- Open Access
Robust gigahertz-range ac magnetometry with an ensemble of centers in diamond using concatenated continuous dynamical decoupling
Phys. Rev. Applied 26, 024018 – Published 10 August, 2026
DOI: https://doi.org/10.1103/8zf5-1zyj
Abstract
Subpicotesla level magnetometry has been demonstrated using negatively charged nitrogen-vacancy () centers in diamond by increasing the number of spins simultaneously used for sensing in an ensemble. However, such scale-up often introduces spatial inhomogeneities in detuning and control field amplitudes, which degrade sensitivity. Although several techniques have been utilized to overcome these challenges, including pulsed dynamical decoupling or shaped pulses, these are not generally compatible with the current state-of-the-art techniques for GHz-range ac magnetometry with ensembles, which are typically based on Rabi oscillations. In this work, we experimentally demonstrate GHz-range ac magnetometry using a large ensemble of centers under spatially inhomogeneous drive fields by employing concatenated continuous dynamical decoupling, which is designed for robustness against such imperfections. We compare its performance with the conventional direct Rabi method and show that the robust dressed states in our method extend significantly the measuring range to weaker signals in GHz-range ac magnetometry.
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References (94)
- C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
- A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. V. Borczyskowski, Scanning confocal optical microscopy and magnetic resonance on single defect centers, Science 276, 2012 (1997).
- G. Wolfowicz, F. J. Heremans, C. P. Anderson, S. Kanai, H. Seo, A. Gali, G. Galli, and D. D. Awschalom, Quantum guidelines for solid-state spin defects, Nat. Rev. Mater. 6, 906 (2021).
- H.-H. Fang, X.-J. Wang, X. Marie, and H.-B. Sun, Quantum sensing with optically accessible spin defects in van der Waals layered materials, Light Sci. Appl. 13, 303 (2024).
- J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, M. V. G. Dutt, E. Togan, A. S. Zibrov, A. Yacoby, R. L. Walsworth, and M. D. Lukin, Nanoscale magnetic sensing with an individual electronic spin in diamond, Nature (London) 455, 644 (2008).
- G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Bratschitsch, F. Jelezko, and J. Wrachtrup, Nanoscale imaging magnetometry with diamond spins under ambient conditions, Nature (London) 455, 648 (2008).
- S. Castelletto, C. T.-K. Lew, W.-X. Lin, and J.-S. Xu, Quantum systems in silicon carbide for sensing applications, Rep. Prog. Phys. 87, 014501 (2023).
- A. J. Healey, S. C. Scholten, T. Yang, J. A. Scott, G. J. Abrahams, I. O. Robertson, X. F. Hou, Y. F. Guo, S. Rahman, Y. Lu, M. Kianinia, I. Aharonovich, and J.-P. Tetienne, Quantum microscopy with van der Waals heterostructures, Nat. Phys. 19, 87 (2023).
- J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, High-sensitivity diamond magnetometer with nanoscale resolution, Nat. Phys. 4, 810 (2008).
- F. Casola, T. van der Sar, and A. Yacoby, Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond, Nat. Rev. Mater. 3, 1 (2018).
- D. Le Sage, K. Arai, D. R. Glenn, S. J. DeVience, L. M. Pham, L. Rahn-Lee, M. D. Lukin, A. Yacoby, A. Komeili, and R. L. Walsworth, Optical magnetic imaging of living cells, Nature (London) 496, 486 (2013).
- R. D. Allert, K. D. Briegel, and D. B. Bucher, Advances in nano- and microscale NMR spectroscopy using diamond quantum sensors, Chem. Commun. 58, 8165 (2022).
- J. Cai, F. Jelezko, N. Katz, A. Retzker, and M. B. Plenio, Long-lived driven solid-state quantum memory, New J. Phys. 14, 093030 (2012).
