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arXiv:2406.17142 · Nature Communications

Microwave quantum heterodyne sensing using a continuous concatenated dynamical decoupling protocol

Charlie J. Patrickson, Valentin Haemmerli, Shi Guo, A. J. Ramsay, Isaac John Luxmoore

Published May 12, 2025• 4 citations
arXivHTMLPDF

Abstract

Abstract By sequentially recording the phase of an AC signal relative to an external clock, quantum heterodyne schemes have recorded MHz and GHz signals with Fourier-limited precision. However, in systems with large inhomogeneous broadening, existing heterodyne protocols provide limited protection of the spin coherence, impacting amplitude sensitivity. Here, we use a continuous microwave scheme that extends spin coherence towards the effective $${T}_{2}\approx \frac{1}{2}{T}_{1}$$ T 2 ≈ 1 2 T 1 limit and resolves the frequency, amplitude and phase of MHz to GHz magnetic fields. In an ensemble of boron vacancies in hexagonal boron nitride the scheme achieves an amplitude sensitivity of $$\eta \approx 3-5\,\mu {{{\rm{T}}}}/\sqrt{{{{\rm{Hz}}}}}$$ η ≈ 3 − 5 μ T / Hz and phase sensitivity of $${\eta }_{\phi }\approx 0.076\,{{{\rm{rads}}}}/\sqrt{{{{\rm{Hz}}}}}$$ η ϕ ≈ 0.076 rads / Hz . We demonstrate that the scheme is compatible with quantum heterodyne detection, recording a GHz signal with a resolution < 1 Hz and SNR of 235 over a 10 s measurement. Achieving this performance in a two-dimensional material platform could have broad applications in probing nanoscale condensed matter systems.

DOI
10.1038/s41467-025-59148-9

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Abstract By sequentially recording the phase of an AC signal relative to an external clock, quantum heterodyne schemes have recorded MHz and GHz signals with Fourier-limited precision. However, in systems with large inhomogeneous broadening, existing heterodyne protocols provide limited protection of the spin coherence, impacting amplitude sensitivity. Here, we use a continuous microwave scheme that extends spin coherence towards the effective T2≈12T1{T}_{2}\approx \frac{1}{2}{T}_{1}T2​≈21​T1​ T 2 ≈ 1 2 T 1 limit and resolves the frequency, amplitude and phase of MHz to GHz magnetic fields. In an ensemble of boron vacancies in hexagonal boron nitride the scheme achieves an amplitude sensitivity of η≈3−5 μT/Hz\eta \approx 3-5\,\mu {{{\rm{T}}}}/\sqrt{{{{\rm{Hz}}}}}η≈3−5μT/Hz​ η ≈ 3 − 5 μ T / Hz and phase sensitivity of ηϕ≈0.076 rads/Hz{\eta }_{\phi }\approx 0.076\,{{{\rm{rads}}}}/\sqrt{{{{\rm{Hz}}}}}ηϕ​≈0.076rads/Hz​ η ϕ ≈ 0.076 rads / Hz . We demonstrate that the scheme is compatible with quantum heterodyne detection, recording a GHz signal with a resolution < 1 Hz and SNR of 235 over a 10 s measurement. Achieving this performance in a two-dimensional material platform could have broad applications in probing nanoscale condensed matter systems.
Abstract Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However, the spectral resolution in such protocols is ultimately limited by the sensor lifetime. Here, we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally, we achieve a spectral resolution below 1 Hz for a 4 GHz signal far below the sensor lifetime limit of kilohertz. Furthermore, we show control over the interaction of the MW-field with the two-level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to improved sensitivity, the Floquet dynamics allow robust control, independent from the system’s resonance frequency. Our work is important for future studies in sensing weak microwave signals in a wide frequency range with high spectral resolution.
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Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However, the spectral resolution in such protocols is ultimately limited by the sensor lifetime. Here, we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally, we achieve a spectral resolution below 1 Hz for a 4 GHz signal far below the sensor lifetime limit of kilohertz. Furthermore, we show control over the interaction of the MW-field with the two-level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to improved sensitivity, the Floquet dynamics allow robust control, independent from the system's resonance frequency. Our work is important for future studies in sensing weak microwave signals in a wide frequency range with high spectral resolution.
Quantum sensors using solid-state spin defects excel in the detection of radiofrequency (RF) fields, serving various applications in communication, ranging, and sensing. For this purpose, pulsed dynamical decoupling (PDD) protocols are typically applied, which enhance sensitivity to RF signals. However, these methods are limited to frequencies of a few megahertz, which poses a challenge for sensing higher frequencies. We introduce an alternative approach based on a continuous dynamical decoupling (CDD) scheme involving dressed states of nitrogen vacancy (NV) ensemble spins driven within a microwave resonator. We compare the CDD methods to established PDD protocols and demonstrate the detection of RF signals up to ~85 MHz, about ten times the current limit imposed by the PDD approach under identical conditions. Implementing the CDD method in a heterodyne/synchronized protocol combines the high-frequency detection with high spectral resolution. This advancement extends to various domains requiring detection in the high frequency (HF) and very high frequency (VHF) ranges of the RF spectrum, including spin sensor-based magnetic resonance spectroscopy at high magnetic fields.
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 high-resolution magnetic spectroscopy, the QFM-CASR protocol extends the signal frequency range by more than an order of magnitude, enabling applications in radio frequency (RF) and MW signal microscopy and analysis, as well as tesla-scale nuclear magnetic resonance (NMR) spectroscopy of small samples.
Quantum relaxometry is one of the most successful applications of nitrogen-vacancy (NV) centers in diamond and, more broadly, solid-state spin qubits, enabling ultrasensitive detection of magnetic noise and paramagnetic species via measurements of the spin-lattice relaxation time T1T_1T1​. Conventional pulsed protocols, however, probe T1T_1T1​ efficiently only over a limited temporal range, which restricts the scope and throughput of the technique. Here we introduce a continuous-wave quantum relaxometry protocol that operates in the frequency domain. By measuring the frequency response of the optically detected magnetic resonance signal under low-frequency microwave amplitude modulation, we extract T1T_1T1​ from the characteristic response time of the spin system. The method enables efficient T1T_1T1​ measurements spanning more than three orders of magnitude -- directly demonstrated from 60 μμμs to 200 ms in our experiments -- across a broad temperature range and under substantial ensemble inhomogeneity. We further show that this protocol enables quantitative relaxometry-based sensing in nanodiamonds, achieving a substantial speed-up over the pulsed methods and offering a practical approach to optimizing nanodiamond size for enhanced sensitivity.