Evolution of collective N atom states in single photon superradiance: Effect of virtual Lamb shift processes

We present analytical solutions for the evolution of collective states of N atoms. On the one hand is a (timed) Dicke state prepared by the conditional absorption of a single photon and exhibiting superradiant decay. This is in strong contrast to the evolution of a symmetric Dicke state which is trapped for large atomic clouds. We show that virtual processes yield only a small effect on the evolution of the rapidly decaying timed Dicke state. However, they change the long time dynamics from exponential decay into a power-law behavior which can be observed experimentally. For trapped states virtual processes are much more important and provide new decay channels resulting in a slow decay of the otherwise trapped state.