Reservoir engineering with localized dissipation: Dynamics and prethermalization

Reservoir engineering lattice states using only localized engineered dissipation is extremely attractive from a resource point of view, but can suffer from long relaxation times. Here we study the relaxation dynamics of bosonic lattice systems locally coupled to a single squeezed reservoir. Such systems can relax into a highly nontrivial pure state with long-range entanglement. In the limit of large system size, analytic expressions for the dissipation spectrum can be found by making an analogy to scattering from a localized impurity. This allows us to study the crossover from perturbative relaxation to a slow, quantum-Zeno regime. We also find the possibility of regimes of accelerated relaxation due to a surprising impedance matching phenomenon. We also study intermediate time behaviors, identifying a long-lived "prethermalized" state that exists within a light-cone like area. This intermediate state can be quasistationary, and can have very different entanglement properties from the ultimate dissipative steady state.