Engineering walk-off-induced orbital angular momentum spectrum in spontaneous parametric downconversion

TL;DR

This paper analyzes how the spatial walk-off of the pump beam in spontaneous parametric downconversion affects the orbital angular momentum spectrum and proposes ways to engineer quantum states despite this effect.

Contribution

It provides a systematic analysis of the walk-off effect on OAM conservation and introduces a scaling law for the OAM distribution related to the walk-off angle.

Findings

Derived a scaling law for OAM distribution based on walk-off angle

Quantified the violation of OAM conservation due to walk-off

Explored using walk-off as a tool for quantum state engineering

Abstract

Spontaneous parametric downconversion (SPDC) has been considered as a reliable source of high- dimensional entangled states in orbital angular momentum (OAM) basis. In real-world experiments, the spatial walk-off of the pump often degrades the fidelity of the generated quantum state. Since the walk-off effect breaks the rotational symmetry of the system, the conservation of total OAM is violated. Although the compensation of walk-off effects has become a well-established experimental technique, a systematic modal analysis of the spatial walk-off effect is still incomplete for SPDC. Here, we quantitatively analyze the violation of OAM conservation due to the pump walk-off effect in SPDC processes. We have derived a scaling law of the total OAM distribution with respect to the pump walk-off angle. We have also explored the feasibility of using the spatial walk-off as a mechanism to engineer the generated quantum state. Our study has provided guidelines for the generation of OAM-entangled state under realistic experimental conditions.