Abstract
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 non-trivial pure states 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 cross-over 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 phenomena. We also study intermediate time behaviors, identifying a long-lived "prethermalized" state associated that exists within a light cone like area. This intermediate state can be quasi-stationary, and can very different entanglement properties from the ultimate dissipative steady state.
Highlights
In quantum information applications, states with entanglement and other nonclassical properties serve as basic resources
Our recent work in Ref. [22] analyzed a striking example of this local approach to reservoir engineering: it demonstrated that an entire class of free boson lattice systems with a generalized chiral symmetry can be stabilized in this manner by making use of the lattice symmetry [23] and a single, localized, squeezed dissipative reservoir
We focus on the simple but paradigmatic case considered in Ref. [22]: a bosonic lattice system described by a quadratic hopping Hamiltonian, coupled to a Markovian reservoir on just a single site
Summary
States with entanglement and other nonclassical properties serve as basic resources. [22] analyzed a striking example of this local approach to reservoir engineering: it demonstrated that an entire class of free boson lattice systems with a generalized chiral symmetry can be stabilized in this manner by making use of the lattice symmetry [23] and a single, localized, squeezed dissipative reservoir This allows the stabilization of nonclassical, often highly nonlocally entangled Gaussian pure states [22]. The site labels n describe an arbitrary d-dimensional lattice with N sites, and we do not assume any symmetry or translational invariance to begin with This Hamiltonian describes a range of bosonic systems, including coupled arrays of superconducting cavities or mechanical oscillators. The Hamiltonian of Eq (1) can be written in diagonal form using its energy eigenmodes bi and corresponding
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