A review of the definition of Crystallized Schrödinger cat states and their statistical properties is presented. The associated Wigner and Husimi quasi-probability distribution functions are also calculated together with the second moment of the Husimi function. The Hamiltonian formulation of the Nöther's theorem is used to get the linear time dependent invariants of until general quadratic Hamiltonians in the quadratures of the electromagnetic field. By means of these invariants, the evolution of Crystallized Schrödinger cats is studied, thus we have explicit time dependent expressions for the means and dispersions of the quadratures of the electromagnetic field together with the corresponding Wigner and Husimi functions. By means of these results, we establish some conditions on the parameters of the Crystallized cat states to have the description of non-classical light.
Theoretical calculations on transmission of quantum states such as Schrödinger cat (SC) states are considered in a periodically poled nonlinear crystal (PPNC). Combinations of various initial states (SC, coherent (C),and vacuum (V)) of light waves at frequencies
ωe and
3ωe at the input of a PPNC are studied. It is shown that the transmission and interference between superposition of macroscopically distinguishable states can be achieved by using a PPNC. Visualization and analyzes of transmission and interference processes are demonstrated with the help of reduced Wigner quasi-probability distribution functions of considered light waves.