Higher order quantum vortex

TL;DR

This paper develops a quantum theoretical framework for photons entangled in higher order Ince-Gauss modes, which are important for advanced quantum communication protocols, filling a gap in the theoretical understanding of these states.

Contribution

The paper introduces the first comprehensive quantum theoretical model for Ince-Gauss modes, enabling better understanding and utilization in quantum information applications.

Findings

Established a quantum framework for Ince-Gauss modes

Identified the role of ellipticity parameter in quantum protocols

Facilitated future experimental and theoretical research

Abstract

In this article we present a quantum theoretical framework of photons entangled in higher order modes like Ince-Gauss modes. Ince-Gauss modes are the natural solution of the quantum harmonic oscillator in elliptical coordinates. These modes are defined by an additional quantum number, the ellipticity parameter which is expected to play a major role in continuous variable quantum key distribution protocols. Although such quantum states have been realized in experiments but a proper theoretical framework has been missing. We aim to address this shortcoming with our article.