Collective radiation spectrum for ensembles with Zeeman splitting in single-photon superradiance

In an ensemble of identical atoms, cooperative effects like sub- and superradiance may alter the decay rates and the energies of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. While such effects in ensembles of two-level systems are by now well understood, realistic multilevel systems are more difficult to handle. In this work we show that in a system of atoms under the action of an external magnetic field, the collective contribution to the level shifts can amount to sizable quantitative and qualitative deviations from the single-atom Zeeman splitting picture. We develop a formalism to describe single-photon superradiance in multilevel systems and identify three-parameter regimes, two of which present measurable deviations in the radiation spectrum compared to the case of single-atom magnetic-field-induced splitting.

Figure 1

Radiation spectrum for the three cases discussed in the text: (a) electromagnetically induced transparency–like spectrum for $\mathrm{\Gamma }=19\gamma$ and $\varphi =15\gamma$; (b) regular Zeeman splitting for $\mathrm{\Gamma }=19\gamma$ and $\varphi =62\gamma$, resembling the single-atom case; and (c) asymmetric Zeeman splitting for $\mathrm{\Gamma }=3\gamma$ and $\varphi =30\gamma$.