Semi-implicit finite-difference methods to study the spin-orbit- and coherently-coupled spinor Bose–Einstein condensates

We develop time-splitting finite difference methods, using implicit Backward-Euler and semi-implicit Crank-Nicolson discretization schemes, to study the spin-orbit coupled spinor Bose Einstein condensates with coherent coupling in quasi-one quasi-two-dimensional traps. The split equations involving kinetic energy operators are solved either time-implicit or methods. explicitly method for pseudospin-1/2, spin-1, spin-2 condensates. results ground states obtained methods excellent agreement Fourier spectral which is one of popular solve mean-field models confirm emergence different phases coupling.