- A. Stark, N. Aharon, T. Unden, D. Louzon, A. Huck, A. Retzker, U. L. Andersen, and F. Jelezko, Narrow-bandwidth sensing of high-frequency fields with continuous dynamical decoupling, Nat. Commun. 8, 1105 (2017).
- A. J. Ramsay, R. Hekmati, C. J. Patrickson, S. Baber, D. R. M. Arvidsson-Shukur, A. J. Bennett, and I. J. Luxmoore, Coherence protection of spin qubits in hexagonal boron nitride, Nat. Commun. 14, 461 (2023).
- J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and R. L. Walsworth, Sensitivity optimization for NV-diamond magnetometry, Rev. Mod. Phys. 92, 015004 (2020).
- P. Wang, Z. Yuan, P. Huang, X. Rong, M. Wang, X. Xu, C. Duan, C. Ju, F. Shi, and J. Du, High-resolution vector microwave magnetometry based on solid-state spins in diamond, Nat. Commun. 6, 6631 (2015).
- P. Appel, M. Ganzhorn, E. Neu, and P. Maletinsky, Nanoscale microwave imaging with a single electron spin in diamond, New J. Phys. 17, 112001 (2015).
- A. Horsley, P. Appel, J. Wolters, J. Achard, A. Tallaire, P. Maletinsky, and P. Treutlein, Microwave device characterization using a widefield diamond microscope, Phys. Rev. Appl. 10, 044039 (2018).
- H. Zhang, Z. Li, C. Yang, R. Chai, Z. Ma, H. Guo, H. Wen, X. Li, J. Tang, and J. Liu, Frequency, intensity, and phase synchronous imaging of microwave with nitrogen-vacancy center microscopy, IEEE Trans. Instrum. Meas. 73, 1 (2024).
- T. van der Sar, F. Casola, R. Walsworth, and A. Yacoby, Nanometre-scale probing of spin waves using single electron spins, Nat. Commun. 6, 7886 (2015).
- I. Bertelli, J. J. Carmiggelt, T. Yu, B. G. Simon, C. C. Pothoven, G. E. W. Bauer, Y. M. Blanter, J. Aarts, and T. van der Sar, Magnetic resonance imaging of spin-wave transport and interference in a magnetic insulator, Sci. Adv. 6, eabd3556 (2020).
- J. J. Carmiggelt, I. Bertelli, R. W. Mulder, A. Teepe, M. Elyasi, B. G. Simon, G. E. W. Bauer, Y. M. Blanter, and T. van der Sar, Broadband microwave detection using electron spins in a hybrid diamond-magnet sensor chip, Nat. Commun. 14, 490 (2023).
- J. W. Sidabras, J. Duan, M. Winkler, T. Happe, R. Hussein, A. Zouni, D. Suter, A. Schnegg, W. Lubitz, and E. J. Reijerse, Extending electron paramagnetic resonance to nanoliter volume protein single crystals using a self-resonant microhelix, Sci. Adv. 5, eaay1394 (2019).
- T. Wolf, P. Neumann, K. Nakamura, H. Sumiya, T. Ohshima, J. Isoya, and J. Wrachtrup, Subpicotesla diamond magnetometry, Phys. Rev. X 5, 041001 (2015).
- J. F. Barry, M. H. Steinecker, S. T. Alsid, J. Majumder, L. M. Pham, M. F. O’Keeffe, and D. A. Braje, Sensitive ac and dc magnetometry with nitrogen-vacancy-center ensembles in diamond, Phys. Rev. Appl. 22, 044069 (2024).
- B. Naydenov, F. Dolde, L. T. Hall, C. Shin, H. Fedder, L. C. L. Hollenberg, F. Jelezko, and J. Wrachtrup, Dynamical decoupling of a single-electron spin at room temperature, Phys. Rev. B 83, 081201(R) (2011).
- G. A. Álvarez, A. Ajoy, X. Peng, and D. Suter, Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath, Phys. Rev. A 82, 042306 (2010).
