  We analyze here a nonclassical state produced by an atom-cavity field
interaction. The two-level atom is passed through the single-mode
electromagnetic cavity field. By deforming the field operators and introducing
nonlinearity to the classic Jaynes-Cummings model, we explore the system in
respect of a nonlinear Hamiltonian. Assuming that the atom is in an excited
state and the field is in a coherent state initially, the analytic expression
for the state vector of the entire system state vector is obtained. With the
help of the derived state vector, we calculate the photon number distribution,
Mandel's $Q_M$ parameter, Wigner function, anti-bunching, squeezing properties
and $Q$ function etc.
