  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.
