Floquet Engineering Using Pulse Driving in a Diamond Two-Level System under Large-Amplitude Modulation

The nitrogen-vacancy center (NVC) in a diamond is a promising platform for Floquet engineering. Using the synchronized readout, we investigate the NVC's Floquet state driven by the Carr-Purcell sequence in a large-amplitude ac magnetic field. We observe the dynamics represented as Bessel functions up to 211th order in a systematic and quantitative agreement with the theoretical model. Furthermore, numerical calculations show that the effect of finite pulse duration and error limits the modulation amplitude available for Floquet engineering. This work provides an approach to precisely investigate Floquet engineering, showing the extendable range of modulation amplitude for two-level systems.