Non-Markovian dynamics and von Neumann entropy evolution of a qubit in a spin environment

TL;DR

This paper investigates the non-Markovian dynamics of a central spin in a spin bath, analyzing how temperature affects population oscillations and entropy evolution, revealing information recovery at low temperatures and thermalization at high temperatures.

Contribution

It provides a detailed analysis of non-Markovian effects on a central spin's dynamics in a spin environment without Markov approximation, highlighting temperature-dependent behaviors.

Findings

Population and entropy oscillations at low temperatures

Pure state formation with information recovery periods

Thermalization to maximum entropy at high temperatures

Abstract

The dynamics of a central spin-1/2 in presence of a local magnetic field and a bath of N spin-1/2 particles is studied in the thermodynamic limit. The interaction between the spins is Heisenberg XY type and the bath is considered to be a perfect thermal reservoir. In this case, the evolution of the populations of the reduced density matrix are obtained for different temperatures. A Born approximation is made but not a Markov approximation resulting a non-Markovian dynamics. The measure of the way that the system mixes is obtained by means of the von Neumann entropy. For low temperatures, results show that there are oscillations of populations and of the von Neumann entropy, indicating that the central spin becomes a pure state with characteristic time periods in which it is possible to extract or recuperate information. In the regime of high temperatures, the evolution shows a final maximum mixed state with entropy S=ln 2 as it is expected for a two level system.