Aspects of the decoherence in high spin environments: Breakdown of the mean-field approximation

TL;DR

This paper investigates how high-spin environments affect qubit decoherence, revealing that the mean-field approximation fails at high spins and that interaction type influences decoherence suppression.

Contribution

It extends decoherence analysis to high-spin environments and shows the breakdown of the mean-field approximation at high spins for certain models.

Findings

Short-time decay accelerates with higher spin magnitude.

Heisenberg XY interactions better suppress decoherence asymptotically.

Mean-field approximation fails for high spins in transverse Ising models.

Abstract

The study of the decoherence of qubits in spin systems is almost restricted to environments whose constituents are spin-$\frac{1}{2}$ particles. In this paper we consider environments that are composed of particles of higher spin, and we investigate the consequences on the dynamics of a qubit coupled to such baths via Heisenberg $XY$ and Ising interactions. It is shown that while the short time decay in both cases gets faster as the magnitude of the spin increases, the asymptotic behavior exhibits an improvement of the suppression of the decoherence when the coupling is through Heisenberg $XY$ interactions. In the case of a transverse Ising model, we find that the mean field approximation breaks down for high values of the spin.