- M. H. Levitt, Composite pulses, Prog. Nucl. Magn. Reson. Spectrosc. 18, 61 (1986).
- I. Niemeyer, J. H. Shim, J. Zhang, D. Suter, T. Taniguchi, T. Teraji, H. Abe, S. Onoda, T. Yamamoto, T. Ohshima, J. Isoya, and F. Jelezko, Broadband excitation by chirped pulses: Application to single electron spins in diamond, New J. Phys. 15, 033027 (2013).
- G. T. Genov, Y. Ben-Shalom, F. Jelezko, A. Retzker, and N. Bar-Gill, Efficient and robust signal sensing by sequences of adiabatic chirped pulses, Phys. Rev. Res. 2, 033216 (2020).
- J. Scheuer, X. Kong, R. S. Said, J. Chen, A. Kurz, L. Marseglia, J. Du, P. R. Hemmer, S. Montangero, T. Calarco, B. Naydenov, and F. Jelezko, Precise qubit control beyond the rotating wave approximation, New J. Phys. 16, 093022 (2014).
- M. M. Müller, R. S. Said, F. Jelezko, T. Calarco, and S. Montangero, One decade of quantum optimal control in the chopped random basis, Rep. Prog. Phys. 85, 076001 (2022).
- H. M. Lim, G. T. Genov, R. Sailer, A. Fahrurrachman, M. A. Majidi, F. Jelezko, and R. S. Said, Efficiency of optimal control for noisy spin qubits in diamond, Phys. Rev. Appl. 24, 054064 (2025).
- C. D. Aiello, M. Hirose, and P. Cappellaro, Composite-pulse magnetometry with a solid-state quantum sensor, Nat. Commun. 4, 1419 (2013).
- Z. Wang, F. Kong, P. Zhao, Z. Huang, P. Yu, Y. Wang, F. Shi, and J. Du, Picotesla magnetometry of microwave fields with diamond sensors, Sci. Adv. 8, eabq8158 (2022).
- S. T. Alsid, J. M. Schloss, M. H. Steinecker, J. F. Barry, A. C. Maccabe, G. Wang, P. Cappellaro, and D. A. Braje, Solid-state microwave magnetometer with picotesla-level sensitivity, Phys. Rev. Appl. 19, 054095 (2023).
- T. Joas, A. M. Waeber, G. Braunbeck, and F. Reinhard, Quantum sensing of weak radio-frequency signals by pulsed Mollow absorption spectroscopy, Nat. Commun. 8, 964 (2017).
- J. Meinel, V. Vorobyov, B. Yavkin, D. Dasari, H. Sumiya, S. Onoda, J. Isoya, and J. Wrachtrup, Heterodyne sensing of microwaves with a quantum sensor, Nat. Commun. 12, 2737 (2021).
- J.-M. Cai, B. Naydenov, R. Pfeiffer, L. P. McGuinness, K. D. Jahnke, F. Jelezko, M. B. Plenio, and A. Retzker, Robust dynamical decoupling with concatenated continuous driving, New J. Phys. 14, 113023 (2012).
- I. Cohen, N. Aharon, and A. Retzker, Continuous dynamical decoupling utilizing time-dependent detuning, Fortschritte Phys. 65, 1600071 (2017).
- D. Farfurnik, N. Aharon, I. Cohen, Y. Hovav, A. Retzker, and N. Bar-Gill, Experimental realization of time-dependent phase-modulated continuous dynamical decoupling, Phys. Rev. A 96, 013850 (2017).
- G. Wang, Y.-X. Liu, and P. Cappellaro, Coherence protection and decay mechanism in qubit ensembles under concatenated continuous driving, New J. Phys. 22, 123045 (2020).
- G. Wang, Y.-X. Liu, and P. Cappellaro, Observation of the high-order Mollow triplet by quantum mode control with concatenated continuous driving, Phys. Rev. A 103, 022415 (2021).
