BEC–BCS crossover in a (p+ipp+ip)-wave pairing Hamiltonian coupled to bosonic molecular pairs

We analyse a (p+ipp+ip)-wave pairing BCS Hamiltonian, coupled to a single bosonic degree of freedom representing a molecular condensate, and investigate the nature of the BEC–BCS crossover for this system. For a suitable restriction on the coupling parameters, we show that the model is integrable and we derive the exact solution by the algebraic Bethe ansatz. In this manner we also obtain explicit formulae for correlation functions and compute these for several cases. We find that the crossover between the BEC state and the strong pairing p+ipp+ip phase is smooth for this model, with no intermediate quantum phase transition.