Phase separation in a mixture of two species of fermionic atoms in one-dimensional optical lattice

In this work, we study the ground-state phase diagram of a mixture of two species of fermionic atoms in one-dimensional optical lattice, as described by an asymmetric Hubbard model. We investigate the quantum phase transition from density wave to phase separation by studying both the corresponding charge order parameter and quantum entanglement, and present phase diagram as function of band-filling. A rigorous prove, that even for the case of a single hole doping, the density wave is unstable to the phase separation in the infinite U limit, will be presented. We also discuss experimental feasibility of observing such a phase separation.