Nonperturbative master equation solution of central spin dephasing dynamics

TL;DR

This paper presents an exact nonperturbative solution to the central spin dephasing problem, capturing full quantum decoherence dynamics without assuming weak coupling, applicable to realistic quantum dot systems.

Contribution

It provides a fully quantum, non-Markovian solution for the central spin problem with inhomogeneous couplings, valid in the large-bath limit and for experimentally relevant parameters.

Findings

Accurately models electron spin decoherence in GaAs quantum dots.

Resums all orders of the time-convolutionless master equation.

Offers a compact solution for predicting decoherence and guiding nuclear state preparation.

Abstract

We solve the long-standing central spin problem for a general set of inhomogeneous bath couplings and a large class of initial bath states. We compute the time evolution of the coherence of a central spin coupled to a spin bath by resumming all orders of the time-convolutionless master equation, thus avoiding the need to assume weak coupling to the bath. The fully quantum, non-Markovian solution is obtained in the large-bath limit and is valid up to a timescale set by the largest coupling constant. Our result captures the full decoherence of an electron spin qubit coupled to a nuclear spin bath in a GaAs quantum dot for experimentally relevant parameters. In addition, our solution is quite compact and can readily be used to make quantitative predictions for the decoherence process and to guide the design of nuclear state preparation protocols.