GPU-assisted numerical simulation of spin-orbit coupling in spinor Bose-Einstein condensates

Ultracold atomic gases serve as an excellent platform for exploring many-body physics. By utilizing Raman processes, we can engineer a spin-orbit coupled Hamiltonian with adjustable interactions, allowing for the investigation of neutral atom dynamics under artificial gauge fields within specific parameter regimes. This study employs the time-splitting spectral method (TSSM), a numerical technique, to efficiently solve the multi-component Gross-Pitaevskii equation and simulate the effects of spin-orbit coupling fields in Bose-Einstein condensates. To tackle the computational challenges associated with increasing degrees of freedom, we leverage GPU hardware, achieving significantly faster run times. By tuning spin-orbit coupling and interparticle interactions, our goal is to emulate magnetic Hamiltonian models, and study the resulting phase diagrams resulting from the competition between interparticle interactions and spin-orbit coupling, including the emergence of superfluid vortices and phase separation. Throughout this work, we focus on realistic implementations in Feshbach-tuned ³⁹K.