The degree of non-Markovianity of a continuous bath can be quantified by
means of the coherence. This simple measure is experimentally accessible
through Ramsey spectroscopy, but it is limited to incoherent dynamical maps. We
propose an extension of this measure and discuss its application to color
centers in diamond, where the optical coherence between two orbital states is
affected by interactions with a structured phonon bath. By taking realistic
phonon spectral density functions into account, we show that this measure is
well-behaved at arbitrary temperatures and that it provides additional insights
about how non-Markoviantiy is affected by the presence of both bulk and
quasi-localized phonon modes. Importantly, with only a little overhead the
measure can be adapted to eliminate the false signs of non-Markovianity from
coherent dynamical maps and is thus applicable for a large class of systems
modeled by the spin-boson Hamiltonian.Comment: 10 pages, 6 figure
