Ce manuscrit porte sur l’étude théorique de techniques expérimentales récemment développées pour réaliser des protocoles d’information quantique en variables continues. Les états Gaussiens multi-modes produits par conversion paramétrique de peignes de fréquences optiques jouent un rôle centrale dans ce travail. Ce phénomène permet de générer de façon déterministe un grand nombre d’états Gaussiens de la lumière. L’état de sortie peut ensuite être de-Gaussifié par soustraction ou addition d’un photon dans une superposition cohérente de modes du champ, puis mesuré par détection homodyne. La thèse est organisée en trois projets principaux. Le premier concerne l’optimisation du spectre du laser de pompe pour manipuler l’état de sortie de la conversion paramétrique. Nous avons développé les outils mathématiques pour traiter des profils spectraux avec amplitude et phase spectrales arbitraires. On a ensuite utilisé un algorithme d’optimisation pour trouver les spectres maximisant des différentes propriétés de l’état de sortie. Une importance particulière est donnée à la production d’"états cluster" en variables continues. Les optimisations ont été développées pour prendre en compte les limitations expérimentales pour assurer la faisabilité des forme spectrales dans les expériences. Dans le deuxième projet nous avons étudié comment les états non-Gaussiens obtenus par soustraction d’un photon d’un état comprimé peuvent être utilisés pour le calcul quantique. Nous proposons un protocole inspiré par le paradigme de "calcul quantique basé sur la mesure" qui combine l’état de-Gaussifié et la mesure homodyne pour approximer des opérateurs unitaires non-Gaussiens. On montre que les mêmes résultats peuvent être obtenus avec des mesure projectives sur des états de photon unique. Finalement, le troisième projet porte sur le partage de secret quantique ("quantum secret sharing"). Dans les protocoles de partage de secret quantique un donneur veut distribuer de l’information codée dans un système quantique à plusieurs joueurs d’une façon qui oblige des sous-ensembles de joueurs à collaborer s’ils veulent retrouver l’information originale. Nous avons développé un protocole qui peut être transféré aux expériences de notre groupe et nous avons participé à la formulation d’une preuve de concept expérimentale. À partir de cela, nous avons dérivé des résultats généraux sur le partage et la reconstruction d’états arbitraires de la lumière en utilisant des ressources Gaussiennes. / The present manuscript reports theoretical investigations about the use of recently developed experimental techniques in the realization of quantum information protocols with continuous variables. The focus of the work is on the multi-mode Gaussian states produced by spontaneous parametric down-conversion of optical frequency combs. Such setup allows to deterministicallyengineer many different Gaussian states of light. The output state can be de-Gaussified subtracting or adding a photon coherently on a superposition of modes and finally measured with pulse-shaped and wavelength-multiplexed homodyne detection. The thesis encompasses three projects. The first concerns the optimization of the spectrum of the pump laser field to engineer the Gaussian output state. We developed mathematical techniques to treat spectral profiles with arbitrary amplitude and spectral phase. We thenran an optimization algorithm to find the spectra maximizing several interesting properties of the state of the down-converted field. A particular emphasis was put on the production of continuous-variable cluster states. The optimizations were developed in such a way as to ensure the experimental feasibility of the optimized pump spectra. In the second project we studied how the non-Gaussian states produced subtracting a photon from a squeezed state can be used for quantum computation. We propose a protocol inspired by the measurement-based paradigm for quantum computation combining the photon subtracted states and homodyne detectionto approximate unitary non-Gaussian operations. We show that the same results can be obtained with projective measurements onsingle-photon states. Finally, the third project deals with quantum secret sharing. In quantum secret sharing schemes a dealer wants to share information encoded in some quantum system with a group of players in such a way that subsets of players need to collaborate if they want to retrieve the information. We devised a secret sharing protocol that could be mapped to the experimental setups developed in our group and participated in the formulation of an experimental proof of principle of such protocol. Starting from this we derived general results for sharing and reconstructing arbitrary quantum states using Gaussian resources.

