Persistent dark states in anisotropic central spin models

TL;DR

This paper investigates the persistence of dark states in anisotropic central spin models, revealing their robustness even far from integrability and their potential relevance to mesoscopic quantum systems.

Contribution

It explains the widespread occurrence of dark states in inhomogeneous central spin models through proximity to integrable lines and analyzes their properties in chaotic regimes.

Findings

Dark states persist as eigenstates at large deviations from integrability.

Eigenstates are chaotic but do not satisfy eigenstate thermalization hypothesis.

Long relaxation times increase exponentially with system size.

Abstract

Long-lived dark states, in which an experimentally accessible qubit is not in thermal equilibrium with a surrounding spin bath, are pervasive in solid-state systems. We explain the ubiquity of dark states in a large class of inhomogenous central spin models using the proximity to integrable lines with exact dark eigenstates. At numerically accessible sizes, dark states persist as eigenstates at large deviations from integrability, and the qubit retains memory of its initial polarization at long times. Although the eigenstates of the system are chaotic, exhibiting exponential sensitivity to small perturbations, they do not satisfy the eigenstate thermalization hypothesis. Rather, we predict long relaxation times that increase exponentially with system size. We propose that this intermediate chaotic but non-ergodic regime characterizes mesoscopic quantum dot and diamond defect systems, as we see no numerical tendency towards conventional thermalization with a finite relaxation time.