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
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.
AI Impact Assessments
(1 model)Scientific Impact Assessment: Precision Hyperfine Spectroscopy of an Individual Nuclear-Spin-9/2
1. Core Contribution
This paper demonstrates single-nucleus NMR spectroscopy of an individual 93Nb (I=9/2) impurity in CaWO4, achieved by using a proximal Er3+ paramagnetic center as a nanoscale magnetic sensor detected via microwave photon counting at 10 mK. The key novelties are threefold: (1) complete characterization of the quadrupolar tensor of a single nuclear spin, enabling chemical identification and structural determination of the 93Nb insertion site; (2) discovery of a spin-dependent quadrupole (SDQ) interaction—a coupling between the Er3+ electron spin state and the 93Nb nuclear quadrupole, attributed partly to a spin-dependent electrostatic interaction; and (3) the first solid-state observation of what appears to be a nuclear hexadecapolar (I4z) interaction term, measured with ~10 mHz spectral resolution using a correlated echo technique.
2. Methodological Rigor
The experimental methodology is exceptionally thorough and well-documented. The authors employ a sophisticated toolkit: Purcell-enhanced radiative decay into a superconducting resonator, single microwave photon detection (SMPD), stimulated Raman driving for NMR transitions, dynamic nuclear polarization for state preparation and bath polarization, and interleaved Ramsey/echo sequences for precision frequency extraction.
The spectral resolution hierarchy is impressive: ~30 Hz for excited-state measurements (limited by Er3+ relaxation), ~1 Hz for ground-state Ramsey (limited by magnetic drift), and ~10 mHz for differential frequency measurements via correlated echo sequences (where common-mode magnetic noise cancels). The bootstrap uncertainty analysis is carefully performed, and the reduced chi-squared values (~1.0–1.2) for their Hamiltonian fits indicate appropriate model complexity.
The identification of 93Nb via gyromagnetic ratio comparison, site assignment through angular-dependent hyperfine measurements, and DFT validation of the quadrupolar tensor (Cq,DFT = 22.7 MHz vs. measured 19.3 MHz; ηDFT = 0.76 vs. measured 0.77) provide strong cross-validation. The MCMC fitting procedure with posterior distributions is statistically rigorous.
One concern is the crystal-field Hamiltonian used for pseudo-quadrupole estimates assumes S4 symmetry, which is explicitly broken by the nearby Nb impurity. The authors acknowledge this but proceed regardless, which introduces systematic uncertainty in the pseudo-quadrupole and pseudo-hexadecapole calculations.
3. Potential Impact
Single-molecule structural analysis: The ability to chemically identify an unknown atomic impurity and determine its precise position (0.57 nm from Er3+) and complete quadrupolar tensor from a single nucleus represents a step toward atomic-resolution structural determination—a longstanding goal of nanoscale magnetic resonance.
Fundamental nuclear physics: The observation of a hexadecapolar term (C4/2π = 9.6 Hz), if confirmed as arising from the nuclear hexadecapolar moment coupling to the crystalline electric field third derivative, would constitute the first measurement of this fourth-order nuclear multipole interaction. This has implications for nuclear structure physics, particularly for understanding nuclear deformation in heavy nuclei.
New spin-spin coupling mechanism: The spin-dependent quadrupole (Qsdq/2π = 66 Hz), potentially arising from electrostatic coupling between the Er3+ spin-dependent electric dipole and the 93Nb nuclear quadrupole, represents a previously unobserved type of electron-nuclear interaction. This could be relevant for understanding spin Hamiltonians in metallic paramagnetic centers, lanthanide complexes, and molecular magnets.
Quantum sensing and computing: The demonstrated control over a 10-dimensional nuclear spin Hilbert space, with coherence times exceeding 300 ms after bath polarization, is relevant for qudit-based quantum information processing and enhanced magnetic sensing using Schrödinger cat states.
4. Timeliness & Relevance
This work addresses a frontier in single-spin magnetic resonance, building on the group's recent demonstrations of single-spin detection via microwave photon counting (Nature 2021, 2023) and nuclear spin control (Science Advances 2025). It competes with and complements NV-center-based approaches for single-nuclear-spin spectroscopy (Taminiau group, Delft) and silicon donor experiments (Morello group, UNSW). The microwave photon counting approach offers advantages in terms of the variety of paramagnetic systems that can be studied, as it only requires long T1 at millikelvin temperatures.
The search for nuclear hexadecapolar interactions has a decades-long history with inconclusive results. Providing a viable solid-state platform for systematic study across different nuclei addresses a genuine gap.
5. Strengths & Limitations
Strengths:
Limitations:
Overall Assessment: This is a tour-de-force experiment that pushes single-spin magnetic resonance spectroscopy to unprecedented precision, yielding genuinely new physics. The potential discovery of a nuclear hexadecapolar interaction and a new electrostatic electron-nuclear coupling mechanism, if confirmed by follow-up studies, would have lasting impact across magnetic resonance, quantum information, and nuclear physics.