<div>Optical signals are a necessary tool for quantum technologies to carry information both for long-range and on-chip application. The scope of their use is determined by their ability to effectively interact with qubits. The deep-subwavelength interaction volume demands the understanding of the properties of optical fields in the near-field and light-matter interaction in this regime. Recent studies have unraveled the rich characteristics in the physical quantity known as the near-field photonic spin density (PSD). Photonic spin density is the spatial distribution of light's spin angular momentum. It is characterized by the degree of circular polarization of an optical field in deep-subwavelength volumes. In this thesis we study the properties of PSD in the near-field regime and demonstrate a platform for coherent light-spin-qubit interaction based on PSD. We show that nitrogen-vacancy (NV) centers in diamond can coherently interact with an optical beam where the interaction strength is determined by PSD in the nanoscale. To understand the near-field characteristics of PSD we study the evanescent waves and spin-momentum locking of light.</div><div><br></div><div>Evanescent electromagnetic waves possess spin-momentum locking, where the direction of propagation (momentum) is locked to the inherent polarization of the wave (transverse spin). We study the optical forces arising from this universal phenomenon and show that the fundamental origin of recently reported optical chiral forces is spin-momentum locking. For evanescent waves, we show that the direction of energy flow, direction of decay, and direction of spin follow a right hand rule for three different cases of total internal reflection, surface plasmon polaritons, and HE₁₁ mode of an optical fiber.</div><div>Furthermore, we explain how the recently reported phenomena of lateral optical force on chiral and achiral particles is caused by the transverse spin of the evanescent field and the spin-momentum locking phenomenon. Our work presents a unified view on spin-momentum locking and how it affects optical forces on chiral and achiral particles. </div><div><br></div><div>To probe the near-field properties of PSD, we propose and employ a single NV center in diamond as a nanoscale sensor. NV centers have emerged as promising room-temperature quantum sensors for probing condensed matter phenomena ranging from spin liquids, two-dimensional (2D) magnetic materials, and magnons to hydrodynamic flow of current. Here, we demonstrate that the NV center in diamond can be used as a quantum sensor for detecting the photonic spin density. We exploit a single spin qubit on an atomic force microscope tip to probe the spinning field of an incident Gaussian light beam. The spinning field of light induces an effective static magnetic field in the single spin qubit probe. We perform room-temperature sensing using Bloch sphere operations driven by a microwave field (XY8 protocol). This nanoscale quantum magnetometer can measure the local polarization of light in ultra-sub-wavelength volumes. We also put forth a rigorous theory of the experimentally measured phase change using the NV center Hamiltonian and perturbation theory involving only virtual photon transitions. </div><div><br></div><div>In order to study the wavelength dependence of the optically induced magnetic field, we demonstrate this effect for an ensemble of NV centers. We characterize the wavelength dependence of the effective static magnetic field caused by the interaction of PSD and the spin qubit. We show that the strength of the field is inversely dependent on the detuning between the frequency of the optical beam and the optical transition of the NV centers. We show an optically induced rotation of over 10 degrees in the spin qubit of NV centers at room temperature. The direct detection of the photonic spin density at the nanoscale using NV centers in diamond opens interesting quantum metrological avenues for studying exotic phases of photons, nanoscale properties of structured light as well as future on-chip applications. </div><div><br></div>

