# Quantum X Waves with Orbital Angular Momentum in Nonlinear Dispersive Media

## TL;DR

This paper develops a comprehensive quantum theory for X waves carrying orbital angular momentum in dispersive media, demonstrating their resilience to dispersion and diffraction, and analyzing their nonlinear interactions in various media.

## Contribution

It introduces a novel quantum framework for X waves with OAM in dispersive media, including their nonlinear interactions, which was not previously established.

## Key findings

- Quantised X waves are unaffected by dispersion and diffraction.
- Nonlinear interactions of these X waves are characterized in quadratic and Kerr media.
- The theory predicts robust quantum states of light with potential applications.

## Abstract

We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum (OAM) in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.