Non-Markovian dissipative dynamics of two coupled qubits in independent reservoirs: a comparison between exact solutions and master equation approaches

TL;DR

This paper compares exact solutions and non-Markovian master equations to analyze the dissipative dynamics of two coupled qubits in independent reservoirs, highlighting the validity and limitations of approximate methods.

Contribution

It provides a detailed comparison between exact dynamics and master equation approaches for two qubits interacting with independent baths, emphasizing non-Markovian effects.

Findings

Master equations can accurately describe one-excitation dynamics under certain conditions.

The validity range of Nakajima-Zwanzig and TCL methods depends on system parameters.

Approximate methods have limitations in capturing non-Markovian features.

Abstract

The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The one-excitation dynamics is derived and compared with that based on the resolution of appropriate non-Markovian master equations. The Nakajima-Zwanzig and the time-convolutionless projection operator techniques are exploited to provide a description of the non-Markovian features of the dynamics of the two-qubits system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.