A recent study associate carbon with single photon emitters (SPEs) in hexagonal boron nitride (h-BN). This observation, together with the high mobility of carbon in h-BN suggest the existence of SPEs based on carbon clusters. Here, by means of density-functional theory calculations we studied clusters of substitutional carbon atoms up to tetramers in hexagonal boron nitride. Two different conformations of neutral carbon trimers have zero-point line energies and shifts of the phonon sideband compatible with typical photoluminescence spectra. Moreover, some conformations of two small C clusters next to each other result in photoluminescence spectra similar to those found in experiments. We also showed that vacancies are unable to reproduce the typical features of the phonon sideband observed in most measurements due to the large spectral weight of low-energy breathing modes, ubiquitous in such defects.

Coherent manipulation of nuclear spins is a highly desirable tool for both quantum metrology and quantum computation. However, most of the current techniques to control nuclear spins lack of being fast impairing their robustness against decoherence. Here, based on Stimulated Raman Adiabatic Passage, and its modification including shortcuts to adiabaticity, we present a fast protocol for the coherent manipulation of nuclear spins. Moreover, we show how to initialise a nuclear spin starting from a thermal state, and how to implement Raman control for performing Ramsey spectroscopy to measure the dynamical and geometric phases acquired by nuclear spins.

We propose the application of a coherence-based measure for non-Markovianity to study the dynamics of color centers in diamond, where the optical coherence between two orbital states is affected by interactions with a structured phonon bath. Although limited to pure dephasing, we show that this measure is well-behaved at arbitrary temperatures and experimentally accessible through Ramsey spectroscopy. By taking realistic phonon spectral density functions into account, we use this quantity to show how non-Markovianity is affected by the presence of both bulk and quasi-localized phonon modes, as relevant for most defects in solids. Importantly, with only a minor modification the measure can be adapted to study the source of non-Markovianity in driven two-level systems and is thus applicable for a large class of systems modeled by the spin-boson Hamiltonian.

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