Nonperturbative stochastic method for driven spin-boson model

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 Schrödinger equation that allows us 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 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 σ x (t) and of σ z (t) under a Landau-Zener sweep of the bias field. We also compute to a high precision the asymptotic long-time dynamics of σ z (t) without bias and demonstrate the wide applicability of our approach by calculating the spin dynamics at non-zero bias and different temperatures.arXiv:1211.1201v2 [cond-mat.str-el]

Generalized multipolaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system

“…This pushes numerical methods even further toward their limits, [12][13][14][15][16][17][18][19][20] and many studies have hitherto focused on simpler analytical approaches 2,3 (master equations, for instance) that may fail at large dissipation and low temperatures.…”

Quantum Dynamics in Noisy Backgrounds: from Sampling to Dissipation and Fluctuations

“…For example in [2], by solving an equivalent stochastic Schrödinger equation, the authors observed an exponential decay in the long time behaviour of the spin correlation functions.…”

“…[1]). An example for the first situation can be found in [2] where the spin-boson Hamiltonian is used to investigate the real-time dissipative dynamics of quantum impurities embedded in a macroscopic environment. Relying on functional methods for quantum dissipative systems [3], the authors reformulated the original problem in terms of a stochastic Schrödinger equation with a Gaussian noise coupled linearly to the quantum system.…”

Dynamics of a qubit in a high-impedance transmission line from a bath perspective

“…The qubit then evolves at later times according to the full spin-boson Hamiltonian (3), and progressively relaxes to its many-body ground state while energy is dissipated into the bath. This theoretical problem has been considered by a great variety of methods, such as quantum Monte Carlo [40,41], stochastic expansions [42][43][44], timedependent NRG [45,46], systematic variational dynamics [47], and analytical weak-coupling calculations [48][49][50][51], but mostly from the perspective of the qubit dynamics. Indeed, in addition to the relaxation properties of the qubit itself, we will examine here in depth the behavior of the states in the bath.…”