Second-order collapses and revivals

Second-order collapses and revivals caused by the photon-number mechanism in the Jaynes-Cummings model with a nonlinear Kerr medium and those in the Dicke model related to the collective mechanism are reviewed. The revival period of the oscillations is dependent on whether the initial mean photon-number is integer or non-integer in the first case, and strongly related to the parity of either n (the photon number) if n<A or A (the number of atoms) if A<n in the latter. The Jaynes-Cummings model describing the interaction of a two-level atom with a single-mode field, is one of the most intensively studied models in quantum optics