We study the evolution of the hybrid entangled states in a bipartite (ultra) strongly coupled qubitoscillator 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.arXiv:1509.07030v1 [quant-ph] 23 Sep 2015

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We study a system of two cavities each encapsulating a qubit and an oscillator degrees of freedom. An ultrastrong interaction strength between the qubit and the oscillator is assumed, and the photons are allowed to hop between the cavities. A partition of the time scale between the fast moving oscillator and the slow moving qubit allows us to set up an adiabatic approximation procedure where we employ the delocalized degrees of freedom to diagonalize the Hamiltonian. The time evolution of the N 00N -type initial states now furnishes, for instance, the reduced density matrix of a bipartite system of two qubits. For a macroscopic size of the N 00N component of the initial state the sudden death of the entanglement between the qubits and its continued null value are prominently manifest as the information percolates to the qubits after long intervals. For the low photon numbers of the initial states the dynamics produces almost maximally entangled two-qubit states, which by utilizing the Hilbert-Schmidt distance between the density matrices, are observed to be nearly pure generalized Bell states. †

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