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arXiv:2606.14437

Spin counting via projection noise measurement of mesoscopic solid-state spin ensemble

Lorenzo Bechelli, Konstantin Herb, Laura Alicia Völker, Christian L. Degen

quant-phSubmitted Jun 12, 2026• Announced Jun 15, 2026
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Abstract

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.

Comments
7 pages, 4 figures

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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.
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.
Efficient readout of individual electronic spins associated with atomlike impurities in the solid state is essential for applications in quantum information processing and quantum metrology. We demonstrate a new method for efficient spin readout of nitrogen-vacancy (NV) centers in diamond. The method is based on conversion of the electronic spin state of the NV to a charge-state distribution, followed by single-shot readout of the charge state. Conversion is achieved through a spin-dependent photoionization process in diamond at room temperature. Using NVs in nanofabricated diamond beams, we demonstrate that the resulting spin readout noise is within a factor of 3 of the spin projection noise level. Applications of this technique for nanoscale magnetic sensing are discussed.
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.
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.
We demonstrate the optical readout of ensembles of nitrogen-vacancy (NV) center spins in a bulk diamond sample via spin-to-charge conversion. A high power 594 nm laser is utilized to selectively ionize these paramagnetic defects in the mS=0 spin state with a contrast of up to 12%. In comparison to the conventional 520 nm spin readout, the spin-to-charge-conversion-based readout provides a higher signal-to-noise ratio, with tenfold sensing measurement speedup for millisecond long pulse sequences. This level of performance was achieved for an NV− ionization of only 25%, limited by the ionization and readout laser powers. These observations pave the way to a range of high-sensitivity metrology applications where the use of NV− ensembles in bulk diamond has proven useful, including sensing and imaging of target materials overlaid on the diamond surface.