Ground state for trapped two-component Bose-Einstein condensates with synthetic spin-orbit interactions and magnetic fields

The experimental realization of synthetic gauge fields in ultracold atomic gases has spurred great interest in the ground state and excitations of multicomponent Bose-Einstein condensates (BECs) in the presence of spin-orbit (SO) interactions and artificial magnetic fields, driven in part by the pursuit of topologically non-trivial states in these systems. While the characteristics of SO-coupled weakly interacting BECs in uniform geometries and in two-dimensional traps are well-understood, for example the existence of stripe phases, little work has been performed for fully three-dimensional harmonic potentials. In this work, the ground state is determined for interacting (effective) two-component BECs in the presence of Raman-induced synthetic SO interactions and magnetic fields, confined in three-dimensional traps. To ensure efficient calculations but also accurate results, the calculations employ a spatial mesh based on a finite element discrete variable representation. The results are compared with previous theory and simulation results and with experimental data where possible.