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 the study of the intriguing equilibration dynamics of spin models with dipolar exchange. Starting with an initial state in which spins of opposite orientation are prepared in each of the legs of a ladder lattice, we show that spin relaxation displays an unexpected dependence on interleg distance and dipole orientation. This dependence, stemming from the interplay between intra- and interleg interactions, results in three distinct relaxation 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 quasilocalized in the initial state and only decays in exceedingly long timescales, resembling false-vacuum decay; and, surprisingly, (iii) partially relaxed, with coexisting fast partial relaxation and partial quasilocalization. The realization of this intriguing dynamics is at hand in current state-of-the-art experiments in dipolar gases.