Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.