Relaxation in dipolar spin ladders: from pair production to false-vacuum decay

Ultracold dipolar particles pinned in optical lattices or tweezers provide an excellent platform for studying out-of-equilibrium quantum magnetism with dipole-mediated couplings. Starting with an initial state with spins of opposite orientation in each of the legs of a ladder lattice, we show that spin relaxation displays an unexpected dependence on inter-leg distance and dipole orientation. This intricate dependence, stemming from the interplay between intra- and inter-leg interactions, results in three distinct dynamical regimes: (i) ergodic, characterized by the fast relaxation towards equilibrium of correlated pairs of excitations generated at exponentially fast rates from the initial state; (ii) metastable, in which the state is quasi-localized in the initial state and only decays at exceedingly long timescales, resembling false vacuum decay; and, surprisingly, (iii) partially-relaxed, with coexisting fast partial relaxation and very long-lived partial quasi-localization. Realizing these intriguing dynamics is within reach of current state-of-the-art experiments in dipolar gases.