Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath

TL;DR

This paper uses the TCL projection operator technique to analytically study the non-Markovian dynamics of a central electron spin coupled to a nuclear spin bath, showing good agreement with numerical simulations especially in strong magnetic fields.

Contribution

It applies the TCL method to a central spin model with nonuniform interactions, providing analytical results that match numerical simulations for both short and long-term dynamics.

Findings

TCL method accurately describes spin dynamics in strong fields

Analytical results agree with numerical simulations

Effective for both short-time and long-time behavior

Abstract

We apply the time-convolutionless (TCL) projection operator technique to the model of a central spin which is coupled to a spin bath via nonuniform Heisenberg interaction. The second-order results of the TCL method for the coherences and populations of the central spin are determined analytically and compared with numerical simulations of the full von Neumann equation of the total system. The TCL approach is found to yield an excellent approximation in the strong field regime for the description of both the short-time dynamics and the long time behavior.