Control of domain-wall motion in multi-domain spin structures in an ultracold ⁸⁷Rb gas

We initialize a pseudo-spin-½ ultracold ⁸⁷Rb gas in ‘up-down’ and ‘up-down-up’ configurations, with a helical domain wall formed between the regions of different magnetization. The interplay between spin currents driven by spin-exchange collisions and diffusive pressure leads to complex domain-wall trajectories. Varying initial longitudinal magnetization and coherence in the domain wall enables tunability of spontaneous domain-wall motion. We use simulations of a quantum Boltzmann equation to train a neural network to predict initial conditions that lead to target domain wall trajectories. However, the realizable spontaneous domain wall trajectories are limited by the restricted phase space of initial parameters. Applying effective magnetic field gradients provides an opportunity to dynamically alter spin-currents through the domain wall. We extend our machine-learning approach to predict time-varying effective magnetic field gradients needed for the dynamic control of domain wall motion.