A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media

We present a fast method for numerically solving the inhomogeneous Helmholtz equation. Our iterative method is based on the Born series, which we modified to achieve convergence for scattering media of arbitrary size and scattering strength. Compared to pseudospectral time-domain simulations, our modified Born approach is two orders of magnitude faster and nine orders of magnitude more accurate in benchmark tests in 1-dimensional and 2-dimensional systems

Referenceless characterisation of complex media using physics-informed neural networks

In this work, we present a method to characterise the transmission matrices of complex scattering media using a physics-informed, multi-plane neural network (MPNN) without the requirement of a known optical reference field. We use this method to accurately measure the transmission matrix of a commercial multi-mode fiber without the problems of output-phase ambiguity and dark spots, leading to upto 58% improvement in focusing efficiency compared with phase-stepping holography. We demonstrate how our method is significantly more noise-robust than phase-stepping holography and show how it can be generalised to characterise a cascade of transmission matrices, allowing one to control the propagation of light between independent scattering media. This work presents an essential tool for accurate light control through complex media, with applications ranging from classical optical networks, biomedical imaging, to quantum information processing

Simultaneously sorting overlapping quantum states of light

The efficient manipulation, sorting, and measurement of optical modes and single-photon states is fundamental to classical and quantum science. Here, we realise simultaneous and efficient sorting of non-orthogonal, overlapping states of light, encoded in the transverse spatial degree of freedom. We use a specifically designed multi-plane light converter (MPLC) to sort states encoded in dimensions ranging from $d = 3$ to $d = 7$. Through the use of an auxiliary output mode, the MPLC simultaneously performs the unitary operation required for unambiguous discrimination and the basis change for the outcomes to be spatially separated. Our results lay the groundwork for optimal image identification and classification via optical networks, with potential applications ranging from self-driving cars to quantum communication systems

L00L and p00p entanglement

We demonstrate the generation of unbalanced two-photon entanglement in the Laguerre-Gaussian (LG) transverse-spatial degree-of-freedom, where one photon carries a fundamental (Gauss) mode and the other a higher-order LG mode with a non-zero azimuthal ($\ell$) or radial ($p$) component. Taking a cue from the $N00N$ state nomenclature, we call these types of states $LOOL$ (L00L) or $p00p$-entangled. They are generated by shifting one photon in the LG mode space and combining it with a second (initially uncorrelated) photon at a beamsplitter, followed by coincidence detection. In order to verify two-photon coherence, we demonstrate a two-photon ``twisted'' quantum eraser, where Hong-Ou-Mandel interference is recovered between two distinguishable photons by projecting them into a rotated LG superposition basis. Using an entanglement witness, we find that our generated $LOOL$ and $p00p$ states have fidelities of 95.31\% and 89.80\% to their respective ideal maximally entangled states. Besides being of fundamental interest, this type of entanglement will likely have a significant impact on tickling the average quantum physicist's funny bone.Comment: Written for submission to the AVS Quantum Science special issue in memory of Jon Dowlin

Inverse-design of high-dimensional quantum optical circuits in a complex medium

Programmable optical circuits form a key part of quantum technologies today, ranging from transceivers for quantum communication to integrated photonic chips for quantum information processing. As the size of such circuits is increased, maintaining precise control over every individual component becomes challenging, leading to a reduction in the quality of the operations performed. In parallel, minor imperfections in circuit fabrication are amplified in this regime, dramatically inhibiting their performance. Here we show how embedding an optical circuit in the higher-dimensional space of a large, ambient mode-mixer using inverse-design techniques allows us to forgo control over each individual circuit element, while retaining a high degree of programmability over the circuit. Using this approach, we implement high-dimensional linear optical circuits within a complex scattering medium consisting of a commercial multi-mode fibre placed between two controllable phase planes. We employ these circuits to manipulate high-dimensional spatial-mode entanglement in up to seven dimensions, demonstrating their application as fully programmable quantum gates. Furthermore, we show how their programmability allows us to turn the multi-mode fibre itself into a generalised multi-outcome measurement device, allowing us to both transport and certify entanglement within the transmission channel. Finally, we discuss the scalability of our approach, numerically showing how a high circuit fidelity can be achieved with a low circuit depth by harnessing the resource of a high-dimensional mode-mixer. Our work serves as an alternative yet powerful approach for realising precise control over high-dimensional quantum states of light, with clear applications in next-generation quantum communication and computing technologies

