Vortex–Antivortex-Pair Lattices in Spin–Orbit Coupled Bose–Einstein Condensates

We investigate theoretically the ground states of Bose–Einstein condensates with Rashba spin–orbit coupling in optical lattices within mean-field framework. We obtain numerically the Bloch states and energy spectrum for the single particle Hamiltonian, meanwhile the analytical solution of Bloch states is also presented. For a spin–orbit coupling Bose–Einstein condensates with a weak interaction, we show the existence of the vortex–antivortex-pair lattices state by simulating the Gross–Pitaevskii equation.