Squeezed Schrödinger kitten states of a qubit-oscillator system: Generation and quantum properties in the phase space

We study the evolution of the hybrid entangled squeezed states of the qubit-oscillator system in the strong coupling domain. Following the adiabatic approximation we obtain the reduced density matrices of the qubit and the oscillator degrees of freedom. The oscillator reduced density matrix is utilized to calculate the quasiprobability distributions such as the Sudarshan-Glauber diagonal P-representation, the Wigner W-distribution, and the nonnegative Husimi Q-function. The negativity associated with the W-distribution indicates the nonclassicality of the developing state. The existence of the multiple time scales induced by the interaction introduces certain features in the bipartite system. In the strong coupling regime the transient evolution to low entropy configurations reveals brief emergence of nearly pure squeezed Schrödinger kitten states that may be regarded as superposition of uniformly separated distinguishable squeezed coherent states. However, the quantum fluctuations with a short time period engender bifurcation and subsequent rejoining of these peaks in the phase space. The abovementioned doubling of the number of peaks increases the entropy to its near maximal value. Nonetheless, these states characterized by high entropy values, are endowed with a large negativity of the W-distribution that points towards their non-Gaussian behavior. This may be ascertained by the significantly large Hilbert-Schmidt distance between the oscillator state and an ensemble of most general statistical mixture of squeezed Gaussian states possessing nearly identical second order quadrature moments as that of the oscillator.