Measuring azimuthal and radial modes of photons

TL;DR

This paper introduces a simple, highly accurate method for measuring azimuthal and radial modes of photons' transverse spatial structure, enhancing quantum communication and state tomography capabilities.

Contribution

A novel measurement scheme using a single phase screen for high-precision detection of photon spatial modes, adaptable to various mode families.

Findings

Achieves over 99% accuracy in mode measurement

Outperforms previous methods in quantum key distribution

Enables advanced experiments on spatial-mode entanglement

Abstract

With the emergence of the field of quantum communications, the appropriate choice of photonic degrees of freedom used for encoding information is of paramount importance. Highly precise techniques for measuring the polarisation, frequency, and arrival time of a photon have been developed. However, the transverse spatial degree of freedom still lacks a measurement scheme that allows the reconstruction of its full transverse structure with a simple implementation and a high level of accuracy. Here we show a method to measure the azimuthal and radial modes of Laguerre-Gaussian beams with a greater than 99% accuracy, using a single phase screen. We compare our technique with previous commonly used methods and demonstrate the significant improvements it presents for quantum key distribution and state tomography of high-dimensional quantum states of light. Moreover, our technique can be readily extended to any arbitrary family of spatial modes, such as mutually unbiased bases, Hermite-Gauss, and Ince-Gauss. Our scheme will significantly enhance existing quantum and classical communication protocols that use the spatial structure of light, as well as enable fundamental experiments on spatial-mode entanglement to reach their full potential.