  In this paper we consider multimode multiphoton Jaynes-Cummings model, which
consists of a two-level atom, initially prepared in an excited atomic state,
interacting with $N$ modes of electromagnetic field prepared in general pure
quantum states. For this system we show that under certain conditions the
evolution of the Wigner function at the phase space origin provides direct
information on the corresponding atomic inversion. This relation is also valid
even if the system includes Kerr-like nonlinearity, Stark shift effect,
different types of the initial atomic state as well as moving atom.
Furthermore, based on this fact we discuss for the single-mode case the
possibility of detecting the atomic inversion by means of techniques similar to
those used for Wigner function.
