Tunable domain-wall dynamics in multi-domain spin structures in an ultracold ⁸⁷Rb gas

We study the controllability of domain-wall motion in a pseudo-spin-½ ultracold ⁸⁷Rb gas. The gas is initialized with multiple domains, such as ‘up-down’ and ‘up-down-up’ configurations, with helical domain walls between the regions of different magnetization. The interplay between diffusive pressure and induced spin-currents due to spin-exchange collisions leads to complex domain-wall dynamics. We demonstrate that spontaneous domain-wall motion may be tuned through altering the initial domain orientation and coherence in the domain wall and have modeled the observed wall trajectories with numerical solutions of a quantum Boltzmann equation. We also use simulations of the quantum Boltzmann equation to train a neural network to predict initial conditions that lead to specific target domain wall trajectories. Achievable spontaneous domain wall trajectories are limited by the restricted phase space of initial parameters; however, optically applying effective magnetic field gradients alters spin currents through the domain wall and offers the possibility of dynamic control of wall motion. We present progress toward this goal using machine-learning techniques to predict time-varying effective magnetic field gradients as control parameters.