Probing the Evolution of Electron Spin Wavefunction of NV Center in diamond via Pressure Tuning

Understanding the profile of a qubit's wavefunction is key to its quantum applications. Unlike conducting systems, where a scanning tunneling microscope can be used to probe the electron distribution, there is no direct method for solid-state-defect based qubits in wide-bandgap semiconductors. In this work, we use pressure as a tuning method and a nuclear spin as an atomic scale probe to monitor the hyperfine structure of negatively charged nitrogen vacancy (NV) centers in diamonds under pressure. We present a detailed study on the nearest-neighbor $^{13}C$ hyperfine splitting in the optically detected magnetic resonance (ODMR) spectrum of NV centers at different pressures. By examining the $^{13}C$ hyperfine interaction upon pressurizing, we show that the NV hyperfine parameters have prominent changes, resulting in an increase in the NV electron spin density and rehybridization from $sp^3$ to $sp^2$ bonds. The $ab$ $initio$ calculations of strain dependence of the NV center's hyperfine levels are done independently. The theoretical results qualitatively agree well with experimental data without introducing any fitting parameters. Furthermore, this method can be adopted to probe the evolution of wavefunction in other defect systems. This potential capability could play an important role in developing magnetometry and quantum information processing using the defect centers.