Two-Tone Pulse Control for Temperature-Insensitive Diamond Frequency Standards

Nitrogen-vacancy (NV) centers in diamond provide a solid-state spin system with long coherence times and efficient optical readout, making them an attractive platform for compact frequency references. A central challenge is the strong temperature dependence of the NV electronic zero-field splitting, which leads to clock instability through lattice-induced frequency shifts. We present a scheme for a temperature-insensitive NV-based clock that exploits the distinct thermal responses of the electronic zero-field splitting and the intrinsic ¹⁴N nuclear quadrupole interaction. This approach is enabled by a two-tone zero-field-splitting (TTZFS) pulse sequence that isolates the half-sum of symmetric transition frequencies while suppressing differential-mode shifts. By interleaving electronic and nuclear measurements, the scheme constructs a composite frequency reference that cancels first-order temperature sensitivity. To suppress undesired spectral components in the signal, we introduce an eight-phase scheme, TTZFS-8, which removes the unwanted peaks arising from imperfections in the central 2π pulse. Alternatively, we propose replacing the standard 2π pulse with a single optimized control pulse that is intrinsically robust to amplitude errors, eliminating the need for phase cycling and improving the control loop dynamics.