Generated May 5, 2026
Comparison History (30)
Paper 1 demonstrates a groundbreaking experimental achievement in single-spin magnetic resonance spectroscopy, detecting an individual nuclear spin with Hertz-level resolution and discovering two previously unobserved terms in the spin Hamiltonian. This represents a fundamental advance in nanoscale sensing with broad implications for materials science, quantum information, and structural chemistry. Paper 2 offers valuable algorithmic improvements to QC-AFQMC but remains largely theoretical/incremental, demonstrated only on small model systems, and its practical impact depends on future fault-tolerant quantum hardware that doesn't yet exist.
Paper 1 demonstrates a groundbreaking experimental achievement in single-spin magnetic resonance spectroscopy, achieving Hertz-level spectral resolution on an individual nuclear spin and discovering two previously unobserved terms in the spin Hamiltonian (quadrupolar coupling and hexadecapolar term). This has broad implications for nanoscale sensing, quantum information, and materials characterization. Paper 2 presents a theoretical construction of exact quantum many-body scar states using a generalized MPS ansatz, which is a nice contribution to the active QMBS field but is more incremental in nature and narrower in scope.
Paper 1 demonstrates a technically demanding, high-resolution single-nucleus NMR measurement and extracts concrete physical parameters (site, position, full quadrupolar tensor) while also revealing previously unobserved Hamiltonian terms—clear novelty with strong methodological rigor and direct relevance to quantum sensing, materials characterization, and spin-based quantum tech. Paper 2 is conceptually interesting and potentially useful for quantum algorithms/cryptography, but its impact depends more on follow-up validation (noise robustness, security proofs, experimental feasibility). Overall, Paper 1 has more immediate, broadly actionable scientific payoff.
Paper 2 innovates on the Linear Combination of Unitaries (LCU), a fundamental primitive in quantum computing. By utilizing discarded ancilla outcomes for low-rank recovery and cryptography, it significantly improves algorithmic efficiency and opens new security applications. Its broad applicability across quantum algorithms and cryptography gives it a wider potential impact compared to Paper 1, which, while methodologically rigorous and experimentally impressive, is more specialized within the field of nanoscale spectroscopy and fundamental physics.
Paper 2 likely has higher impact: it demonstrates hertz-resolution NMR of an individual nuclear spin using a nanoscale quantum sensor, enabling atom-level structural/chemical inference and uncovering previously unobserved spin-Hamiltonian terms (quadrupole–electron coupling, hexadecapolar term). This is timely for quantum sensing, precision spectroscopy, and materials/chemistry characterization, with broad experimental applicability. Paper 1 is novel for many-body scar theory and exact MPS constructions, but its immediate real-world applications and cross-field reach are narrower and depend on subsequent adoption.
Paper 2 demonstrates groundbreaking experimental capabilities in single-spin magnetic resonance spectroscopy, achieving Hertz-level spectral resolution on an individual nuclear spin and discovering two previously unobserved terms in the spin Hamiltonian (spin-dependent quadrupolar coupling and nuclear hexadecapolar term). This has profound implications for nanoscale structural characterization, quantum sensing, and fundamental physics. Paper 1 improves entropic uncertainty relation bounds, which is technically valuable but incremental. Paper 2's experimental novelty, discovery of new physical phenomena, and broad applicability across quantum sensing, materials science, and fundamental physics give it substantially higher impact potential.
Paper 2 presents a major experimental breakthrough in single-spin magnetic resonance with Hertz resolution, offering tangible real-world applications in atomic-level structural and chemical analysis. Its discovery of unobserved spin Hamiltonian terms also advances fundamental physics. Paper 1, while theoretically rigorous, is highly specialized within quantum information theory and has a narrower immediate impact compared to the broader practical and interdisciplinary utility of Paper 2.
Paper 1 demonstrates a breakthrough in single-spin magnetic resonance spectroscopy, achieving Hertz-level spectral resolution of an individual nuclear spin and discovering two previously unobserved terms in the spin Hamiltonian. This has profound implications for nanoscale sensing, quantum computing, and materials characterization. Paper 2 improves entropic uncertainty relation bounds, which is technically valuable but incremental within quantum information theory. Paper 1's experimental novelty, discovery of new physical phenomena, and broad applicability across quantum sensing and materials science give it substantially higher impact potential.
Paper 1 presents a major experimental breakthrough in single-spin magnetic resonance spectroscopy, enabling atomic-level structural mapping and discovering new physical interactions. This has broad, tangible applications across quantum sensing, chemistry, and materials science. Paper 2 offers solid theoretical advances in quantum information theory, but its impact is likely confined to a narrower theoretical community. Thus, Paper 1 has higher potential for widespread scientific impact.
Paper 2 presents a significant experimental breakthrough in nanoscale NMR spectroscopy, achieving Hertz-level resolution on an individual nuclear spin. This enables non-invasive structural determination at the atomic level and reveals previously unobserved quantum interactions. Paper 1 offers a theoretical reformulation of a basic quantum algorithm, which, while useful for error analysis, lacks the broad, transformative real-world applications and fundamental physics discoveries demonstrated in Paper 2.