Bistability and quantum fluctuations in coherent photoassociation of a Bose-Einstein condensate

Existence of bistability in coherent photoassociation of a Bose-Einstein condensate was proved using two-mode model, and analytical expressions of the bistable steady states were presented. Results indicated that the two-mode model under the semiclassical approximation could be put into a couple of canonical Hamiltonian equations for the conjugate variables atom number and a phase difference. Analytical expressions obtained demonstrated how to sweep adiabatically the frequency of the driving laser to convert a condensate of atoms into a condensate of molecules in an optimum way.