  In this paper we discuss the quantum properties for superposition of squeezed
displaced number states against multiphoton Jaynes-Cummings model (JCM). In
particular, we investigate atomic inversion, photon-number distribution,
purity, quadrature squeezing, Mandel $Q$ parameter and Wigner function. We show
that the quadrature squeezing for three-photon absorption case can exhibit
revivals and collapses typical to those occurring in the atomic inversion for
one-photon absorption case. Also we prove that for odd number absorption
parameter there is a connection between the evolution of the atomic inversion
and the evolution of the Wigner function at the origin in phase space.
Furthermore, we show that the nonclassical states whose the Wigner functions
values at the origins are negative will be always nonclassical when they are
evolving through the JCM with even absorption parameter. Also we demonstrate
that various types of cat states can be generated via this system.
