Quantum gas mixtures in different correlation regimes

We present a many-body description for two-component ultracold bosonic gases when one of the species is in the weakly interacting regime and the other is either weakly or strongly interacting. In the one-dimensional limit the latter is a hybrid in which a Tonks-Girardeau gas is immersed in a Bose-Einstein condensate, which is an example of a class of quantum system involving a tunable, superfluid environment. We describe the process of phase separation microscopically as well as semiclassically in both situations and show that quantum correlations are maintained even in the separated phase.