Wavelet-resolved coherence beats in the Overhauser field of a thermal nuclear spin ensemble

TL;DR

This paper employs the synchrosqueezed wavelet transform to analyze nuclear spin bath dynamics in diamond, revealing detailed coherence beats and spatial information about nuclear spin clusters, with applications in noise filtering.

Contribution

It introduces a wavelet-based method to resolve coherence beats and spatial structure in nuclear spin ensembles, enhancing analysis of quantum bath dynamics and noise filtering techniques.

Findings

Identification of multiple coherence beating patterns in nuclear spin noise

Wavelet scalograms reveal spatial and spectral information of spin clusters

Effective denoising of noisy signals using thresholding in the wavelet domain

Abstract

This work introduces the so-called synchrosqueezed wavelet transform, to shed light on the dipolar fluctuations of a thermal ensemble of nuclear spins in a diamond crystal structure, hyperfine-coupled to a central spin. The raw time series of the nuclear spin bath coherent dynamics is acquired through the two-point correlation function computed using the cluster correlation expansion method. The dynamics can be conveniently analyzed according to zero-, single-, and double-quantum transitions derived from the dipolar pairwise spin flips. We show that in the early-time behavior when the coherence is preserved in the spin ensemble, the Overhauser field fluctuations are modulated by dipole-dipole-induced small inhomogeneous detunings of nearly resonant transitions within the bath. The resulting beating extending over relatively longer time intervals is featured on the scalograms where both temporal and spectral behaviors of nuclear spin noise are unveiled simultaneously. Moreover, a second kind of beating that affects faster dynamics is readily discernible, originating from the inhomogeneous spread of the hyperfine coupling of each nucleus with the central spin. Additionally, any quadrupolar nuclei within the bath imprint as beating residing in the zero-quantum channel. The nuclear spin environment can be directionally probed by orienting the hyperfine axis. Thereby, crucial spatial information about the closely separated spin clusters surrounding the central spin are accessible. Thus, a wavelet-based post processing can facilitate the identification of proximal nuclear spins as revealed by their unique beating patterns on the scalograms. Finally, when these features are overwhelmed by either weakly or strongly coupled classical noise sources, we demonstrate the efficacy of thresholding techniques in the wavelet domain in denoising contaminated scalograms.