Spatially structured photons have attracted a lot of attention in quantum photonics, where they often serve as powerful tools for investigating fundamental properties of light, and for realizing high-dimensional quantum states with beneficial properties in quantum information tasks such as cryptography or quantum simulations [1] . One way of describing any spatial structure, in the paraxial limit, is through orthogonal transverse-spatial modes e.g. Laguerre-Gaussian (LG) modes. A unique feature of higher order LG modes is their twisted phase front, to which a theoretically unbounded orbital angular momentum can be attributed.
Structured photons often serve as physical realizations of high-dimensional quantum states beneficial to quantum information. One popular way of discretizing the space is through Laguerre-Gaussian modes that can have twisted phase front and, thus, orbital angular momentum (OAM). We demonstrate that using multi-plane light-conversion techniques enables the performance of complex unitary transformations between multiple input-modes and output-modes in the quantum regime. We demonstrate various complex two-photon interferences observed in spatial modes, thereby realizing a linear optical network along a single beam path. Finally, we show that using this ability allows the generation of spatial-mode NOON-states, which offer angular super-sensitivity.
Optique quantique avec lumière structurée La présente thèse a pour objectif d'analyser la lumière structurée non-classique et ses caractéristiques. L'optique quantique et la lumière structurée sont deux sujets qui font l'objet d'examens nombreux. Ils sont néanmoins rarement examinés en combinaison. Les propriétés quantiques de la lumière structurée sont moins bien étudiées qu'ils devraient l'être. Par la lumière structurée nous entendons les champs lumineux qui montrent une structure transverse complexe de l'intensité, la phase ou la polarisation. Nous voulons lier les deux sujets de l'optique quantique et la lumière structurée dans la présente thèse. Dans ce but, nous générons expérimentalement des champs lumineux structurés non-classiques. En particulier, nous réalisons une expérience qui permet de générer des faisceaux vectoriels vectoriels - c'est-à-dire des faisceaux lumineux dont l'état de polarisation présente une structure transverse complexe - qui montrent une réduction du bruit quantique. En outre, nous étudions théoriquement les propriétés spatiales de faisceaux lumineux, ainsi que leur bruit. Plus spécifiquement, nous analysons l'incertitude quantique dans la largeur d'un faisceau lumineux. Pour prouver la faisabilité de la vérification expérimentales de nos résultats théoriques, nous réalisons des simulations pour la mesure de paramètres spatiales utilisant un détecteur mulitpixels.
This thesis explores the development and application of multi-plane light conversion (MPLC) technol-ogy, focusing on its integration into experimental setups that push the boundaries of quantum opticsand spatial state tomography. Central to this study is a custom-built, research-grade MPLC devicedesigned around a programmable spatial light modulator (SLM), which facilitates two groundbreak-ing experiments: the manipulation of high-dimensional qudits for quantum gate operations, and thedevelopment of a high-dimensional Stokes-space spatial beam analyser for single-shot spatial statetomography.The first experiment involved implementing quantum gates — specifically the X-gate, Z-gate, andDFT-gate — for a 17-dimensional qudit, represented through the first 17 azimuthal Laguerre-Gaussianspatial modes on a MPLC device. This experiment not only demonstrated MPLC’s capability tohandle complex, high-dimensional quantum states but also underscored its potential to enhance thescalability and efficiency of quantum computing architectures. By leveraging the precise control overspatial modes afforded by MPLC and the programmability of SLM-based MPLC, the experimentdemonstrated high-dimensional gate operations, paving the way for more complex quantum computingoperations for qudits.The second project focused on using MPLC to develop a device capable of performing high-dimensional Stokes-space spatial beam analysis. This innovative instrument marks a significantbreakthrough in optical beam characterisation, providing a reference-free, single-shot technique forconducting spatial state tomography on beams characterisable by a six-mode or six-dimensional system.The device’s capacity to swiftly and precisely characterise the wavefront and coherence of opticalfields renders it an invaluable asset for advancing optical communication technologies and enhancingoptical sensing methodologies.Throughout this thesis, the theoretical foundations of MPLC technology are presented, with adetailed account of the MPLC device design and operational principles. Experimental results arepresented to validate the effectiveness of the MPLC device in both quantum gate operations andspatial state tomography. Comparisons with existing technologies highlight the MPLC’s enhancedperformance and versatility.This work not only expands the understanding and application of MPLC in quantum and opticalsciences but also sets the stage for future innovations in these fields. The continuous refinement andadaptation of MPLC technology promise to unlock new possibilities in both fundamental research andpractical applications.
Programmable linear optical interferometers are a core primitive in optical signal processing, quantum information processing, and photonic computing. Existing photonic-integrated implementations realize arbitrary
M-mode unitaries using Mach--Zehnder-interferometer meshes whose footprint and accumulated loss scale with
O(M2) optical components. Here we analyze and experimentally demonstrate a programmable architecture for implementing linear optical transformations directly on spatially tiled free-space {\em pixel modes} using multi-plane light conversion (MPLC). In this architecture,
M spatial modes arranged on a transverse lattice undergo a unitary transformation and are mapped to
M output modes of identical geometry through a sequence of programmable phase masks separated by free-space propagation segments. Numerical simulations show that arbitrary
M-mode unitaries can be compiled to a desired high fidelity using a number of phase planes that scales approximately linearly with
M. Using a spatial-light-modulator-based MPLC, we experimentally demonstrate programmable interferometers acting on up to
16 spatial pixel modes, including tunable beamsplitters, Hadamard unitaries, spatial permutations, and partial unitaries on select subsets of modes. These results establish MPLC-based pixel-mode interferometers as a promising architecture for programmable linear optics with applications in classical and quantum optical interconnects, photonic switching, and quantum information processing.