Non-Markovian dynamics of a qubit coupled to an Ising spin bath

Abstract

We study the analytically solvable Ising model of a single qubit system coupled to a spin bath. The purpose of this study is to analyze and elucidate the performance of Markovian and non-Markovian master equations describing the dynamics of the system qubit, in comparison to the exact solution. We find that the time-convolutionless master equation performs particularly well up to fourth order in the system-bath coupling constant, in comparison to the Nakajima-Zwanzig master equation. Markovian approaches fare poorly due to the infinite bath correlation time in this model. A recently proposed post-Markovian master equation performs comparably to the time-convolutionless master equation for a properly chosen memory kernel, and outperforms all the approximation methods considered here at long times. Our findings shed light on the applicability of master equations to the description of reduced system dynamics in the presence of spin-baths.

17 pages, 16 figures

References in corpus (5)

• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Non-Markovian generalization of the Lindblad theory of open quantum systems
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Optimal strategy for a single-qubit gate and trade-off between opposite types of decoherence
• Non-Markovian master equations from entanglement with stationary unobserved degrees of freedom

Cited by in corpus (5)

• Structure of completely positive quantum master equations with memory kernel
• Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
• On the conundrum of deriving exact solutions from approximate master equations
• Bang-Bang control of a qubit coupled to a quantum critical spin bath
• Systematic Perturbation Theory for Dynamical Coarse-Graining