Cyclic transformation of orbital angular momentum modes

TL;DR

This paper demonstrates an experimental four-fold cyclic transformation of photonic orbital angular momentum modes using linear optics, with the setup designed by a computer algorithm, advancing high-dimensional quantum information processing.

Contribution

It introduces a novel experimental implementation of cyclic transformations in high-dimensional OAM space, including extensions to hybrid OAM-polarization systems, designed by an algorithm.

Findings

Successful four-fold cyclic transformation of OAM modes

Algorithm-designed setup for high-dimensional cycles

Potential applications in quantum cryptography and entanglement

Abstract

The spatial modes of photons are one realization of a QuDit, a quantum system that is described in a D-dimensional Hilbert space. In order to perform quantum information tasks with QuDits, a general class of D-dimensional unitary transformations is needed. Among these, cyclic transformations are an important special case required in many high-dimensional quantum communication protocols. In this paper, we experimentally demonstrate a cyclic transformation in the high-dimensional space of photonic orbital angular momentum (OAM). Using simple linear optical components, we show a successful four-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states.