A proposed paradigm for out-of-equilibrium quantum systems is that an analogue of quantum phase transitions exists between parameter regimes of qualitatively distinct time-dependent behavior. Here, we present evidence of such a transition between dyn
amical phases in a cold-atom quantum simulator of the collective Heisenberg model. Our simulator encodes spin in the hyperfine states of ultracold fermionic potassium. Atoms are pinned in a network of single-particle modes, whose spatial extent emulates the long-range interactions of traditional quantum magnets. We find that below a critical interaction strength, magnetization of an initially polarized fermionic gas decays quickly, while above the transition point, the magnetization becomes long-lived, due to an energy gap that protects against dephasing by the inhomogeneous axial field. Our quantum simulation reveals a non-equilibrium transition predicted to exist but not yet directly observed in quenched s-wave superconductors.
