Entanglement dynamics of non-linearly coupled spin-boson model using hierarchical equation of motion approach

Abstract

One of the most intensively studied problems in the field of open quantum systems is the spin-boson model. In this paper, we consider an extension of the spin-boson model with non-linear coupling. We solve the entanglement dynamics of two independent spins quadratically coupled to a bath of harmonic oscillators, using numerically ”exact” approach of hierarchical equations of motion (HEOM). Without Markovian approximation, generalized influence functional formulation by Hu et.al is used to describe the environmental effect of noisy quadratic bath in high-temperature regime. Wotters concurrence is then applied to numerically solved reduced density matrix to visualize the entanglement dynamics. By adjusting the environmental parameters, we vary the degree of non-markovianity and found the elongated time of entanglement.