Non-Makovian decoherence of a two-level system weakly coupled to a bosonic bath

TL;DR

This paper critically examines the limitations of the Born approximation in the Bloch-Redfield equation for qubit decoherence, developing a self-consistent approach that captures non-Markovian effects and long-time relaxation.

Contribution

It introduces a diagrammatic technique to improve the Born approximation, revealing non-Markovian exponential decay effects in qubit relaxation.

Findings

High-order divergences undermine the standard Born approximation.

The improved self-consistent approach captures exponential non-Markovian relaxation.

Dephasing remains well-described by the Born-Markov approximation.

Abstract

Bloch-Redfield equation is a common tool for studying evolution of qubit systems weakly coupled to environment. We investigate the accuracy of the Born approximation underlying this equation. We find that the high order terms in the perturbative expansion contain accumulating divergences that make straightforward Born approximation inappropriate. We develop diagrammatic technique to formulate, and solve the improved self-consistent Born approximation. This more accurate treatment reveals an exponential time dependent prefactor in the non-Markovian contribution dominating the qubit long-time relaxation found in Phys. Rev. B 71, 035318 (2005). At the same time, the associated dephasing is not affected and is described by the Born-Markov approximation.