A field-biased quantum master equation and its Markovian limit

TL;DR

This paper derives a modified quantum master equation for driven open quantum systems, accounting for non-Markovian effects and drive-dependent noise correlations, relevant for quantum optics and circuits.

Contribution

It introduces a field-biased quantum master equation with explicit memory effects, extending the Hu-Paz-Zhang framework to include drive-dependent bath correlations.

Findings

The master equation captures non-Markovian dynamics induced by external drives.

Drive-induced corrections are reflected in diffusion and drift terms.

The framework applies to a broad range of quantum optical and circuit experiments.

Abstract

We present a non-equilibrium quantum master equation for a driven open quantum system in the presence of a continuously applied electromagnetic field. Starting from a driven Caldeira-Leggett (CL) model in which the external electromagnetic field couples simultaneously to the subsystem and reservoir degrees of freedom, the canonical fluctuation-dissipation theorem (FDT) relations that encode the coefficients of the master equation can no longer be expected to hold. The bath statistics acquire an explicit dependence on the two-time autocorrelation function of the applied field, leading to drive-biased noise correlations and the potential for non-Markovian dynamics. By eliminating the reservoir degrees of freedom at the operator level, we obtain a modified Hu-Paz-Zhang (HPZ) master equation, in which the diffusion coefficients and coherent forces inherit an explicit memory dependence on the external field. We demonstrate that the physically observable resonant frequency remains encoded in the homogeneous Green's function of the Generalized Langevin equation (GLE), while the drive-induced corrections manifest exclusively through modified diffusion and drift terms, should the drive be treated classically. The resultant field-modified HPZ master provides a unified microscopic framework for understanding field-biased open quantum systems with direct pertinence to a wide variety of experiments in quantum optics and microscopic quantum circuits.