Nonclassicality and decoherence of photon-added squeezed coherent Schr\"{o}dinger kitten states in a Kerr medium

We study the nonclassicality of the evolution of a superposition of an arbitrary number of photon-added squeezed coherent Schr\"{o}dinger cat states in a nonlinear Kerr medium. The nonlinearity of the medium gives rise to the periodicities of the quantities such as the Wehrl entropy $S_{Q}$ and the negativity $\delta_{W}$ of the $W$-distribution, and a series of local minima of these quantities arise at the rational submultiples of the said period. At these local minima the evolving state coincides with the transient Yurke-Stoler type of photon-added squeezed kitten states, which, for the choice of the phase space variables reflecting their macroscopic nature, show extremely short-lived behavior. Proceeding further we provide the closed form tomograms, which furnish the alternate description of these short-lived states. The increasing complexity in the kitten formations induces more number of interference terms that trigger more quantumness of the corresponding states. The nonclassical depth of the photon-added squeezed kitten states are observed to be of maximum possible value. Employing the Lindblad master equation approach we study the amplitude and the phase damping models for the initial state considered here. In the phase damping model the nonclassicality is not completely erased even in the long time limit when the dynamical quantities, such as the negativity $\delta_{W}$ and the tomogram, assume nontrivial asymptotic values.