Collective magnetic splitting in single-photon superradiance

In an ensemble of identical atoms, cooperative effects like subor superradiance may alter the decay rates and the energy of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. So far, one has considered these effects in ensembles of two-level systems only. In this work we show that in a system with atoms or nuclei under the action of an external magnetic field, an additional, so far unaccounted for collective contribution to the level shifts appears that can amount to seizable deviations from the single-atom Zeeman or magnetic hyperfine splitting. We develop a formalism to describe single-photon superradiance in multi-level systems and quantify the parameter regime for which the collective Lamb shift leads to measurable deviations in the magnetic-field-induced splitting. In particular, we show that this effect should be observable in the nuclear magnetic hyperfine splitting in Mössbauer nuclei embedded in thin-film x-ray cavities.