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.
Cite
@article{arxiv.2106.07762,
title = {Semi-Implicit finite-difference methods to study the spin-orbit and coherently coupled spinor Bose-Einstein condensates},
author = {Paramjeet Banger and Pardeep Kaur and Sandeep Gautam},
journal= {arXiv preprint arXiv:2106.07762},
year = {2023}
}