Collective Lamb Shift and Spontaneous Emission of a dense Atomic Gas

A long-studied open question is to find a comprehensive and general description of the collective Lamb shift and spontaneous emission rate in a many-body radiative system. Both decay and energy levels are modified due to the dipole-dipole interaction between the radiators. We introduce a method to theoretically study weakly-driven, low-excited ensembles of two-level atoms, and obtain an analytic description of the collective Lamb shift and collective decay rate via a self-consistent relation. We predict the dependency of these measurable quantities on system parameters such as the number density of radiators, the Rabi frequency and the detuning of the external driving field as well as shape and size of the sample.