Coherent Interaction of Spins Induced by Thermal Bosonic Environment

TL;DR

This paper investigates how two spins interact indirectly through a thermal bosonic environment, revealing conditions under which their interaction remains coherent enough to generate entanglement, influenced by quantum fluctuations and temperature.

Contribution

It introduces a combined perturbative and non-perturbative framework to analyze environment-induced spin interactions and their coherence properties at low temperatures.

Findings

Interaction remains coherent at low temperatures

Entanglement can be generated over specific time scales

Zero-point quantum fluctuations dominate the interaction

Abstract

We obtain and analyze the indirect exchange interaction between two two-state systems, e.g., spins, in a formulation that also incorporates the quantum noise that they experience, due to a bosonic environment, for instance, phonons. We utilize a perturbative approach to obtain a quantum evolution equation for the two-spin dynamics. A non-perturbative approach is used to study the onset of the induced interaction, which is calculated exactly. We predict that for low enough temperatures the interaction is coherent over time scales sufficient to create entanglement, dominated by the zero-point quantum fluctuations of the environment. We identify the time scales for which the spins develop entanglement for various spatial separations.