Wigner Functions of Time-Dependent Cat-like Even/Odd Superpositions of Nonlinear Coherent States

We calculate and plot 2D slices of the Wigner functions of several families of highly excited even and odd superpositions of nonlinear coherent states, looking for conditions under which such superpositions can be interpreted as models of the "Schrödinger cat" states. The decisive factor seems to be the form of the number distribution function over the Fock basis: it must have well localized peaks. Otherwise, no "cat-like" structures are observed.