  A two-level atom interacting with an electromagnetic mode in a cavity
experiences population collapses and revivals. They are an indirect signature
of the field quantization, and also hold information about the mode. Thus, they
may be harnessed for quantum-state reconstruction. In this work, we study the
revival structures with the characteristic function approach. The
characteristic function is essentially a spectral decomposition of the
photon-number probability distribution. Exploiting the characteristic function
periodicity, we find that the atomic population inversion can be understood as
the result of interference between a set of structures akin to a free
quantum-mechanical wave packet, each structure corresponding to snapshots of
this packet for different degrees of dispersion. When these structures do not
overlap, each of which can be identified to one of the inversion revivals, in
which case we may also retrieve the photon-number distribution.
