Spin Bath Decoherence Mediated by Phonons

TL;DR

This paper presents an exactly solvable model for central spin decoherence mediated by phonons, revealing how phonon states and temperature influence decoherence dynamics.

Contribution

It introduces a new solvable model for spin decoherence with phonon-mediated coupling, analyzing effects of phonon states and temperature on decoherence behavior.

Findings

Decoherence decays Gaussianly and becomes phonon-frequency independent at short times.

High phonon energies or fully polarized spins lead to phonon-independent decoherence times.

Increasing temperature enhances phonon role in decoherence.

Abstract

We introduce an exactly solvable model to study decoherence of a central spin interacting with a spin bath where the coupling is mediated by phonons which we assume to be in a coherent state or thermal distribution. For the coherent state case, we find that the decoherence factor decays in a Gaussian fashion and it becomes independent of the phonon frequencies at short times. If the phonon energies are much larger than spin-phonon coupling or bath spins are fully polarized, decoherence time becomes independent of the initial phonon state. For the thermal state case, phonons play more important role in decoherence with increasing temperature. We also discuss possible effects of the temperature on spin bath contribution to decoherence.