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The degree of non-Markovianity of a continuous bath can be quantified bymeans of the coherence. This simple measure is experimentally accessiblethrough Ramsey spectroscopy, but it is limited to incoherent dynamical maps. Wepropose an extension of this measure and discuss its application to colorcenters in diamond, where the optical coherence between two orbital states isaffected by interactions with a structured phonon bath. By taking realisticphonon spectral density functions into account, we show that this measure iswell-behaved at arbitrary temperatures and that it provides additional insightsabout how non-Markoviantiy is affected by the presence of both bulk andquasi-localized phonon modes. Importantly, with only a little overhead themeasure can be adapted to eliminate the false signs of non-Markovianity fromcoherent dynamical maps and is thus applicable for a large class of systemsmodeled by the spin-boson Hamiltonian.

Coherence as a measure for non-Markovianity and its applications to color centers in diamond