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arXiv:2605.02857

Precision hyperfine spectroscopy of an individual nuclear-spin-9/2

J. Travesedo, Z. W. Huang, L. Mykolyshyn, N. Thill, L. Pallegoix, P. Goldner, T. Chaneliere, S. Bertaina, T. Charpentier, D. Esteve, P. Abgrall, D. Vion, J. OSullivan, E. Flurin, P. Bertet

quant-phSubmitted May 4, 2026• Announced May 5, 2026
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Abstract

Single-spin magnetic resonance spectroscopy promises to yield structural and chemical information at the level of individual atoms or molecules, in a non-invasive way. Here, we use an Er3+ paramagnetic center in a CaWO4 crystal, detected by microwave photon counting at 10 mK, as a nanoscale magnetic sensor to measure the NMR spectrum of a proximal individual nuclear-spin-9/2 93Nb impurity with Hertz spectral resolution. From these measurements, we determine the 93Nb insertion site, its position relative to the Er3+ , and its complete quadrupolar tensor. We moreover harness the high spectral resolution of our measurements to establish the presence of two previously unobserved terms in the spin Hamiltonian. The first describes a coupling between the Er3+ spin and the 93Nb nuclear quadrupole; it possibly originates from a spin-dependent electrostatic interaction between the two systems. The second is a nuclear hexadecapolar term, and may be caused by the coupling of the electric field third derivative to the 93Nb nuclear hexadecapolar moment.

