Quantum Sensing via Large Spin-Clusters in Solid-State NMR: Optimal coherence order for practical sensing

TL;DR

The paper addresses practical quantum sensing with large spin ensembles where higher coherence orders promise greater sensitivity but decoherence constrains performance. It demonstrates, using multiple-quantum solid-state NMR in a plastic crystal, how to create, manipulate, and detect large coherence-order spin clusters and map their coherence-order distributions to sense RF pulse-width jitters, complemented by a minimal numerical model to estimate information content. A key finding is the existence of an optimal maximum coherence order that maximizes sensing efficiency in nonuniform coherence-order mixtures, with jitters as small as tens of nanoseconds being detectable despite experimental imperfections. This work validates solid-state NMR as a realistic platform for many-body quantum metrology and offers design principles for robust sensors that balance coherence order against decoherence.

Abstract

Quantum entanglement has long been recognized as an important resource for quantum sensing. In this work, we demonstrate the use of multiple-quantum solid-state NMR for quantum sensing by creating, manipulating, and detecting large clusters of correlated nuclear spins. We show that such clusters can sensitively detect pulse-width jitters in radio-frequency control fields at the level of tens of nanoseconds. By analyzing the response of high-order quantum coherences to these control-field jitters, we investigate the critical interplay between the enhanced sensitivity offered by large coherence orders, their relative distributions, and their varying susceptibility to decoherence. We further demonstrate that, even within a non-uniform distribution of coherence orders, there exists an optimal maximum coherence order that maximizes sensing efficiency. To support our interpretation, we supplement the experimental results with a simplified numerical model that estimates the corresponding quantum Fisher information. These results support the solid-state NMR platform as a valuable testbed for investigating many-body quantum metrology protocols.

Figures (5)

• Figure 1: (a) Molecules undergoing random tumbling in adamantane plastic crystal. (b) The overall sensing protocol and the RF sequence with eight $\pi/2$ pulses for generating or manipulating correlated spin clusters. The aim is to sense the RF pulse-width jitters introduced in $\mathcal{U}_\phi^\dagger$ in the middle block with loop number $L_2$. We set $\Delta = 1.5 ~\mu s$, $\Delta' = 2\Delta + \tau_{\pi/2}$, with $\tau_{\pi/2} = 2.9~ \mu s$, and vary the phase $\phi$ in the range $[0,\pi]$ in 181 steps. (c) Illustrating the growth of correlated spin clusters as evolution under ${\cal H}_\mathrm{eff}$ progresses with increasing $L_1$ from top to bottom. (d) The experimentally obtained distributions of coherence orders at different values of $L_1$ (with $L_2=0$) and their Gaussian fits to extract the corresponding cluster sizes $N_{CL}$. Here, the zeroth-order coherence, which is prone to spurious contributions, is suppressed by subtracting the average of signals before the Fourier transform. For $L_2>0$ implementing jitters, distortion in the coherence order distribution can be quantified by the distortion variance defined in Eq. \ref{['eq:dv']}.
• Figure 2: The dots are the experimental distortion variance $D(\delta,m_c)$ plotted versus the maximum coherence order $m_c$, for $L_1=10$, at different values of $L_2$, and with various values of the pulse-width jitter amplitudes as indicated in the legend bar. The lines are to guide the eye.
• Figure 3: Symbols represent experimental distortion variance $D(\delta,m_c)$ versus pulse width jitter amplitude $\delta$ in units of $\tau_{\pi/2}$ for $L_1=10$ at different $L_2$ values as indicated. Here, the optimal coherence orders are $m_c = 10,~26,~38$. In each case, two other $m_c$ values are shown for comparision.
• Figure 4: The quantum Fisher information (QFI) versus maximum coherence order $m_c$ for a cluster of 40 spins with dephasing strength $p$ ranging from 0.7 to 0.8.
• Figure 5: Normalized coherence order distributions for each total spin value $N$. The width of the Gaussian was chosen to be $N/3.5$ to maximize the width of the Gaussian for that $N$ while simultaneously keeping its value negligible beyond $N$ to prevent spillover.