Dynamics and control of a qubit in spin environment: an exact master equation study

TL;DR

This paper derives an exact master equation for a central spin-1/2 system interacting with a spin bath, enabling analysis of decoherence, controllability, and decoherence suppression in quantum information processing.

Contribution

It introduces a unified formalism for free and controlled dynamics of a central spin in a spin bath, accounting for non-Markovian effects and decoherence suppression techniques.

Findings

Exact master equation for central spin in spin environment derived

Analysis of decoherence dynamics under various bath spectra

Demonstration of leakage elimination to suppress decoherence

Abstract

We present an exact master equation for a central spin-$1/2$ system coupled to a spin-$1/2$ bath in terms of hyperfine interaction, which provides a unified formalism for both free evolution and controlled dynamics of the central spin. The equation enables us to study controllability of dynamics processes with various degrees of non-Markovianity. We investigate the Overhauser's effect on decoherence dynamics of the central spin under different bath spectra and the system-bath coupling strengths. Nonperturbative leakage elimination approach is applied to the system to suppress decoherence in solid-state quantum information processing.