  Taking the decoherence into account, we investigate nonclassical features of
the optical Schr\"odinger cat states in one mode and two coupled-modes systems
with two-photon driving. In the one mode system, the relationship between the
Schr\"odinger cat states and the system parameters is derived. We observe that
in the presence of single-photon decay the steady states would be a mixture of
Schr\"odinger cats. The dynamics and steady states of such a cat versus
single-photon decay are examined. In the two coupled-modes cases with linear
and nonlinear couplings, the dynamics of entanglement and mutual information
are examined with two different initial states and single-photon decay.
Compared to the linear coupling case, more complicated structure appears in the
Wigner function in the nonlinear coupling case. The joint quadrature
distributions are also explored. Such nonclassical states can be used not only
in exploring the boundary between the classical and the quantum worlds but also
in quantum metrology and quantum information processing.
