Atom-molecule dark state: the exact quantum solution

Developments in ultracold atomic physics have enabled the generation of an atom-molecule dark state in dilute quantum gases. Previous studies of this dark state were all carried out in the mean-field regime. Here we present an exact quantum many-body wave function for the atom-molecule dark state for an ideal system (in the absence of losses and two-body collisions). Using this exact quantum wave function, we are able to validate the mean-field solution to be a good approximation when the particle number N is large. For small N, unique quantum features will become important.