- J. Teissier, A. Barfuss, and P. Maletinsky, Hybrid continuous dynamical decoupling: A photon-phonon doubly dressed spin, J. Opt. 19, 044003 (2017).
- N. Staudenmaier, S. Schmitt, L. P. McGuinness, and F. Jelezko, Phase-sensitive quantum spectroscopy with high-frequency resolution, Phys. Rev. A 104, L020602 (2021).
- A. Salhov, Q. Cao, J. Cai, A. Retzker, F. Jelezko, and G. Genov, Protecting quantum information via destructive interference of correlated noise, Phys. Rev. Lett. 132, 223601 (2024).
- Alon Salhov, Sagi Nechushtan, and Alex Retzker, Optimally driven dressed qubits, arXiv:2601.19719.
- C. J. Patrickson, S. Baber, B. B. Gaál, A. J. Ramsay, and I. J. Luxmoore, High frequency magnetometry with an ensemble of spin qubits in hexagonal boron nitride, npj Quantum Inf. 10, 5 (2024).
- C. J. Patrickson, V. Haemmerli, S. Guo, A. J. Ramsay, and I. J. Luxmoore, Microwave quantum heterodyne sensing using a continuous concatenated dynamical decoupling protocol, Nat. Commun. 16, 4380 (2025).
- G. T. Genov, N. Aharon, F. Jelezko, and A. Retzker, Mixed dynamical decoupling, Quantum Sci. Technol. 4, 035010 (2019).
- H. De Raedt, B. Barbara, S. Miyashita, K. Michielsen, S. Bertaina, and S. Gambarelli, Quantum simulations and experiments on Rabi oscillations of spin qubits: Intrinsic vs extrinsic damping, Phys. Rev. B 85, 014408 (2012).
- A. Stark, N. Aharon, A. Huck, H. A. R. El-Ella, A. Retzker, F. Jelezko, and U. L. Andersen, Clock transition by continuous dynamical decoupling of a three-level system, Sci. Rep. 8, 14807 (2018).
- N. R. S. Reddy, N. B. Manson, and E. R. Krausz, Two-laser spectral hole burning in a colour centre in diamond, J. Lumin. 38, 46 (1987).
- E. van Oort, N. B. Manson, and M. Glasbeek, Optically detected spin coherence of the diamond N-V centre in its triplet ground state, J. Phys. C: Solid State Phys. 21, 4385 (1988).
- M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, The nitrogen-vacancy colour centre in diamond, Phys. Rep. 528, 1 (2013).
- F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, Observation of coherent oscillations in a single electron spin, Phys. Rev. Lett. 92, 076401 (2004).
- K. Sasaki, Y. Monnai, S. Saijo, R. Fujita, H. Watanabe, J. Ishi-Hayase, K. M. Itoh, and E. Abe, Broadband, large-area microwave antenna for optically detected magnetic resonance of nitrogen-vacancy centers in diamond, Rev. Sci. Instrum. 87, 053904 (2016).
- O. Rezinkin, M. Rezinkina, T. Kitamura, R. Paul, and F. Jelezko, Uniform microwave field formation for control of ensembles of negatively charged nitrogen vacancy in diamond, Rev. Sci. Instrum. 95, 104706 (2024).
- H. Fedder, F. Dolde, F. Rempp, T. Wolf, P. Hemmer, F. Jelezko, and J. Wrachtrup, Towards T1-limited magnetic resonance imaging using Rabi beats, Appl. Phys. B 102, 497 (2011).
- D. W. Allan, Should the classical variance be used as a basic measure in standards metrology?, IEEE Trans. Instrum. Meas. IM-36, 646 (1987).
- N. F. Zhang, Allan variance of time series models for measurement data, Metrologia 45, 549 (2008).
- E. Benkler, C. Lisdat, and U. Sterr, On the relation between uncertainties of weighted frequency averages and the various types of Allan deviations, Metrologia 52, 565 (2015).
