Optimal Microwave Pulse Trains for Ramsey Metrology of ¹³C in Diamond

The electronic spin of a nitrogen-vacancy (NV) center in diamond forms the basis of numerous quantum sensing applications, including NMR spectroscopy, nanoscale magnetometry, accelerometers, and quantum gyroscopes. We present ongoing work in building a complete dissipative model for the interaction of an NV center with proximal ¹³C nuclear spins driven by optical and microwave pulse trains. Chirped microwave pulses have been shown to map between the electronic spin of the NV center and the nuclear spin of the ¹³C atom, providing interferometric access to the ¹³C nuclear spins. A train of microwave pulses in combination with the laser field realizes the metrological scheme consisting of dynamic hyperpolarization of bulk ¹³C, Ramsey interferometry, and optical readout. A numerical simulation of the hyperfine interactions between nuclear and electronic spins in diamond with a natural abundance of ¹³C and the interplay between optical and microwave fields, as well as the diffusion of spin polarization, provides an understanding of the fluorescence signal spectra in the experiment, and allows optimization of the relevant pulse parameters. We employ optimal control theory to maximize signal contrast and robustness, advancing the design for high-performance quantum metrology in real-world environments.