Generalized Parametric Approximation and a Hybrid Atom-Molecule Quantum Gas

An approximate method, treating the molecular field as a mean field and the atomic field as a second-quantized field, is applied to association in an atomic Bose-Einstein condensate and dissociation of the resulting molecular condensate, due to Feshbach resonance in a time-dependent magnetic field. The model takes into account inelastic collisions of the resonant molecules. An adaptation of the Heisenberg-Langevin formalism to matter fields is used to eliminate the molecular "dump" states of the collisions. Conditions are studied for converting an atomic BEC to a metastable molecular BEC with optimal lifetimes and for maximal production of a gas of entangled atoms in a two-mode squeezed state as a result of the molecular dissociation.