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arXiv:2509.11854 · Nature Communications

Readout of a solid state spin ensemble at the projection noise limit

Rouven Maier, Cheng-I Ho, Andrej Denisenko, Marina Davydova, Peter Knittel, Jörg Wrachtrup, Vadim Vorobyov

Published May 4, 2026• 1 citation
arXivHTMLPDF

Abstract

Abstract Spin ensembles are central to quantum science, from fundamental physics searches to magnetic resonance spectroscopy and quantum sensing. The standard quantum limit for their performance is ultimately posed by spin projection noise, yet solid-state implementations have so far been limited by significantly larger photon shot noise. Here, we demonstrate a direct quantum non-demolition readout of a mesoscopic ensemble of nitrogen-vacancy (NV) centers in diamond that surpasses the photon shot-noise limit and approaches the intrinsic spin projection noise. By stabilizing the intrinsic 14 N nuclear spin bath at high magnetic fields and employing a repetitive nuclear-assisted spin readout, we achieve a noise reduction of 3.8 dB below the thermal projection noise level. This enables direct access to the intrinsic fluctuations of the spin ensemble, allowing us to directly observe the signatures of correlated spin states. Our results establish projection noise-limited readout as a practical tool for solid-state quantum sensors, opening pathways to quantum-enhanced metrology, direct detection of many-body correlations, and the implementation of spin squeezing in mesoscopic solid-state ensembles.

