Quasi-classical Limit of a Spin Coupled to a Reservoir

TL;DR

This paper investigates how a spin's decoherence behavior varies when coupled to a reservoir with quantum or classical features, revealing that quantum reservoirs cause full decoherence while classical ones lead to partial decoherence.

Contribution

The authors derive an explicit formula for the spin's reduced density matrix for all reservoir classicality levels and analyze how decoherence and Markovianity depend on this parameter.

Findings

Quantum reservoirs induce full decoherence of the spin.

Classical reservoirs result in partial decoherence.

Markovianity properties are sensitive to the reservoir's classicality parameter.

Abstract

A spin (qubit) is in contact with a bosonic reservoir. The state of the reservoir contains a parameter {\varepsilon} interpolating between quantum and classical reservoir features. We derive the explicit expression for the time-dependent reduced spin density matrix, valid for all values of {\varepsilon} and for energy conserving interactions. We study decoherence and markovianity properties. Our main finding is that the spin decoherence is enhanced (full decoherence) when the spin is coupled to quantum reservoir states while it is dampened (partial decoherence) when coupled to classical reservoir states. The markovianity properties depend in a subtle way on the classicality parameter {\varepsilon} and on the finer details of the spin-reservoir interaction. We further examine scattering and periodicity properties for energy exchange interactions.