The Numerical Study of the Ground States of Spin-1 Bose-Einstein Condensates with Spin-Orbit-Coupling

Abstract

A projection gradient method for computing the ground state of the spin-orbit-coupled spin-1 Bose-Einstein condensate at extremely low temperatures is proposed. The continuous gradient flows are discretised by a second-order finite difference method in space and the Crank-Nicolson method in time. Our discretisation preserves the total mass conservation and the energy diminishing property. Numerical results show the efficiency of the method.