Unifying the dynamical effects of quantum and classical noises

TL;DR

This paper introduces a unified master equation to describe combined quantum and classical noise effects on a system, revealing that second-order interference vanishes and supporting additive noise models in weak coupling regimes.

Contribution

A novel formalism that captures interference effects between quantum and classical noises, including the first demonstration of vanishing second-order interference.

Findings

Second-order interference between quantum and classical noises vanishes.

The formalism justifies additive noise treatments in weak coupling regimes.

Application to a Zeeman-splitted atom shows accurate decoherence rate calculation.

Abstract

We develop a new master equation as a unified description of the effects of both quantum noise (system-bath interaction) and classical noise on a system's dynamics, using a two-dimensional series expansion method. When quantum and classical noises are both present, their combined effect on a system's dynamics is not necessarily a simple sum of the two individual effects. Thus previous master equations for open systems and those for classical noise, even when jointly used, may not capture the full physics. Our formalism can determine whether there is interference between quantum and classical noises and will be able to capture and describe such interference if there is any (in a perturbative manner). We find that, interestingly, second-order interference between quantum and classical noises vanishes identically. This work thus also serves to justify simple additive treatments of quantum and classical noises, especially in the weak coupling regime. For a Zeeman-splitted atom in a stochastic magnetic field interacting with an optical cavity, we use the formalism developed herein to find the overall decoherence rate between the atom's energy levels.