Exact non-Markovian master equation for a driven damped two-level system

TL;DR

This paper derives an exact non-Markovian master equation for a driven two-level quantum system, revealing limitations of perturbative approaches and analyzing the validity of common approximations in quantum dynamics.

Contribution

It presents the first exact non-Markovian master equation for a driven two-level system using influence functional theory, and compares it with perturbative methods.

Findings

Exact non-Markovian master equation derived

Limitations of TCL and NZ master equations identified

Significant effects of nonsecular terms in dynamics

Abstract

Driven two-level system is a useful model to describe many quantum objects, particularly in quantum information processing. However, the exact master equation for such a system is barely explored. Making use of the Feynman-Vernon influence functional theory, we derive an exact non-Markovian master equation for the driven two-level system and show the lost feature in the perturbative treatment for this system. The perturbative treatment leads to the time-convolutionless (TCL) and the Nakajima-Zwanzig (NZ) master equations. So to this end, we derive the time-convolutionless (TCL) and the Nakajima-Zwanzig (NZ) master equations for the system and compare the dynamics given by the three master equations. We find the validity condition for the TCL and NZ master equations. Based on the exact non-Markovian master equation, we analyze the regime of validity for the secular approximation in the time-convolutionless master equation and discuss the leading corrections of the nonsecular terms to the quantum dynamics, significant effects are found in the dynamics of the driven system.