Time evolution and decoherence of a spin-1/2 particle coupled to a spin bath in thermal equilibrium

TL;DR

This paper provides an exact analytical analysis of the time evolution and decoherence of a central spin-1/2 particle interacting with an anisotropic spin bath in thermal equilibrium, exploring effects of external fields, anisotropy, and temperature.

Contribution

It derives explicit formulas for the reduced density matrix of the central spin for finite and infinite bath sizes, including the convergence to Gaussian variables and Bloch vector dynamics.

Findings

Exact reduced density matrix for finite bath spins

Analytical Bloch vector components in the infinite limit

Decoherence behavior influenced by magnetic field, anisotropy, and temperature

Abstract

The time evolution of a spin-1/2 particle under the influence of a locally applied external magnetic field, and interacting with anisotropic spin environment in thermal equilibrium at temperature $T$ is studied. The exact analytical form of the reduced density matrix of the central spin is calculated explicitly for finite number of bath spins. The case of an infinite number of environmental spins is investigated using the convergence of the rescaled bath operators to normal Gaussian random variables. In this limit, we derive the analytical form of the components of the Bloch vector for antiferromagnetic interactions within the bath, and we investigate the short-time and long-time behavior of reduced dynamics. The effect of the external magnetic field, the anisotropy and the temperature of the bath on the decoherence of the central spin is discussed.