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arXiv:2506.20416 · Physical Review Letters

Overcoming Frequency Resolution Limits Using a Solid-State Spin Quantum Sensor

Qingyun Cao, Genko T. Genov, Yaoming Chu, Jianming Cai, Yu Liu, Alex Retzker, Fedor Jelezko

Published Nov 24, 2025• 0 citations
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Abstract

The ability to determine precisely the separation of two frequencies is fundamental to spectroscopy, yet the resolution limit poses a critical challenge: distinguishing two incoherent signals becomes impossible when their frequencies are sufficiently close. Here, we demonstrate a simple and powerful approach, dubbed superresolution quantum sensing, which experimentally resolves two nearly identical incoherent signals using a solid-state spin quantum sensor. By carefully choosing interrogation times that satisfy the superresolution condition, we eliminate quantum projection noise, overcoming the vanishing distinguishability of signals with near-identical frequencies. This leads to improved resolution, which scales as t^{-2} in comparison to the standard t^{-1} scaling. Together with a greatly reduced classical readout noise assisted by a nuclear spin, we are able to achieve sub-kHz resolution with a signal detection time of 80 μs. Our results highlight the potential of quantum sensing to overcome conventional frequency resolution limitations, with broad implications for precision measurements.

DOI
10.1103/llfg-s4rr

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The ability to determine precisely the separation of two frequencies is fundamental to spectroscopy, yet the resolution limit poses a critical challenge: distinguishing two incoherent signals becomes impossible when their frequencies are sufficiently close. Here, we demonstrate a simple and powerful approach, dubbed superresolution quantum sensing, which experimentally resolves two nearly identical incoherent signals using a solid-state spin quantum sensor. By carefully choosing interrogation times that satisfy the superresolution condition, we eliminate quantum projection noise, overcoming the vanishing distinguishability of signals with near-identical frequencies. This leads to improved resolution, which scales as t^{-2} in comparison to the standard t^{-1} scaling. Together with a greatly reduced classical readout noise assisted by a nuclear spin, we are able to achieve sub-kHz resolution with a signal detection time of 80 μs. Our results highlight the potential of quantum sensing to overcome conventional frequency resolution limitations, with broad implications for precision measurements.
The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. While for static signals the main figure of merit is sensitivity, for time dependent signals it is spectral resolution, i.e. the ability to resolve two different frequencies. Here we study this problem, and develop new superresolution methods that rely on quantum features. We first formulate a general criterion for superresolution in quantum problems. Inspired by this, we show that quantum detectors can resolve two frequencies from incoherent segments of the signal, irrespective of their separation, in contrast to what is known about classical detection schemes. The main idea behind these methods is to overcome the vanishing distinguishability in resolution problems by nullifying the projection noise.
Resolving signals with closely spaced frequencies is central to applications in communications, spectroscopy and sensing. Recent results have shown that quantum sensing protocols can exhibit superresolution, the ability to discriminate between spectral lines with arbitrarily small frequency separation. Here, we revisit this problem from the perspective of quantum control theory, utilizing the filter function formalism to derive general, analytic conditions on quantum control protocols for achieving superresolution. Building on these conditions, we develop an optimal control framework, the utility of which is demonstrated through numerical identification of superresolution control protocols in the presence of realistic, experimentally-relevant constraints. We further extend our results to entangled initial states and assess their potential advantage. Our approach is broadly applicable to a wide variety of quantum sensing platforms, and it provides a systematic path to discover novel protocols that surpass conventional resolution limits in these systems.
Abstract The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. While for static signals the main figure of merit is sensitivity, for time dependent signals it is spectral resolution, i.e. the ability to resolve two different frequencies. Here we study this problem, and develop new superresolution methods that rely on quantum features. We first formulate a general criterion for superresolution in quantum problems. Inspired by this, we show that quantum detectors can resolve two frequencies from incoherent segments of the signal, irrespective of their separation, in contrast to what is known about classical detection schemes. The main idea behind these methods is to overcome the vanishing distinguishability in resolution problems by nullifying the projection noise.
Recent advances in engineering and control of nanoscale quantum sensors have opened new paradigms in precision metrology. Unfortunately, hardware restrictions often limit the sensor performance. In nanoscale magnetic resonance probes, for instance, finite sampling times greatly limit the achievable sensitivity and spectral resolution. Here we introduce a technique for coherent quantum interpolation that can overcome these problems. Using a quantum sensor associated with the nitrogen vacancy center in diamond, we experimentally demonstrate that quantum interpolation can achieve spectroscopy of classical magnetic fields and individual quantum spins with orders of magnitude finer frequency resolution than conventionally possible. Not only is quantum interpolation an enabling technique to extract structural and chemical information from single biomolecules, but it can be directly applied to other quantum systems for superresolution quantum spectroscopy.
Quantum spectroscopy with single two-level systems has considerably improved our ability to detect weak signals. Recently it was realized that for classical signals, precision and resolution of quantum spectroscopy is limited mainly by coherence of the signal and the stability of the clock used to measure time. The coherence time of the quantum probe, which can be significantly shorter, is not a major limiting factor in resolution measurements. Here, we address a similar question for spectroscopy of quantum signals, for example, a quantum sensor is used to detect a single nuclear spin. We present and analyze a novel correlation spectroscopy technique with performance that is limited by the coherence time of the target spins and the stability of the clock.
Abstract Quantum systems composed of solid-state electronic spins can be sensitive detectors of narrowband magnetic fields. A prominent example is the nitrogen-vacancy (NV) center in diamond, which has been employed for magnetic spectroscopy with high spatial and spectral resolution. However, NV-diamond spectroscopy protocols are typically based on dynamical decoupling sequences, which are limited to low-frequency signals (≲ 20 MHz) due to the technical requirements on microwave (MW) pulses used to manipulate NV electronic spins. In this work, we experimentally demonstrate a high-resolution magnetic spectroscopy protocol that integrates a quantum frequency mixing (QFM) effect in a dense NV ensemble with coherently averaged synchronized readout (CASR) to provide both a wide range of signal frequency detection and sub-Hz spectral resolution. We assess the sensitivity of this QFM-CASR protocol across a frequency range of 10 MHz to 4 GHz. By measuring the spectra of multi-frequency signals near 0.6, 2.4 and 4 GHz, we demonstrate sub-Hz spectral resolution with a nT-scale noise floor for the target signal, and precise phase measurement with error <1°. Compared to state-of-the-art NV-diamond techniques for narrowband magnetic spectroscopy, the QFM-CASR protocol greatly extends the detectable frequency range, enabling applications in high-frequency radio frequency (RF) and MW signal microscopy and analysis, as well as tesla-scale nuclear magnetic resonance (NMR) spectroscopy of small samples.