Spin-boson model under dephasing: Markovian vs Non-Markovian dynamics

TL;DR

This paper investigates the combined effects of Markovian dephasing and non-Markovian bath interactions on the spin-boson model, developing an exact non-perturbative method and deriving analytic results to understand the spin dynamics.

Contribution

It introduces a non-perturbative stochastic Schrödinger equation approach to analyze spin-boson dynamics with dephasing, extending understanding of combined Markovian and non-Markovian effects.

Findings

Characteristic frequency of spin dynamics is minimally affected by dephasing.

Developed an exact numerical method combining stochastic magnetic fields and Lindblad equations.

Derived weak-coupling analytic results using non-interacting blip approximation.

Abstract

The spin-boson model, describing a two-level system strongly coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or doesn't change at all) with dephasing. To obtain these results, we develop an exact non-perturbative method known as the stochastic Schr\"{o}dinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known non-interacting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.