Phase diagram of multi-component bosonic mixtures: emergence of mixed superfluid and insulating phases

A three-component bosonic mixture is capable of demonstrating a significantly rich phase diagram in comparison with a two-component mixture or a single-component fluid. With experimental studies of multi-component mixtures gaining momentum and comparatively few theoretical efforts, we consider an interacting three-component Bose gas on a lattice and, via a strong coupling expansion of the Bose-Hubbard model, look into a variety of situations, such as the intraspecies and intraspecies interactions being the same and different, attractive and repulsive, etc. A scenario of rich phase diagrams emerges where one species of atoms can be in the superfluid phase while the other two may be in insulating phases. Such a mixed-phase diagram with different species coexisting in different phases is an exciting one: a possibility that can be explored in experiments. Numerical solution of the mean field equations has further demonstrated the occurrence of insulating phases with fractional filling of each species of atoms. Such insulating phases with fractional occupancies are counterintuitive in the context of incompressible phases.