Non-invasive vibrational mode spectroscopy of ion Coulomb crystals through resonant collective coupling to an optical cavity field

We report on a novel non-invasive method to determine the normal mode frequencies of ion Coulomb crystals in traps based on the resonance enhanced collective coupling between the electronic states of the ions and an optical cavity field at the single photon level. Excitations of the normal modes are observed through a Doppler broadening of the resonance. An excellent agreement with the predictions of a zero-temperature uniformly charged liquid plasma model is found. The technique opens up for investigations of the heating and damping of cold plasma modes, as well as the coupling between them.