Identifying high-energy electronic states of NV$^-$ centers in diamond

Abstract: The negatively charged nitrogen-vacancy center in diamond is a prototype photoluminescent point defect spin qubit with promising quantum technology applications, enabled by its efficient optical spin polarization and readout. Its low-lying electronic states and optical spin polarization cycle have been well characterized over decades, establishing it as a benchmark system for state-of-the-art computational methods in point defect research. While the optical cycle is well understood, a comprehensive energetic analysis of higher-lying states has received less attention until recently. In this joint experimental theoretical study, we identify and characterize five high-energy states beyond those involved in the optical cycle. Using transient absorption spectroscopy, we determine their transition energies and relative oscillator strengths. Additionally, we perform two independent numerical studies employing two state-of-the-art post-DFT methods to support the experimental findings and assign energy levels. These results enhance our understanding of the NV center's energy spectrum and providing a broader reference for benchmarking high-level first-principles methods.