Decoupling transition in a one-dimensional fermionic gas interacting via a Feshbach resonance

We study a fermionic atomic gas confined to move in one dimension and interacting via an s-wave Feshbach resonance. At low energies the system is characterized by a model of two Josephson-coupled Luttinger liquids, corresponding to fermionic atoms and their diatomic molecules. In contrast to higher dimensions, we find that this system exhibits a quantum phase transition from a phase in which the two superfluids are strongly coupled to one where the Feshbach resonance coupling becomes irrelevant and the two types of superfluid decouple.