Quantifying spectral signatures of non-Markovianity beyond the Born-Redfield master equation

TL;DR

This paper introduces a spectroscopic measure and a frequency-domain quantum master equation to detect and quantify persistent non-Markovian effects in open quantum systems, overcoming limitations of traditional time-domain methods.

Contribution

It proposes a novel spectroscopic measure of non-Markovianity with an information-theoretic interpretation and derives a frequency-domain quantum master equation that captures full memory effects.

Findings

The measure detects persistent non-Markovianity in steady states.

The frequency-domain master equation retains full memory of the system.

The approach reliably diagnoses non-Markovianity in complex environments.

Abstract

Memory or time-non-local effects in open quantum dynamics pose theoretical as well as practical challenges in the understanding and control of noisy quantum systems. While there has been a comprehensive and concerted effort towards developing diagnostics for non-Markovian dynamics, all existing measures rely on time-domain measurements which are typically slow and expensive as they require averaging several runs to resolve small transient features on a broad background, and scale unfavorably with system size and complexity. In this work, we propose a spectroscopic measure of non-Markovianity which can detect persistent non-Markovianity in the system steady state. In addition to being experimentally viable, the proposed measure has a direct information theoretic interpretation: a large value indicates the information loss per unit bandwidth of making the Markov approximation. In the same vein, we derive a frequency-domain quantum master equation (FD-QME) that goes beyond the standard Born-Redfield description and retains the full memory of the state of the reduced system. Using the FD-QME and the proposed measure, we are able to reliably diagnose and quantify non-Markovianity in several system-environment settings including those with environmental correlations and retardation effects.