Superradiance in an inhomogeneously broadened atomic system

The problem of superradiant emission from a small atomic system is treated under conditions in which the effects of inhomogeneous broadening are important, as in a solid. The treatment is semiclassical, with the assumption that all atoms see the same electromagnetic field. A set of coupled integrodifferential equations is obtained characterizing the state of each atom of resonant frequency ω at time $t$. It is found that, in general, atoms of different frequencies evolve differently in time, whether or not they start from the same initial state. The effect of the inhomogeneous broadening is generally to delay the onset and to reduce the amplitude of the superradiant pulse. Some effects of inhomogeneous broadening are manifest even when the inhomogeneous lifetime is much longer than the usual superradiance time. When the atomic system starts in the ground state and is then exposed to a coherent excitation pulse, superradiant effects can appear even when the inhomogeneous lifetime is very short compared with the usual superradiance time.