Theory of laser cooling of nuclear spins based on coherent population trapping

Nuclear spins, associated with $^{13}$C impurities in diamond, can be controlled via optical manipulation of localized atom-like impurities. Specifically, spectroscopic techniques involving coherent population trapping were recently used to control and monitor the nuclear state evolution. In this work, we present the physical mechanism which leads~to optical pumping of the nuclear spin ensemble into particular nuclear states. We propose an optimized scheme for achieving maximal control over the system. Specifically, cooling and control of the nuclear environment of the Nitrogen Vacancy Centers in diamond~leads to improved electronic coherence properties. In addition, it opens up the possibility of using the nuclear ensemble itself for quantum information applications.