DOI
10.1038/s41467-026-72721-0

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Abstract Spin ensembles are central to quantum science, from fundamental physics searches to magnetic resonance spectroscopy and quantum sensing. The standard quantum limit for their performance is ultimately posed by spin projection noise, yet solid-state implementations have so far been limited by significantly larger photon shot noise. Here, we demonstrate a direct quantum non-demolition readout of a mesoscopic ensemble of nitrogen-vacancy (NV) centers in diamond that surpasses the photon shot-noise limit and approaches the intrinsic spin projection noise. By stabilizing the intrinsic 14 N nuclear spin bath at high magnetic fields and employing a repetitive nuclear-assisted spin readout, we achieve a noise reduction of 3.8 dB below the thermal projection noise level. This enables direct access to the intrinsic fluctuations of the spin ensemble, allowing us to directly observe the signatures of correlated spin states. Our results establish projection noise-limited readout as a practical tool for solid-state quantum sensors, opening pathways to quantum-enhanced metrology, direct detection of many-body correlations, and the implementation of spin squeezing in mesoscopic solid-state ensembles.
The nitrogen-vacancy (NV) center in diamond is a prominent quantum-sensing platform. Combining readout at the quantum projection noise limit with strong dipolar interactions promises substantial gains in sensitivity. However, experimentally accessing this regime has remained a longstanding challenge. In this work, we demonstrate quantum-projection-noise-resolved readout of a strongly-interacting, two-dimensional ensemble of NV centers. Our approach leverages repetitive readout via the NV's intrinsic 15^{15}15N nuclear memory at a moderate magnetic field (∼0.3\sim 0.3∼0.3 T), improving the readout fidelities by nearly an order of magnitude. This enables us to directly resolve the quantum projection noise of a coherent spin state and to watch the ensemble's intrinsic dipolar interactions shear this noise into an anisotropic profile. Our results open the door to direct measurements of spin squeezing and entanglement-enhanced sensing in the solid state.
Solid-state quantum sensors based on ensembles of nitrogen-vacancy (NV) centers in diamond have emerged as powerful platforms for high-precision metrology. Coupling the NV ensemble to a microwave cavity mode in a cavity quantum electrodynamics (cQED) configuration enables spin readout that surpasses the limitations of conventional optical detection, achieving sub-picotesla magnetic sensitivities. However, existing continuous-wave cQED approaches remain far from the intrinsic spin-projection-noise limit due to spin saturation and power broadening. Here, we introduce a dispersive cQED readout technique to overcome these fundamental limitations in NV ensemble sensing. We develop a comprehensive theoretical framework describing the dispersive interaction and analyze the time-domain dynamics of a strongly-coupled NV-cavity system. Our results indicate near-unity inverse readout fidelity and femtotesla-level sensitivity using a commercially available diamond NV ensemble. Importantly, the dispersive readout exhibits a distinct sensitivity scaling that improves as 1/N with increasing number of spins N, providing a practical pathway toward approaching the standard quantum limit for solid-state spin-ensemble sensors.
Quantum projection noise is the fundamental noise source for the population measurement of spin ensembles. While projection-noise-limited measurements have been extensively studied in atomic systems, corresponding experiments on solid-state spin ensembles remain challenging due to dominant classical readout noise. Here, we report direct measurement of the quantum projection noise of mesoscopic ensembles of nitrogen-vacancy (NV) spin defects at room temperature. Our experiment is enabled by a high optically-detected magnetic resonance (ODMR) contrast of over 20% for a single crystallographic orientation of the defect spins, obtained by combining polarization-selective optical excitation with spin-to-charge conversion. We use our protocol to demonstrate projection noise measurements and spin counting from nanoscale NV ensembles of up to 43 spins. We further demonstrate that the protocol allows for significant gains in sensitivity for magnetometry applications without need for cryogenic operation or high bias magnetic fields.
We theoretically explore protocols for measuring the spin polarization of an ensemble of solid-state spins, with precision at or below the standard quantum limit. Such measurements in the solid-state are challenging, as standard approaches based on optical fluorescence are often limited by poor readout fidelity. Indirect microwave resonator-mediated measurements provide an attractive alternative, though a full analysis of relevant sources of measurement noise is lacking. In this work we study dispersive readout of an inhomogeneously broadened spin ensemble via coupling to a driven resonator measured via homodyne detection. We derive generic analytic conditions for when the homodyne measurement can be limited by the fundamental spin-projection noise, as opposed to microwave-drive shot noise or resonator phase noise. By studying fluctuations of the measurement record in detail, we also propose an experimental protocol for directly detecting spin squeezing, i.e. a reduction of the spin ensemble's intrinsic projection noise from entanglement. Our protocol provides a method for benchmarking entangled states for quantum-enhanced metrology.
Overcoming poor readout is an increasingly urgent challenge for devices based on solid-state spin defects, particularly given their rapid adoption in quantum sensing, quantum information, and tests of fundamental physics. However, in spite of experimental progress in specific systems, solid-state spin sensors still lack a universal, high-fidelity readout technique. Here we demonstrate high-fidelity, room-temperature readout of an ensemble of nitrogen-vacancy centers via strong coupling to a dielectric microwave cavity, building on similar techniques commonly applied in cryogenic circuit cavity quantum electrodynamics. This strong collective interaction allows the spin ensemble's microwave transition to be probed directly, thereby overcoming the optical photon shot noise limitations of conventional fluorescence readout. Applying this technique to magnetometry, we show magnetic sensitivity approaching the Johnson-Nyquist noise limit of the system. Our results pave a clear path to achieve unity readout fidelity of solid-state spin sensors through increased ensemble size, reduced spin-resonance linewidth, or improved cavity quality factor.
Abstract Solid state spins have demonstrated significant potential in quantum sensing with applications including fundamental science, medical diagnostics and navigation. The quantum sensing schemes showing best performance under ambient conditions all utilize microwave or radio-frequency driving, which poses a significant limitation for miniaturization, energy efficiency, and non-invasiveness of quantum sensors. We overcome this limitation by demonstrating a purely optical approach to coherent quantum sensing. Our scheme involves the 15N nuclear spin of the Nitrogen-Vacancy (NV) center in diamond as a sensing resource, and exploits NV spin dynamics in oblique magnetic fields near the NV’s excited state level anti-crossing to optically pump the nuclear spin into a quantum superposition state. We demonstrate all-optical free-induction decay measurements—the key protocol for low-frequency quantum sensing—both on single spins and spin ensembles. Our results pave the way for highly compact quantum sensors to be employed for magnetometry or gyroscopy applications in challenging environments.