Non-perturbative stochastic method for driven spin-boson model

TL;DR

This paper presents a numerically exact stochastic method for analyzing the real-time dynamics of the driven spin-boson model, capturing dissipation effects beyond weak coupling in quantum impurity systems.

Contribution

The authors develop an exact stochastic Schrödinger equation approach that extends previous work, enabling detailed analysis of spin-boson dynamics beyond weak coupling and including non-Markovian effects.

Findings

Accurate computation of spin coherence and correlation functions.

Analysis of non-Markovian effects on spin dynamics.

Demonstration of method's applicability at various biases and temperatures.

Abstract

We introduce and apply a numerically exact method for investigating the real-time dissipative dynamics of quantum impurities embedded in a macroscopic environment beyond the weak-coupling limit. We focus on the spin-boson Hamiltonian that describes a two-level system interacting with a bosonic bath of harmonic oscillators. This model is archetypal for investigating dissipation in quantum systems and tunable experimental realizations exist in mesoscopic and cold-atom systems. It finds abundant applications in physics ranging from the study of decoherence in quantum computing and quantum optics to extended dynamical mean-field theory. Starting from the real-time Feynman-Vernon path integral, we derive an exact stochastic Schr\"odinger equation that allows to compute the full spin density matrix and spin-spin correlation functions beyond weak coupling. We greatly extend our earlier work (P. P. Orth, A. Imambekov, and K. Le Hur, Phys. Rev. A {\bf 82}, 032118 (2010)) by fleshing out the core concepts of the method and by presenting a number of interesting applications. Methodologically, we present an analogy between the dissipative dynamics of a quantum spin and that of a classical spin in a random magnetic field. This analogy is used to recover the well-known non-interacting-blip-approximation in the weak-coupling limit. We explain in detail how to compute spin-spin autocorrelation functions. As interesting applications of our method, we explore the non-Markovian effects of the initial spin-bath preparation on the dynamics of the coherence $\sigma^x(t)$ and of $\sigma^z(t)$ under a Landau-Zener sweep of the bias field. We also compute to a high precision the asymptotic long-time dynamics of $\sigma^z(t)$ without bias and demonstrate the wide applicability of our approach by calculating the spin dynamics at non-zero bias and different temperatures.