Families of Orthogonal Schrodinger cat-like-states

TL;DR

This paper investigates the conditions for orthogonality between optical Schrödinger cat-like states, revealing a quantization condition for the symplectic form and providing a complete analytical solution.

Contribution

It offers a comprehensive analytical analysis of orthogonality conditions for cat-like states, highlighting the quantization of the symplectic form.

Findings

Orthogonality leads to quantization of the symplectic form

The metric form values are continuous

Complete analytical solution provided

Abstract

We analyze condition of orthogonality between optical Schrodinger cat-like-states constructed as superposition of two coherent states. We show that the orthogonality condition leads to quantization of values of a naturally emerging symplectic form, while values of the corresponding metric form are continuous. A complete analytical solution of the problem is presented.