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I am trying to understand the phenomenon of off-resonant excitation. In NV-centers, instead of exciting the NV centers at their resonance frequency, often the electron spin is excited off-resonantly.

This can be done because of the phonons which broaden the emission and absorption spectrum. But why can the electron spins be excited off-resonantly? I am assumning that some part of the energy will 'go' into phonons. Why is it then still more likely that photons are emitted at the frequency of the zero-Phonon line? At the zero-phonon line, there is no interaction between the phonons and the emitted photon. Therefore, if one excites the NV Center off-resonantly (with higher energy), where does the energy go if not in the the phonons (since at the zero-phonon line there is no interaction between phonons and photons).

Edit: I would like to add something to my question. How is it possible to initialize (from the spin up config) the ground state with spin $m_s=0$ using off-resonant excitation?

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