Generalized Schr\"odinger cat states and their classical emulation

TL;DR

This paper introduces a method to generate generalized Schr"odinger cat states using nonlinear displacement operators and demonstrates their classical analogs in photonic lattices, enabling observation of quantum features in classical systems.

Contribution

It presents a novel approach to creating generalized Schr"odinger cat states via nonlinear displacement operators and links them to classical photonic lattices with unique coupling properties.

Findings

Generalized cat states can be generated by nonlinear displacement operators.

Classical photonic lattices can emulate quantum cat states.

The propagator contains the Wigner operator, enabling classical observation of quantum features.

Abstract

We demonstrate that superpositions of coherent and displaced Fock states, also referred to as generalized Schr\"odinger cats cats, can be created by application of a nonlinear displacement operator which is a deformed version of the Glauber displacement operator. Consequently, such generalized cat states can be formally considered as nonlinear coherent states. We then show that Glauber-Fock photonic lattices endowed with alternating positive and negative coupling coefficients give rise to classical analogs of such cat states. In addition, it is pointed out that the analytic propagator of these deformed Glauber-Fock arrays explicitly contains the Wigner operator opening the possibility to observe Wigner functions of the quantum harmonic oscillator in the classical domain.