Dynamical probing of high-order spin coherence in one-dimensional mixtures

We investigate the dynamics of one-dimensional SU(2) ultracold fermions near the Tonks-Girardeau limit, confined in a box potential. The system is driven out of equilibrium by initially preparing the two spin components in a fully separated configuration, and its evolution is described by the Hamiltonian in the presence of strong repulsive interactions. Building on the results in G. Aupetit-Diallo et al., Phys. Rev. A 107, L061301 (2023), we extend the analysis to out-of-equilibrium dynamics, uncovering the emergence of time-dependent oscillating high-momentum tails in the momentum distribution. These oscillations, due to the finite size of the system, are governed by a nonlocal, high-order spin coherence term, whose amplitude and phase evolve over time. We show that this term initially grows as tN/2 and subsequently follows the spin-mixing dynamics of the system. Notably, when the spin components are fully mixed, the amplitude of this border-to-border spin coherence reaches its maximum value.