Generalized positive P representation with third-order noise in intracavity coherent photoassociation of Bose-Einstein condensates

We investigate the process of intracavity photoassociation of Bose-Einstein-condensed atoms to form a molecular condensate. As shown previously, this process can only be successfully described by a quantum treatment of all the interacting fields. We extend our previous work by representing the full quantum aspects of the problem using an extension of the positive P representation to model non-Wiener noises, This allows the mapping of a generalized Fokker-Planck equation with third-order derivatives onto a set of coupled stochastic difference equations. We also investigate parameter regimes not covered previously, as well as the effects of spontaneous dissociation of the condensed molecules