Capturing non-Markovian polaron dressing with the master equation formalism

TL;DR

This paper extends the polaron master equation approach to better capture non-Markovian effects in open quantum systems, especially for observables that do not commute with the polaron transformation, validated through comparisons with exact methods.

Contribution

The authors introduce correction terms derived from the Nakajima-Zwanzig formalism to improve the PME's accuracy for non-commuting observables in non-Markovian regimes.

Findings

Standard PME predicts populations well but struggles with coherences.

Correction terms significantly improve the description of non-commuting observables.

The approach is validated on spin-boson and Landau-Zener models.

Abstract

Understanding the dynamics of open quantum systems in strong coupling and non-Markovian regimes remains a formidable theoretical challenge. One popular and well-established method of approximation in these circumstances is provided by the polaron master equation (PME). In this work we reevaluate and extend the validity of the PME to capture the impact of non-Markovian polaron dressing, induced by non-equilibrium open system dynamics. By comparing with numerically exact techniques, we confirm that while the standard PME successfully predicts the dynamics of system observables that commute with the polaron transformation (e.g. populations in the Pauli z-basis), it can struggle to fully capture those that do not (e.g. coherences). This limitation stems from the mixing of system and environment degrees of freedom inherent to the polaron transformation, which affects the accuracy of calculated expectation values within the polaron frame. Employing the Nakajima-Zwanzig projection operator formalism, we introduce correction terms that provide an accurate description of observables that do not commute with the transformation. We demonstrate the significance of the correction terms in two cases, the canonical spin-boson model and a dissipative time-dependent Landau-Zener protocol, where they are shown to impact the system dynamics on both short and long timescales.