- K. Sasaki, T. Taniguchi, and K. Kobayashi, Nitrogen isotope effects on boron vacancy quantum sensors in hexagonal boron nitride, Appl. Phys. Express 16, 095003 (2023).
- F. M. Stürner, A. Brenneis, J. Kassel, U. Wostradowski, R. Rölver, T. Fuchs, K. Nakamura, H. Sumiya, S. Onoda, J. Isoya, and F. Jelezko, Compact integrated magnetometer based on nitrogen-vacancy centres in diamond, Diam. Relat. Mater. 93, 59 (2019).
- F. M. Stürner, A. Brenneis, T. Buck, J. Kassel, R. Rölver, T. Fuchs, A. Savitsky, D. Suter, J. Grimmel, S. Hengesbach, M. Förtsch, K. Nakamura, H. Sumiya, S. Onoda, J. Isoya, and F. Jelezko, Integrated and portable magnetometer based on nitrogen-vacancy ensembles in diamond, Adv. Quantum Technol. 4, 2000111 (2021).
- D. Yudilevich, A. Salhov, I. Schaefer, K. Herb, A. Retzker, and A. Finkler, Coherent manipulation of nuclear spins in the strong driving regime, New. J. Phys. 25, 113042 (2023).
- D. Deshmukh, R. B. González, R. Sailer, F. Jelezko, R. S. Said, and J. Ankerhold, Observation of period doubling and higher multiplicities in a driven single-spin system, arXiv:2507.18387.
- L. Shao, M. Zhang, M. Markham, A. M. Edmonds, and M. Lončar, Diamond radio receiver: Nitrogen-vacancy centers as fluorescent transducers of microwave signals, Phys. Rev. Appl. 6, 064008 (2016).
- B. Yang, Y. Dong, Z.-Z. Hu, G.-Q. Liu, Y.-J. Wang, and G.-X. Du, Noninvasive imaging method of microwave near field based on solid-state quantum sensing, IEEE Trans. Microw. Theory Tech. 66, 2276 (2018).
- G.-B. Chen, B.-X. Gu, W.-H. He, Z.-G. Guo, and G.-X. Du, Vectorial near-field characterization of microwave device by using micro diamond based on tapered fiber, IEEE J. Quantum Electron. 56, 1 (2020).
- X.-D. Chen, H.-X. Zang, Y. Dong, Z.-W. Liu, M.-Q. Ma, S.-C. Zhang, Y. Zheng, G.-C. Guo, and F.-W. Sun, Microwave remote sensing with hybrid quantum receiver, ACS Nano 18, 27393 (2024).
- X. Jia, Y. Qin, Z. Luo, S. Zhu, X. Li, and H. Guo, Near-field microwave imaging method of monopole antennas based on nitrogen-vacancy centers in diamond, Micromachines 15, 679 (2024).
- I. O. Robertson, B. C. Johnson, G. Thalassinos, S. C. Scholten, K. J. Rietwyk, B. C. Gibson, J.-P. Tetienne, and D. A. Broadway, Radiofrequency receiver based on isotropic solid-state spins, ACS Photonics 12, 581 (2025).
- Q. Zeng, J. Zhang, M. Gupta, Z. Chu, and K. Huang, Towards ubiquitous radio access using nanodiamond based quantum receivers, Commun. Eng. 4, 1 (2025).
- K. Ogawa, M. Tsukamoto, Y. Mori, D. Takafuji, J. Shiogai, K. Ueda, J. Matsuno, K. Sasaki, and K. Kobayashi, Wideband wide-field imaging of spin-wave propagation using diamond quantum sensors, Phys. Rev. Appl. 23, 054001 (2025).
- J. C. Hermann, R. Rizzato, F. Bruckmaier, R. D. Allert, A. Blank, and D. B. Bucher, Extending radiowave frequency detection range with dressed states of solid-state spin ensembles, npj Quantum Inf. 10, 1 (2024).