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Single-spin magnetic resonance spectroscopy promises to yield structural and chemical information at the level of individual atoms or molecules, in a non-invasive way. Here, we use an Er3+ paramagnetic center in a CaWO4 crystal, detected by microwave photon counting at 10 mK, as a nanoscale magnetic sensor to measure the NMR spectrum of a proximal individual nuclear-spin-9/2 93Nb impurity with Hertz spectral resolution. From these measurements, we determine the 93Nb insertion site, its position relative to the Er3+ , and its complete quadrupolar tensor. We moreover harness the high spectral resolution of our measurements to establish the presence of two previously unobserved terms in the spin Hamiltonian. The first describes a coupling between the Er3+ spin and the 93Nb nuclear quadrupole; it possibly originates from a spin-dependent electrostatic interaction between the two systems. The second is a nuclear hexadecapolar term, and may be caused by the coupling of the electric field third derivative to the 93Nb nuclear hexadecapolar moment.
We report microwave spectroscopy of 167^{167}167Er3+^{3+}3+ doped in CaWO4_44​ which reveals the hyperfine splitting of the erbium electronic ground state (Z1Z_1Z1​, Jeff.J_\mathrm{eff.}Jeff.​=15/2) induced by the III=7/2 nuclear spin. From spectra measured below$\sim$50 mK in magnetic fields up to 200 mT, we extract spin Hamiltonian parameters including the electron g\textbf{g}g, hyperfine A\textbf{A}A, and nuclear electric quadrupolar Q\textbf{Q}Q tensors. Crucially, our analysis demonstrate unambiguously, that the previously unobserved nuclear electric quadrupolar moment is essential to reproduce the experimental data. With these refined parameters, we identify zero first-order Zeeman (ZEFOZ) transitions at zero magnetic field. Extending the analysis to finite fields, we uncover that ZEFOZ points lie either along the ccc axis or within the aaa-bbb plane. These results establish CaWO4_44​ as a promising host for long lifetime quantum memories.
Echo-based spectroscopy of the superhyperfine interaction of an electronic spin with nuclear spins in its surroundings enables detailed insights into the microscopic magnetic environment of spins in solids. Still, it is an outstanding challenge to resolve individual nuclear spins in a dense bath, in which many of them exhibit a comparable coupling strength. This simultaneously requires a high spectral resolution and a large signal-to-noise ratio. However, when probing spin ensembles, dipolar interactions between the dopants can lead to a concentration-dependent trade-off between resolution and signal. Here, we fully eliminate this limitation of previous optical-echo-envelope-modulation spectroscopy experiments by integrating the emitters into a high-finesse resonator, which allows for strong optical echoes even at very low concentrations. To demonstrate its potential, the technique is applied to erbium dopants in yttrium orthosilicate ( Er : YSO ). Achieving an unprecedented spectral resolution enables precise measurements of the superhyperfine interaction with four of the Y nuclear spins densely surrounding each emitter. The achieved boost of the signal, enabled by the resonator, allows for extending the approach to the lowest concentration possible—to the level of single dopants, thereby providing a tool for detecting and studying individual nuclear spins. Thus, our technique paves the way for an improved understanding of dense nuclear-spin baths in solids.
Nuclear magnetic resonance (NMR) at the single-molecule level with atomic resolution holds transformative potential for structural biology and surface chemistry. Near-surface solid-state spin sensors with optical readout ability offer a promising pathway toward this goal. However, their extreme proximity to target molecules demands exceptional robustness against surface-induced perturbations. Furthermore, life science applications require these sensors to operate in biocompatible spectral ranges that minimize photodamage. In this work, we demonstrate that the PL6 quantum defect in 4H silicon carbide (4H-SiC) can serve as a robust near-infrared spin sensor. This sensor operates at tissue-transparent wavelengths and exhibits exceptional near-surface stability even at depth of 2 nm. Using shallow PL6 centers, we achieve nanoscale NMR detection of proton (1H\mathrm{^{1}H}1H) spins in immersion oil and fluorine (19F\mathrm{^{19}F}19F) spins in Fomblin, attaining a detection volume of (3 nm)3\mathrm{(3~nm)^3}(3 nm)3 and a sensitivity reaching the requirement for single-proton spin detection. This work establishes 4H-SiC quantum sensors as a compelling platform for nanoscale magnetic resonance, with promising applications in probing low-dimensional water phases, protein folding dynamics, and molecular interactions.
Nuclear magnetic resonance spectroscopy with solid-state spin sensors is a promising pathway for the detection of nuclear spins at the micro- and nanoscale. Although many nanoscale experiments rely on a single sensor spin for the detection of the signal, leveraging spin ensembles can enhance sensitivity, particularly in cases in which the signal merely originates from statistically polarized nuclear spins. In this Letter, we introduce multipoint correlation spectroscopy, which combines the advantages of two well-established methods-correlation spectroscopy and quantum heterodyne detection-to enable temporally efficient measurements of statistically polarized samples at the nanoscale with spin ensembles. We present a theoretical framework for this approach and demonstrate an experimental proof of concept with a nitrogen vacancy center in diamond. We achieve single hertz uncertainty in the estimated signal frequency, highlighting the potential applications of the technique for nanoscale nuclear magnetic resonance.
Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for analyzing the structure and function of molecules, and for performing three-dimensional imaging of the spin density. At the heart of NMR spectrometers is the detection of electromagnetic radiation, in the form of a free induction decay (FID) signal, generated by nuclei precessing around an applied magnetic field. While conventional NMR requires signals from 1e12 or more nuclei, recent advances in sensitive magnetometry have dramatically lowered this number to a level where few or even individual nuclear spins can be detected. It is natural to ask whether continuous FID detection can still be applied at the single spin level, or whether quantum back-action modifies or even suppresses the NMR response. Here we report on tracking of single nuclear spin precession using periodic weak measurements. Our experimental system consists of a 13C nuclear spin in diamond that is weakly interacting with the electronic spin of a nearby nitrogen-vacancy center, acting as an optically readable meter qubit. We observe and minimize two important effects of quantum back-action: Measurement-induced decoherence and frequency synchronization with the sampling clock. We use weak measurements to demonstrate nanoscale NMR spectroscopy with a simultaneous enhancement of the signal-to-noise ratio (SNR), frequency bandwidth and spectral resolution. Our method may provide the optimum route for performing single-molecule NMR at atomic resolution.
Abstract Nuclear magnetic resonance (NMR) of single spins have recently been detected by quantum sensors. However, the spectral resolution has been limited by the sensor’s relaxation to a few kHz at room temperature. This can be improved by using quantum memories, at the expense of sensitivity. In contrast, classical signals can be measured with exceptional spectral resolution by using continuous measurement techniques, without compromising sensitivity. When applied to single-spin NMR, it is critical to overcome the impact of back action inherent of quantum measurement. Here we report sequential weak measurements on a single 13C nuclear spin. The back-action causes the spin to undergo a quantum dynamics phase transition from coherent trapping to coherent oscillation. Single-spin NMR at room-temperature with a spectral resolution of 3.8 Hz is achieved. These results enable the use of measurement-correlation schemes for the detection of very weakly coupled single spins.