Squeezing and Entanglement of two-modes Quantum $\mathrm{X}$ Waves

TL;DR

This paper explores the quantum properties of X waves with orbital angular momentum, introducing velocity phase matching, analyzing squeezing dependence on spectral order, and demonstrating entanglement in nonlinear media.

Contribution

It introduces velocity phase matching for X waves, analyzes squeezing dependence on spectral order, and demonstrates entanglement in quantum X waves with nonlinear interactions.

Findings

Velocity phase matching determines nonlinear crystal length.

Maximal squeezing occurs at a characteristic axicon aperture for spectral orders > 0.

Entanglement is detected using a separability criterion.

Abstract

quantum theory of generalized $\mathrm{X}$ waves with orbital angular momentum in dispersive media, and the interaction of quantized $\mathrm{X}$ waves in quadratic nonlinear media were studied in (J. opt,20,065201(2018)). We present a kind of phase matching, which is called velocity phase matching, and this phase matching can be used for determining the length of the nonlinear crystal or the interaction time in the experiment setup, to produce $\mathrm{X}$ waves with particular velocity $v$. Moreover, we introduce more analysis for the dependence of squeezing of $\mathrm{X}$ waves on its spectral order, and for spectral orders $j>0$, we predict the existence of a characteristic axicon aperture for maximal squeezing. Then we find the quantum squeezed state of down-converted state generated by the $\chi^{2}$-nonlinear process. Finally, we detect their entanglement using a criterion of separability.