- P. London, J. Scheuer, J.-M. Cai, I. Schwarz, A. Retzker, M. B. Plenio, M. Katagiri, T. Teraji, S. Koizumi, J. Isoya, R. Fischer, L. P. McGuinness, B. Naydenov, and F. Jelezko, Detecting and polarizing nuclear spins with double resonance on a single electron spin, Phys. Rev. Lett. 111, 067601 (2013).
- R. Maier, C.-I. Ho, H. Sumiya, S. Onoda, J. Isoya, V. Vorobyov, and J. Wrachtrup, Efficient detection of statistical RF fields with a quantum sensor, Phys. Rev. Lett. 135, 250802 (2025).
- A. P. Nizovtsev, S. Y. Kilin, F. Jelezko, T. Gaebal, I. Popa, A. Gruber, and J. Wrachtrup, A quantum computer based on NV centers in diamond: Optically detected nutations of single electron and nuclear spins, Opt. Spectrosc. 99, 233 (2005).
- J. M. Binder, A. Stark, N. Tomek, J. Scheuer, F. Frank, K. D. Jahnke, C. Müller, S. Schmitt, M. H. Metsch, T. Unden, T. Gehring, A. Huck, U. L. Andersen, L. J. Rogers, and F. Jelezko, Qudi: A modular python suite for experiment control and data processing, SoftwareX 6, 85 (2017).
- S. Felton, A. M. Edmonds, M. E. Newton, P. M. Martineau, D. Fisher, D. J. Twitchen, and J. M. Baker, Hyperfine interaction in the ground state of the negatively charged nitrogen vacancy center in diamond, Phys. Rev. B 79, 075203 (2009).
- B. R. Mollow, Power spectrum of light scattered by two-level systems, Phys. Rev. 188, 1969 (1969).
- V. M. Acosta, E. Bauch, M. P. Ledbetter, A. Waxman, L.-S. Bouchard, and D. Budker, Temperature dependence of the nitrogen-vacancy magnetic resonance in diamond, Phys. Rev. Lett. 104, 070801 (2010).
- M. W. Doherty, V. M. Acosta, A. Jarmola, M. S. J. Barson, N. B. Manson, D. Budker, and L. C. L. Hollenberg, Temperature shifts of the resonances of the center in diamond, Phys. Rev. B 90, 041201(R) (2014).
- L. M. K. Vandersypen and I. L. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys. 76, 1037 (2005).
- J. T. Merrill and K. R. Brown, Progress in compensating pulse sequences for quantum computation, in Quantum Information and Computation for Chemistry (John Wiley & Sons, Ltd, New York, 2014), pp. 241–294.
- D. Suter and G. A. Álvarez, Colloquium: Protecting quantum information against environmental noise, Rev. Mod. Phys. 88, 041001 (2016).
- S. Wimperis, Broadband, narrowband, and passband composite pulses for use in advanced NMR experiments, J. Magn. Reson. A 109, 221 (1994).
- S. Kukita, H. Kiya, and Y. Kondo, Geometric property of off resonance error robust composite pulse, Sci. Rep. 12, 9574 (2022).
- H. K. Cummins, G. Llewellyn, and J. A. Jones, Tackling systematic errors in quantum logic gates with composite rotations, Phys. Rev. A 67, 042308 (2003).
- S. Nomura, K. Kaida, H. Watanabe, and S. Kashiwaya, Near-field radio-frequency imaging by spin-locking with a nitrogen-vacancy spin sensor, J. Appl. Phys. 130, 024503 (2021).
- S. Bertaina, H. Vezin, H. De Raedt, and I. Chiorescu, Experimental protection of quantum coherence by using a phase-tunable image drive, Sci. Rep. 10, 21643 (2020).
- H. De Raedt, S. Miyashita, K. Michielsen, H. Vezin, S. Bertaina, and I. Chiorescu, Sustaining Rabi oscillations by using a phase-tunable image drive, Eur. Phys. J. B 95, 158 (2022).