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

Abstract

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

References in corpus (5)

• Degenerate Quantum Gases with Spin-Orbit Coupling
• Spin-Orbit Coupled Spinor Bose-Einstein Condensates
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Precision measurement of spin-dependent interaction strengths for spin-1 and spin-2 87Rb atoms
• Spin-1 spin-orbit- and Rabi-coupled Bose-Einstein condensate solver