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

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 the Floquet theory. Our analytical and numerical calculations could reproduce the ESDR spectra obtained by measuring the spin-dependent photoluminescence under the continuous application of microwaves and an 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 $2n$-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.