Das Stickstoff-Fehlstellen-Zentrum (NV-Zentrum) in Diamant ist eines der vielver- sprechendsten Spinsysteme für Anwendungen im Bereich Quanten-Computing, -Information und -Sensorik. Die Abhängigkeit der Fluoreszenzintensität vom Spinzu- stand ermöglicht dabei das rein optische Auslesen des Spinzustandes. Für alle Anwendungen, die auf aktive Spinmanipulation angewiesen sind, ist Mikrowellen- strahlung unverzichtbar. Die Fähigkeit, den Spinzustand von NV-Zentren vollständig zu kontrollieren, wird durch die Richtung, Intensität und Polarisation der Mikrow- ellenstrahlung definiert. Es gibt verschiedene Ansätze, um geeignete Mikrowellen- strahlung zu erzeugen, aber oft ist die Feldintensität zu gering oder es gibt andere Einschränkungen, z.B. eine geringe Frequenzbandbreite. Im ersten Teil meiner Arbeit untersuche ich transparente Leiter auf Basis von Indium- Zinn-Oxid (ITO), um die Mikrowellenansteuerung von NV-Zentren zu optimieren. Dabei wird eine detaillierte Analyse von ITO auf Diamant bezüglich einzelner NV-Zentren vorgestellt. Ein mathematisches Modell wurde entwickelt, um die Feldverteilung vorherzusagen. Zusätzlich wird eine Methode zur Kontrolle der Mikrowellenpolarisation mit einer transparenten ITO-Struktur vorgestellt, die zu einer vollständigen Kontrolle des Spinzustands des NV-Zentrums führt. Weiterhin werden Simulationen in Kombination mit einem analytischen Modell verwendet, um optimale Mikrowellenparameter für die Spinkontrolle vorherzusagen. Für eine kommerzielle Anwendung von NV-Zentren als Magnetfeldsensor sind Pro- duktionskosten und Bauteilkomplexität wichtige Faktoren, die in der Forschung oft vernachlässigt werden. Der zweite Teil meiner Arbeit konzentriert sich da- her auf einen mikrowellenfreien Ansatz zur Magnetometrie mit NV-Zentren. Der Einfluss der Laseranregung auf den magnetischen Kontrast wird an einzelnen NV- Zentren, Ensembles von NV-Zentren und Nano-Diamantpulver mit einer hohen NV- Zentrenkonzentration dargestellt und nachfolgend zur Demonstration von isotropen Magnetfeldmessung verwendet. Abschließend wird die Anwendbarkeit durch die Konstruktion eines Magnetfeldsensors aus Komponenten der Automobilbranche gezeigt. / The nitrogen vacancy center (NV center) in diamond is one of the most promising spin systems for applications in quantum computing, information and sensing. The dependency of the fluorescence intensity on the spin state allows a purely optical readout of the spin state. A green laser can be used to pump the NV center in the spin ground state while microwave radiation can manipulate the spin state of the NV center. For all applications depending on active spin manipulation, microwave radiation is indispensable. The ability to fully control the spin state of NV centers is defined by direction, strength and polarization of the microwave radiation. Different approaches exist to deliver the microwave radiation, but they often lack in strength or have other restrictions, e.g. a small frequency band width. In the first part of my thesis, I investigate transparent conductors based on indium tin oxide (ITO) to optimize microwave delivery. In this process a detailed analysis of ITO on diamond concerning confocal microscopy through this transparent film is presented. A mathematical model was developed and tested to predict the field distribution in possible applications. Additionally a method to control microwave polarization with a transparent ITO structure is shown which results in full spin state control of the NV center. Furthermore simulations combined with a analytical model are used to predict optimal microwave parameters for spin control. For a commercial application of NV centers as a magnetic field sensor, important factors are production cost and device complexity which are often neglected in research. The second part of my thesis therefore focuses on a microwave free approach of NV center magnetometry for industry applications. The influence of laser excitation on magnetic contrast was studied on single NV centers, ensembles of NV centers and nano diamond powder with a high NV center concentration. The findings were used to demonstrate isotropic magnetic field sensing. Finally, the applicability was shown by constructing a magnetic field sensor from automotive grade components.