Traitement de l'information quantique avec une fibre multimode

Transport of information through a multimode optical fibre raises challenges when one wants to increase the data traffic using many spatial modes due to modal cross-talk and dispersion. Instead of considering those complex mixing of modes as a detrimental process, in this dissertation, we harness its mode mixing to process quantum optical information. We implement a reconfigurable linear optical network, a fundamental building block for scalable quantum technologies, based on an inverse photonic approach exploiting the technology of wavefront shaping. We experimentally demonstrate manipulation of two-photon quantum interference on various linear optical networks across both spatial and polarization degrees of freedom. In particular, we experimentally show the zero-transmission law in Fourier and Sylvester interferometers, which are used to certificate the degree of indistinguishability of an input state. Moreover, thanks to the ability to implement a non-unitary network, we observe the photon anti-coalescence effect in all output configurations, as well as the realization of a tunable coherent absorption experiment. Therefore, we demonstrate the reconfigurability, accuracy, scalability and robustness of the implemented linear optical networks for quantum information processing. Furthermore, we study the statistical properties of one-and two-photon speckles generated from various ground-truth states of light after propagating through a multimode fibre. These statistical properties of speckles can be used to extract information about the dimensionality, purity, and indistinguishability of an unknown input state of light, therefore allowing for state classification. Our results highlight the potential of complex media combined with wavefront shaping for quantum information processing.Le transport à haut débit de données à travers des fibres optiques grâce au multiplexage spatial est en pratique limité par la diaphonie modale. Au lieu de considérer ce couplage modal comme une limitation, nous exploitons ici ce mélange de modes comme une ressource. Nous mettons en oeuvre un réseau optique linéaire programmable basé sur le concept de design photonique inverse, exploitant les techniques de mise en forme du front d’onde. Nous démontrons la manipulation d’interférences quantiques à deux photons sur divers réseaux linéaires, comprenant des degrés de liberté spatiaux et de polarisations. En particulier, nous vérifions expérimentalement la « zero transmission law » dans des interféromètres de Fourier et de Sylvester, permettant de quantifier le degré d’indiscernabilité d’un état d’entrée. De plus, grâce à la possibilité de mettre en oeuvre un réseau non unitaire, nous mettons en évidence l’anti-coalescence de photons dans toutes les configurations de sortie, et réalisons une expérience d’absorption cohérente. Nous démontrons ainsi l’aspect reconfigurable de l’implémentation de tels réseaux optiques linéaires dans des fibres multimodes. De plus, nous étudions les propriétés statistiques du speckle à un et à deux photons générés à partir de divers états d’entrée, après propagation dans une fibre multimode. Ces propriétés statistiques du speckle peuvent être utilisées pour extraire des informations sur la dimensionnalité, la pureté et l’indiscernabilité d’un état quantique inconnu, permettant ainsi leur classification. Ce travail met en évidence le potentiel du contrôle de front d’onde en milieux complexes pour le traitement quantique de l’information

Study of top and anti-top mass difference

The invariance of the standard model under CPT transformations leads to the equality of particle and antiparticle masses. The recent measurements performed by the CMS experiment on the top anti-top mass difference are a test of such symmetry. In this work non-perturbative QCD effects, which may eventually lead to an apparent difference in the mass of a top and anti-top quark, are studied

Entangled ripples and twists of light:Radial and azimuthal Laguerre-Gaussian mode entanglement

It is well known that photons can carry a spatial structure akin to a "twisted" or "rippled" wavefront. Such structured light fields have sparked significant interest in both classical and quantum physics, with applications ranging from dense communications to light-matter interaction. Harnessing the full advantage of transverse spatial photonic encoding using the Laguerre-Gaussian (LG) basis in the quantum domain requires control over both the azimuthal (twisted) and radial (rippled) components of photons. However, precise measurement of the radial photonic degree-of-freedom has proven to be experimentally challenging primarily due to its transverse amplitude structure. Here we demonstrate the generation and certification of full-field Laguerre-Gaussian entanglement between photons pairs generated by spontaneous parametric down conversion in the telecom regime. By precisely tuning the optical system parameters for state generation and collection, and adopting recently developed techniques for precise spatial mode measurement, we are able to certify fidelities up to 85\% and entanglement dimensionalities up to 26 in a 43-dimensional radial and azimuthal LG mode space. Furthermore, we study two-photon quantum correlations between 9 LG mode groups, demonstrating a correlation structure related to mode group order and inter-modal cross-talk. In addition, we show how the noise-robustness of high-dimensional entanglement certification can be significantly increased by using measurements in multiple LG mutually unbiased bases. Our work demonstrates the potential offered by the full spatial structure of the two-photon field for enhancing technologies for quantum information processing and communication

Characterizing and Tailoring Spatial Correlations in Multimode Parametric Down-Conversion

Photons entangled in their position-momentum degrees of freedom (DoFs) serve as an elegant manifestation of the Einstein-Podolsky-Rosen paradox, while also enhancing quantum technologies for communication, imaging, and computation. The multi-mode nature of photons generated in parametric downconversion has inspired a new generation of experiments on high-dimensional entanglement, ranging from complete quantum state teleportation to exotic multi-partite entanglement. However, precise characterisation of the underlying position-momentum state is notoriously difficult due to limitations in detector technology, resulting in a slow and inaccurate reconstruction riddled with noise. Furthermore, theoretical models for the generated two-photon state often forgo the importance of the measurement system, resulting in a discrepancy between theory and experiment. Here we formalise a description of the two-photon wavefunction in the spatial domain, referred to as the collected joint-transverse-momentum-amplitude (JTMA), which incorporates both the generation and measurement system involved. We go on to propose and demonstrate a practical and efficient method to accurately reconstruct the collected JTMA using a simple phase-step scan known as the $2D\pi$-measurement. Finally, we discuss how precise knowledge of the collected JTMA enables us to generate tailored high-dimensional entangled states that maximise discrete-variable entanglement measures such as entanglement-of-formation or entanglement dimensionality, and optimise critical experimental parameters such as photon heralding efficiency. By accurately and efficiently characterising photonic position-momentum entanglement, our results unlock its full potential for discrete-variable quantum information science and lay the groundwork for future quantum technologies based on multi-mode entanglement.Comment: 19 pages, 9 figure