\emph{Ab initio} calculation of spin-orbit coupling for NV center in diamond exhibiting dynamic Jahn-Teller effect

Point defects in solids may realize solid state quantum bits. The spin-orbit coupling in these point defects plays a key role in the magneto-optical properties that determine the conditions of quantum bit operation. However, experimental data and methods do not directly yield this highly important data, particularly, for such complex systems where dynamic Jahn-Teller (DJT) effect damps the spin-orbit interaction. Here, we show for an exemplary quantum bit, nitrogen-vacancy (NV) center in diamond, that \emph{ab initio} supercell density functional theory provide quantitative prediction for the spin-orbit coupling damped by DJT. We show that DJT is responsible for the multiple intersystem crossing rates of NV center at cryogenic temperatures. Our results pave the way toward optimizing solid state quantum bits for quantum information processing and metrology applications.