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We analyse a p+ip-wave pairing BCS Hamiltonian, coupled to a single bosonicdegree of freedom representing a molecular condensate, and investigate thenature of the BEC-BCS crossover for this system. For a suitable restriction onthe coupling parameters, we show that the model is integrable and we derive theexact solution by the algebraic Bethe ansatz. In this manner we also obtainexplicit formulae for correlation functions and compute these for severalcases. We find that the crossover between the BEC state and the strong pairingp+ip phase is smooth for this model, with no intermediate quantum phasetransition.

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