Spin decoherence due to a randomly fluctuating spin bath

TL;DR

This paper investigates how a spin in a quantum dot loses coherence due to hyperfine interactions with a nuclear spin bath, using exact quantum methods to explore different magnetic field regimes and the impact of weakly coupled spins.

Contribution

It provides a non-perturbative quantum mechanical analysis of spin decoherence in a fluctuating nuclear bath, including the zero-field limit and effects of weakly coupled spins.

Findings

Large non-decaying coherence fraction at zero magnetic field

Good agreement with semiclassical decoherence models

Weakly coupled spins eventually cause complete decoherence

Abstract

We study the decoherence of a spin in a quantum dot due to its hyperfine coupling to a randomly fluctuating bath of nuclear spins. The system is modelled by the central spin model with the spin bath initially being at infinite temperature. We calculate the spectrum and time evolution of the coherence factor using a Monte Carlo sampling of the exact eigenstates obtained via the algebraic Bethe ansatz. The exactness of the obtained eigenstates allows us to study the non-perturbative regime of weak magnetic fields in a full quantum mechanical treatment. In particular, we find a large non-decaying fraction in the zero-field limit. The crossover from strong to weak fields is similar to the decoherence starting from a pure initial bath state treated previously. We compare our results to a simple semiclassical picture [Merkulov et al., Phys. Rev. B 65, 205309 (2002)] and find surprisingly good agreement. Finally, we discuss the effect of weakly coupled spins and show that they will eventually lead to complete decoherence.