Free-induction decay and envelope modulations in a narrowed nuclear spin bath

TL;DR

This paper analyzes the free-induction decay of a localized electron spin coupled to a nuclear spin bath, revealing unexpected envelope modulations and non-monotonic decoherence rates, especially under narrowed bath conditions and high Zeeman energy.

Contribution

It introduces a unified perturbative method to study decoherence, uncovering new envelope modulations and corrections to decoherence rates in electron-nuclear spin systems.

Findings

Discovery of envelope modulations in free-induction decay.

Identification of a non-monotonic dependence of decoherence rate on Zeeman splitting.

Validation of the method against previous short- and long-time results.

Abstract

We evaluate free-induction decay for the transverse components of a localized electron spin coupled to a bath of nuclear spins via the Fermi contact hyperfine interaction. Our perturbative treatment is valid for special (narrowed) bath initial conditions and when the Zeeman energy of the electron $b$ exceeds the total hyperfine coupling constant $A$: $b>A$. Using one unified and systematic method, we recover previous results reported at short and long times using different techniques. We find a new and unexpected modulation of the free-induction-decay envelope, which is present even for a purely isotropic hyperfine interaction without spin echoes and for a single nuclear species. We give sub-leading corrections to the decoherence rate, and show that, in general, the decoherence rate has a non-monotonic dependence on electron Zeeman splitting, leading to a pronounced maximum. These results illustrate the limitations of methods that make use of leading-order effective Hamiltonians and re-exponentiation of short-time expansions for a strongly-interacting system with non-Markovian (history-dependent) dynamics.