Non-Markovian dynamics of a biased qubit coupled to a structured bath

TL;DR

This paper introduces an analytical method to study the non-Markovian dynamics of a biased qubit coupled to a structured bath, revealing new oscillation frequencies and transition points, enhancing understanding of quantum dissipation.

Contribution

It develops a novel analytical approach beyond the rotating wave approximation for the biased spin boson model with a structured bath, providing explicit expressions for various dynamical properties.

Findings

Identification of additional damping oscillation frequencies due to bias

Analytical expressions for non-Markovian dynamics and spectrum

Determination of transition points and validation of sum rule and Shiba relation

Abstract

A new analytical approach, beyond rotating wave approximation, based on unitary transformations and the non-Markovian master equation for the density operator, is applied to treat the biased spin boson model with a Lorentzian structured bath for arbitrary detunings at zero temperature. Compared to zero bias, we find that the dynamics demonstrates two more damping oscillation frequencies and one additional relaxation frequency for non-zero bias, where one of the damping oscillation frequencies is a new effect. Analytical expressions for the non-Markovian dynamics and the corresponding spectrum, the localized-delocalized transition point, the coherent-incoherent transition point, the analytical ground energy, the renormalized tunneling factor and the susceptibility are determined. The sum rule and the Shiba relation are checked in the coherent regime.