Probing non-equilibrium steady-state phase transitions with trapped-ion quantum simulators

Open quantum many-body systems with controllable dissipation can exhibit novel features in their dynamics and steady states. A paradigmatic example is the driven-dissipative transverse field Ising model (TFIM). It has been shown recently that the steady state of this model with all-to-all interactions is genuinely non-equilibrium near criticality, exhibiting a modified time-reversal symmetry violating the fluctuation-dissipation theorem. We demonstrate that such non-equilibrium behavior persists when the interactions are sufficiently long range, and this behavior can be observed in near-term ion trap quantum simulator experiments. In addition, we show that the driven-dissipative TFIM can be approximately simulated by a stroboscopic optical pumping process that is easier to achieve experimentally than continuous optical pumping. This stroboscopic protocol preserves the non-equilibrium signatures of the steady states, and can be employed to simulate correlated dissipation or prepare many-body entangled states in a robust way.