Statistical mechanics of entanglement mediated by a thermal reservoir I

Abstract

Two defect particles that couple to a harmonic chain, acting as common reservoir, can become entangled even when the two defects do not directly interact and the harmonic chain is effectively a thermal reservoir for each individual defect. This dynamics is encountered for sufficiently low temperatures of the chain and depends on the initial state of the two oscillators. In particular, when each defect is prepared in a squeezed state, entanglement can be found at time scales at which the steady state of a single defect is reached. We provide a microscopic description of the coupled quantum dynamics of chain and defects. By means of numerical simulations, we explore the parameter regimes for which entanglement is found under the specific assumption that both particles couple to the same ion of the chain. This model provides the microscopic setting where bath-induced entanglement can be observed.

18 pages, 14 figures

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• Gaussian entanglement induced by an extended thermal environment
• Entangling two defects via a surrounding crystal
• Quantum reservoirs with ion chains
• Rise and fall of entanglement between two qubits in a non-Markovian bath
• Entanglement balance of quantum $(e,2e)$ scattering processes
• Energy and information propagation in a finite coupled bosonic heat bath
• Dynamics of entanglement creation between two spins coupled to a chain