  We study the evolution of the hybrid entangled states in a bipartite (ultra)
strongly coupled qubit-oscillator system. Using the generalized rotating wave
approximation the reduced density matrices of the qubit and the oscillator are
obtained. The reduced density matrix of the oscillator yields the phase space
quasi probability distributions such as the diagonal P-representation, the
Wigner W-distribution and the Husimi Q-function. In the strong coupling regime
the Q-function evolves to uniformly separated macroscopically distinct Gaussian
peaks representing 'kitten' states at certain specified times that depend on
multiple time scales present in the interacting system. For the ultra-strong
coupling realm a large number of interaction-generated modes arise with a
complete randomization of their phases. A stochastic averaging of the dynamical
quantities sets in while leading to the decoherence of the system. The
delocalization in the phase space of the oscillator is studied by using the
Wehrl entropy. The negativity of the W-distribution, while registering its
departure from the classical states, allows us to compare the
information-theoretic measures such as the Wehrl entropy with the Wigner
entropy. Other features of nonclassicality such as the existence of the
squeezed states and appearance of negative values of the Mandel parameter are
realized during the course of evolution of the bipartite system. In the
parametric regime studied here these properties do not survive after a
time-averaging process.
