Phase Separation in Bose-Bose Mixtures in an Optical Lattice

TL;DR

This paper investigates phase separation phenomena in strongly interacting Bose-Bose mixtures within optical lattices, deriving analytical conditions and exploring spatial density profiles using mean-field and local density approximations.

Contribution

It provides new analytical expressions for phase boundaries and phase separation conditions, and applies these to realistic Rb-K mixtures in combined traps.

Findings

Phase separation depends on on-site interactions and occupation numbers.

Analytical phase boundary expressions are derived for zero-hopping limit.

Density profiles show nesting structures in phase-separated mixtures.

Abstract

We study the ground-state properties of mixtures of strongly interacting bosonic atoms in an optical lattice. Applying a mean-field approximation to the Hubbard model for Bose-Bose mixtures, we calculate the densities and superfluid order parameters for both species. Due to the repulsive interaction between the two species, the system exhibits phase separation. First, in the extreme limit of the zero-hopping case, we derive analytical expressions for the phase boundaries. In particular, we derive the conditions for phase separation in the Mott insulator phase. We find that the conditions for the phase separation depend on the on-site interactions as well as the occupation numbers. In particular, we show that the coexisting state appears by varying the on-site inter-species interaction. We also show the phase diagram of the finite hopping case. Second, we calculate the spatial density profile of $^{87}$Rb-$^{41}$K mixtures in the combined potential of a parabolic trap and an optical lattice using the local density approximation. We fixed the number of $^{87}$Rb and varied the number of $^{41}$K, and used the parameters estimated by experiments. We show that the phase separated $^{87}$Rb-$^{41}$K mixtures distribute like in a parabolic trap case. Furthermore, we find that phase separated mixtures distribute a nesting structure.