Non-Markovian dynamics of a damped driven two-state system

TL;DR

This paper investigates the non-Markovian dynamics of a driven two-state quantum system interacting with structured environments, providing analytic solutions and conditions for physical validity related to reservoir spectra.

Contribution

It introduces a non-Markovian master equation with analytic solutions for general reservoir spectra and derives conditions for complete positivity with physical interpretation.

Findings

Analytic solutions for non-Markovian dynamics with Ohmic and Lorentzian reservoirs

Conditions for complete positivity linked to phase diffusion and relaxation timescales

Comparison of dynamics under different reservoir spectral classes

Abstract

We study a driven two-state system interacting with a structured environment. We introduce the non-Markovian master equation ruling the system dynamics, and we derive its analytic solution for general reservoir spectra. We compare the non-Markovian dynamics of the Bloch vector for two classes of reservoir spectra: the Ohmic and the Lorentzian reservoir. Finally, we derive the analytic conditions for complete positivity with and without the secular approximation. Interestingly, the complete positivity conditions have a transparent physical interpretation in terms of the characteristic timescales of phase diffusion and relaxation processes.