Photoassociation of Atomic BEC within Mean-Field Approximation: Exact Solutions

We propose an exactly solvable method to study the coherent two-colour photoassociation of an atomic Bose--Einstein condensate, by linearizing the bilinear atom--molecule coupling, which allows us to conveniently probe the quantum dynamics and statistics of the system. By preparing different initial states of the atomic condensate, we can observe very different quantum statistical properties of the system by exactly calculating the quadrature-squeezed and mode-correlated functions.