Non-Markovian master equation for interacting qubits coupled to a bosonic bath: analytic form and asymptotic approximation

TL;DR

This paper derives an analytic non-Markovian master equation for two interacting qubits coupled to a bosonic bath, validating it through entanglement and purity analysis, and proposes an asymptotic approximation neglecting first-order noise.

Contribution

The paper provides an explicit analytic form of the non-Markovian master equation for interacting qubits, offering a new perspective and validation methods compared to previous stochastic approaches.

Findings

Master equation accurately describes entanglement and purity dynamics.

Neglecting first-order noise yields a good asymptotic approximation.

Analytic form facilitates understanding of non-Markovian effects.

Abstract

Non-Markovian dynamics of two interacting two-level qubits coupled to a bosonic bath was previously studied using the quantum-state-diffusion (QSD) equation, where a stochastic state is used to describe the system. In this study, we provide another perspective on this system by deriving the analytic form of the master equation, which describes the system with a reduced density matrix. Then, we validate the master equation by examining entanglement generation and state purity. In addition, with the master equation, we observe the effects from first-order noise and notice that a good asymptotic approximation to the master equation can be made by neglecting the first-order noise.