Interaction time of Schrödinger cat states with a periodically driven quantum system: Symplectic covariance approach

The symplectic invariance property of the Wigner-R\'enyi entropies family is used to estimate the interaction time for the propagating Schr"odinger cat state that interacts with the periodically changing potential. With the help of this property, the hierarchy of the interaction times is specified for the quantum dynamics of the periodically driven system. It is also demonstrated that the lower and upper bounds of the interaction time are determined by the Wigner-R\'enyi entropies corresponding to increasing R\'enyi index values, respectively. The interpretation of the presented results is supported by calculations of the dynamical transmission and capture coefficients, which give a clear insight into the scattering of the non-Gaussian state on the periodically changing potential, which switches between the Gaussian potential barrier and the well.