Reservoir-mediated spin entanglement in the mean-force Gibbs state

TL;DR

This paper derives analytic expressions for the equilibrium state of two qubits coupled to a common reservoir, revealing how reservoir properties influence entanglement.

Contribution

It provides the first analytic approximation for the mean-force Gibbs state of two qubits, elucidating reservoir-mediated entanglement in thermal equilibrium.

Findings

Entanglement peaks at low temperatures.

Entanglement is non-monotonic with coupling strength.

Broader reservoir spectral density can enhance entanglement.

Abstract

Two qubits strongly coupled to a common bosonic reservoir can become entangled with each other, despite having no direct interaction. In equilibrium, such coupling-induced coherences can be described by the mean-force Gibbs state. Here we derive approximate, analytic expressions for the two-qubit mean-force Gibbs state, and use these to characterize equilibrium qubit-qubit entanglement mediated by a thermal reservoir. Entanglement, which is highest at lowest temperatures, is a non-monotonic function of the system-reservoir coupling strength. Moreover, we find that broadening the reservoir spectral density beyond a single mode, as is realistic for typical baths, can enhance the qubit entanglement. Our results provide a comprehensive understanding of reservoir-mediated two-qubit entanglement in thermal equilibrium and provide a benchmark to compare with numerical methods, as well as demonstrating the utility of strong system-reservoir coupling as a resource.