Entanglement and Quantum Noise Due to a Thermal Bosonic Field

TL;DR

This paper investigates how a thermal bosonic environment influences entanglement and quantum noise between two spins, revealing conditions under which entanglement can be generated and maintained before noise destroys it.

Contribution

It provides a nonperturbative exact solution for the induced interaction and analyzes the interplay between coherent entanglement formation and noise effects over time.

Findings

Entanglement can be generated at low temperatures within certain time scales.

Quantum noise eventually destroys the initially created entanglement.

The study offers estimates relevant for impurity spins in semiconductors.

Abstract

We analyze the indirect exchange interaction between two two-state systems, e.g., spins 1/2, subject to a common finite-temperature environment modeled by bosonic modes. The environmental modes, e.g., phonons or cavity photons, are also a source of quantum noise. We analyze the coherent vs noise-induced features of the two-spin dynamics and predict that for low enough temperatures the induced interaction is coherent over time scales sufficient to create entanglement. A nonperturbative approach is utilized to obtain an exact solution for the onset of the induced interaction, whereas for large times, a Markovian scheme is used. We identify the time scales for which the spins develop entanglement for various spatial separations. For large enough times, the initially created entanglement is erased by quantum noise. Estimates for the interaction and the level of quantum noise for localized impurity electron spins in Si-Ge type semiconductors are given.