^{23}$Na mixture by MIT group, and in $^{40}$K-$^{87}$Rb mixture by JILA group. We point out that the fermion-boson bound state, namely the heteronuclear molecules, will coexist with the fermionic atoms in a wide parameter region, and the attraction between fermionic atoms and molecules will lead to the formation of atom-molecule pairs. The pairing structure is studied in detail, and, in particular, we highlight the possible realization of the Fulde-Ferrel-Larkin-Ovchinnikov state in this system.