Electron-spin double resonance of nitrogen-vacancy centers in diamond under a strong driving field

Takumi Mikawa, Ryusei Okaniwa, Yuichiro Matsuzaki, Norio Tokuda, and Junko Ishi-Hayase

Phys. Rev. A 108, 012610 – Published 10 July 2023

Abstract

The nitrogen-vacancy (NV) center in diamond has been the focus of research efforts because of its suitability for use in applications such as quantum sensing and quantum simulations. Recently, the electron-spin double resonance (ESDR) of NV centers has been exploited for detecting radio-frequency (RF) fields with continuous-wave optically detected magnetic resonance. However, the characteristic phenomenon of ESDR under a strong RF field remains to be fully elucidated. In this study, we theoretically and experimentally analyzed the ESDR spectra under strong RF fields by adopting Floquet theory. Our analytical and numerical calculations could reproduce the ESDR spectra obtained by measuring the spin-dependent photoluminescence under the continuous application of a microwave and a RF field for a DC bias magnetic field perpendicular to the NV axis. We found that anticrossing structures that appear under a strong RF field are induced by the generation of RF-dressed states owing to the two-RF-photon resonances. Moreover, we found that $2 n$ -RF-photon resonances were allowed by an unintentional DC bias magnetic field parallel to the NV axis. These results should help in the realization of precise MHz-range AC magnetometry with a wide dynamic range beyond the rotating wave approximation regime as well as Floquet engineering in open quantum systems.

Received 6 March 2023
Accepted 31 May 2023

DOI:https://doi.org/10.1103/PhysRevA.108.012610

Physics Subject Headings (PhySH)

Quantum sensing Strong electromagnetic field effects

Floquet systems Nitrogen vacancy centers in diamond

Electron spin resonance Optically detected magnetic resonance

Nuclear Physics

Authors & Affiliations

Takumi Mikawa ^1,2,*, Ryusei Okaniwa^1,2, Yuichiro Matsuzaki^3,4,†, Norio Tokuda ^5,6, and Junko Ishi-Hayase ^1,2,‡

¹School of Fundamental Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan
²Center for Spintronics Research Network, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan
³Research Center for Emerging Computing Technologies, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
⁴NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
⁵Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan
⁶Nanomaterials Research Institute, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan

^*mikawa_jukusei@keio.jp
^†Present address: Department of Electrical, Electronic, and Communication Engineering, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan; ymatsuzaki872@g.chuo-u.ac.jp
^‡hayase@appi.keio.ac.jp

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Vol. 108, Iss. 1 — July 2023

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Images

Figure 1
(a) Energy diagram of electronic spin-triplet ground state of NV center under DC bias magnetic field perpendicular to a NV axis under continuous application of an MW and a RF field. ${\tilde{D}}_{GS}$ is zero-field splitting, and ${\tilde{M}}_{x}$ is effective strain under perpendicular magnetic field. (b) CW-ODMR spectra without and with the RF fields for the amplitude $B_{RF} = 69.8 µ T$ and frequency $ω_{RF} / (2 π) = 9.09 M Hz$ . In CW-ODMR spectrum under RF field (i.e., ESDR spectrum), four dips are observed owing to creation of RF-dressed states [see (a)]. Solid lines indicate fitting curves calculated using a multiple harmonic oscillator model.
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Figure 2
(a) ESDR spectra under a DC bias magnetic field perpendicular to the NV axis as measured by sweeping MW and RF frequencies for a weak RF field with $B_{RF} = 69.8 µ T$ . (b) Comparison of the resonant frequencies obtained experimentally and those obtained from analytical solutions under a weak RF field. Experimental resonant frequencies were extracted from (a), while analytical solutions without and with parallel DC bias magnetic field $ω_{L}$ were obtained using Eqs. (11), (12), and (22). (c), (d) Results of numerical simulations performed using Floquet Hamiltonian (c) without and (d) with a parallel DC bias magnetic field. Parameters used for simulation in (c) [(d)] are ${\tilde{D}}_{GS} / (2 π) = 2.8825 G Hz, {\tilde{M}}_{x} / (2 π) = 9.09 M Hz / 2 [{\tilde{M}}_{x} / (2 π) = 4.40 M Hz, ω_{L} / (2 π) = 0.50 M Hz]$ and $λ^{b^{'}} / (2 π) = λ^{d^{'}} / (2 π) = 0.12 M Hz$ . Dashed lines in (a) and (b) indicate resonant frequency between $| B 〉$ ( $| B^{'} 〉$ ) and $| D 〉$ ( $| D^{'} 〉$ ), and anticrossing structures emerge near dashed lines. There is good agreement between experimental and analytical results, and the parallel bias magnetic field had no effect under the weak RF field.
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Figure 3
(a) ESDR spectra under a DC bias magnetic field perpendicular to the NV axis as measured by sweeping MW frequencies and RF frequencies under a strong RF field with $B_{RF} = 136.8 µ T$ . (b) Comparison of extracted resonant frequencies obtained experimentally and those obtained from numerical simulations (c, d) under a strong RF field. Experimental resonant frequencies were extracted from (a), and numerically determined were extracted from (c) and (d). (c, d) Results of numerical simulations performed using Floquet Hamiltonian (c) without and (d) with a parallel bias magnetic field. Parameters used are same as in Fig. 2. In (a)–(d) dashed lines indicate resonant frequency, $ω_{RF} / (2 π) = 9.09 M Hz$ , of single-RF-photon resonances, and dotted lines indicate resonant frequency, $ω_{RF} / (2 π) = 5.50 M Hz$ , of two-RF-photon resonances. There is good agreement between experimental results and those of theoretical calculations that consider a parallel bias magnetic field. In contrast, theory without a parallel bias magnetic field could not reproduce anticrossing structures induced by two-RF-photon resonances.
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Figure 4
(a), (c) ESDR spectra under bias magnetic field perpendicular to NV axis as measured by changing RF amplitude $B_{RF}$ while keeping the RF frequency at (a) $ω_{RF} / (2 π) = 9.09 M Hz$ (single-RF-photon resonance) and (c) $4.54 M Hz$ (two-RF-photon resonance). (b) Comparison of resonant frequencies extracted from (a) and the analytical solutions given by Eqs. (11), (12), and (22). Analytical solutions obtained using Eqs. (11), (12), and (22), which were obtained with and without a parallel DC magnetic field, respectively, agree with experimental results. (d) Comparison of resonant frequencies extracted from (c) and those obtained from analytical solutions given by Eq. (22), which was based on RWA, and in Eq. (27), which was based on vV transformation. In (a) and (b) [(c) and (d)], dotted lines indicate boundaries of RWA conditions $Ω_{RF} > ω_{RF} / 2$ [25, 36], which was calculated from $ω_{RF} / (2 π) = 9.09 M Hz$ ( $4.54 MHz$ ). Analytical solutions given by Eqs. (11), (12), and (22) use RWA, which starts being violated in the area above the dotted line. In contrast, the analytical solution given by Eq. (27) does not use RWA and can reproduce resonant frequencies beyond RWA conditions.
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Figure 5
Comparison of the resonant RF frequencies for two-RF-photon resonances between the analytical solutions given by $ω_{RF} \approx {\tilde{M}}_{x} + Ω_{RF}^{2} / {\tilde{M}}_{x}$ , the numerical results, and the experimental results extracted in Fig. 3.
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