QUANTUM PHASE TRANSITION IN SPIN-ORBIT COUPLED BOSE-EINSTEIN CONDENSATES IN OPTICAL LATTICES OF DIFFERENT GEOMETRIES

Abstract

Mott insulator to superfluid phase transitions and unconventional superfluid phases in spin-orbit coupled Bose-Einstein condensate in one dimensional, square and hexagonal optical lattices are investigated using decoupling approximation and variational Gutzwiller wave function. We considered a system with two components. In the first part, we used decoupling approximation along side perturbation to chart the phase diagrams of the system in the absence of spin-orbit coupling. Our results show that the occupation number of the species, interspecies interaction and the ratio of the hopping matrix of the species dictate the critical point and the separation of the insulating phases. Applying decoupling approximation to spin-orbit coupled Bose-Einstein condensate in one dimensional optical we find that spin-orbit coupling reduces the phase boundary of Mott insulator-superfluid transition and also modifies the critical point in a way that the critical point reduces as the coupling strength increases. In the second part, we applied the variational Gutzwiller wave function to spin-orbit coupled Bose-Einstein condensate in square and hexagonal lattice. Our results show that the geometry of the optical lattice plays a role in the transition. We find that the mean-field Mott insulator-superfluid phase transition boundary of hexagonal lattice is smaller than that of square lattice for the same system. Finally, we showed that the Gutzwiller variational approach gives us access to the twisted superfluid phase realized in the system. The nonuniformity of the superfluid phase is different for the two lattices.