Abstract :

We discuss a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. The dynamics can be described by a many-body Landau-Zener model. The solution becomes poss ible due to the integrability of the model Hamiltonian.
Our solution predicts a dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate for both atoms-to-molecule pairing and molecular dissociation processes. We find that for the latter process with a linear energy dispersion of atomic modes, the emerging phase can have a thermalized energy distribution of noninteracting bosons with the temperature defined by the rate of the transition. This provides a simple interpretation of the phase transition in terms of the creation of equilibrium Bose-Einstein condensate.