Quantum dynamics of a qubit coupled with structured bath

TL;DR

This paper theoretically investigates the quantum dynamics of a qubit coupled to a structured Lorentzian bath, revealing the coherent-incoherent transition point and calculating key correlation functions.

Contribution

It introduces a perturbation theory based on a unitary transformation to analyze the spin-boson model with structured spectral density, including the first demonstration of the transition point for such a bath.

Findings

Calculated non-equilibrium correlation function $P(t)$ and susceptibility $ ext{Im} \, ilde{ ext{chi}}( ext{omega})$

Determined the coherent-incoherent transition point $ ext{alpha}_c$ for structured bath

Validated approach with Shiba's relation and sum rule

Abstract

The dynamics of an unbiased spin-boson model with Lorentzian spectral density is investigated theoretically in terms of the perturbation theory based on a unitary transformation. The non-equilibrium correlation function $P(t)$ and susceptibility $\chi^{\prime\prime}(\omega)$ are calculated for both the off-resonance case $\Delta\lesssim 0.5\Omega$ and the on-resonance case $\Delta\sim \Omega$. The approach is checked by the Shiba's relation and the sum rule. Besides, the coherent-incoherent transition point $\alpha_c$ can be determined, which has not been demonstrated for the structured bath by previous authors up to our knowledge.