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

## TL;DR

This paper explores how certain quantum states can resemble Schrödinger cat states by analyzing their Wigner functions.

## Contribution

The study identifies the number distribution function's localization as key to forming cat-like quantum states.

## Key findings

- Well-localized number distribution functions in the Fock basis lead to cat-like structures in Wigner functions.
- Superpositions without localized peaks do not exhibit Schrödinger cat characteristics.
- The analysis is based on 2D slices of Wigner functions for nonlinear coherent states.

## Abstract

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.