Abstract：Recent experimental advances make possible to monitor and manipulate the real-time dynamics of single quantum spins in solid state environments. This opens a road to harnessing the spins of electrons and nuclei for high precision metrology and quantum information processing. It also enables us to study most fundamental problems, such as destruction of quantum coherence due to interaction with the outside world. Understanding of this decoherence process, and finding ways to mitigate it, are exciting scientific endeavors. I will present the results of our theoretical research on two closely related systems: phosphorus donors in silicon, and nitrogen-vacancy centers in diamond. These systems, in spite of conceptual simplicity, demonstrate a rich spectrum of interesting dynamical regimes. I will discuss modern dynamical decoupling (DD) techniques which aim at preserving coherence of quantum spins and controlling their coherence. Implementation of these techniques in real experiments may lead to appearance of interesting features, such as decoherence freezing, under the action of DD protocols. Using a variety of analytical and numerical tools, we can characterize and optimize the factors which limit our control over these quantum spin systems.

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