Les photons apparaissent comme des vecteurs d'information fiables, car ils interagissent peu avec leur environnement. Malheureusement, ils interagissent si faiblement entre eux que la réalisation directe de portes logiques optiques à deux qubits est impossible. La propagation à travers des milieux atomiques non-linéaires permet néanmoins d'engendrer des interactions photon-photon effectives. L'utilisation du phénomène de transparence électromagnétiquement induite (EIT) permet d'induire une forte non-linearité résonante -- néanmoins pas encore détectable dans le domaine quantique, sur une transition d'un système à trois niveaux en “échelle”. Pour augmenter les effets non-linéaires et atteindre le régime quantique, il a récemment été proposé de combiner l'approche EIT au blocage d'excitation induit par les fortes interactions dipôle-dipôle entre atomes de Rydberg. En plaçant le milieu en cavité, on impose à la lumière des passages multiples et on accroît encore la non-linéarité optique. Ce type de dispositif a été étudié théoriquement et expérimentalement dans le régime dispersif et pour une non-linéarité faible, pour lequel un traitement classique du champ est adapté. Dans le présent mémoire, nous nous intéressons aux effets optiques non-linéaires induits par un milieu Rydberg dans le régime quantique.Dans le chapitre 1, nous présentons notre système d'étude, ses équations dynamiques et rappelons la définition et les principales propriétés de la fonction de corrélation d'intensité g^{2}que nous utilisons pour caractériser l'action de la non-linéarité sur le champ incident. Dans le chapitre 2, nous considérons le régime dispersif, i.e. lorsque l'état intermediaire est très désaccordé et peut être éliminé adiabatiquement. Nous utilisons l'approximation des bulles Rydberg selon laquelle le système peut être effectivement ramené à un ensemble de superatomes à deux niveaux couplés au mode de la cavité, décrit par le modèle de Tavis-Cummings forcé. Nous calculons analytiquement et numériquement la fonction g^{2}pour la lumière transmise, qui, selon les paramètres de la cavité, peut être “groupée” ou “dégroupée”. Dans le chapitre 3, nous présentons un traitement alternatif du système, qui nous permet d'étudier le régime résonant. Dans la limite d'un champ incident faible, nous dérivons analytiquement la fonction de corrélation g^{2} pour les lumières transmise et réfléchie, grâce à la factorisation des moyennes de produits d'opérateurs à l'ordre le plus bas de la théorie de perturbation. Nous proposons ensuite un modèle effectif non-linéaire à trois bosons pour le système couplé atomes-cavité. Enfin, nous étudions le régime résonant et observons de nouvelles caractéristiques de la fonction de corrélation g^{2}qui attestent la relation entre les conditions d'adaptation d'impédance de la cavité pour les différentes composantes du champ et les interactions dipôle-dipôle entre les atomes. Dans le chapitre 4, nous analysons le système dans le formalisme de Schwinger-Keldysh. En appliquant le théorème de Wick, nous développons perturbativement les fonctions de corrélation par rapport au Hamiltonien d'alimentation de la cavité et au Hamiltonien d'interaction dipôle-dipôle et effectuons une resommation complète par rapport à ce dernier. Nous retrouvons par cette méthode les résultats du Chapitre 3, sous une forme analytique. Nous allons aussi au-delà et derivons des expressions analytiques pour les composantes élastique et inélastique du spectre en transmission de la cavité. Nous identifions une structure de résonance polaritonique, jusque-là inconnue, que nous interprétons physiquement. Dans le chapitre 5, nous décrivons un protocole de porte photonique de phase de haute fidélité fondé sur le blocage Rydberg dans un ensemble atomique placé dans une cavité optique. Ce protocole peut être réalisé avec des cavités de finesse modérée et permet en principe un traitement efficace de l'information quantique codée dans des photons. / Photons appear as reliable information messengers since they interact very weakly with their environment. Unfortunately, they interact so weakly with each other that the direct implementation of optical two-qubit gates is impossible. The propagation through atomic nonlinear media however allows one to achieve effective photon-photon interactions. The technique of electromagnetically induced transparency (EIT) allows one to induce a strong resonant non-linearity -- not strong enough to be noticeable in the quantum domain though, on one of the transitions of a three-level ladder system. To enhance the nonlinear effects and reach the quantum regime, it was recently proposed to combine the EIT approach with the excitation blockade induced by the strong dipole-dipole interactions between Rydberg atoms. By putting the medium in a cavity, one imposes multiple passes to the light therefore increasing the optical nonlinearity. This kind of setup was studied both theoretically and experimentally in the dispersive regime and for a relatively weak nonlinearity, for which a classical treatment of the field is still valid. In this dissertation, we investigate the optical nonlinear effects induced by a Rydberg medium in the quantum regime.In chapter 1, we present our system, its dynamical equations and recall the definition and basic properties of the intensity correlation function g^{left(2right)}that we use to characterize the action of nonlinearity on the photonic field. In chapter 2, we consider the so-called dispersive regime, i.e. when the intermediate state is far detuned and can be adiabatically eliminated. We employ the Rydberg bubble approximation in which the system effectively consists in an ensemble of two-level superatoms coupled to the cavity mode, described by the driven Tavis-Cummings model. We compute analytically and numerically the g^{left(2right)}function of the transmitted light, which, depending on the cavity parameters, is shown to be either bunched or antibunched. In chapter 3, we present an alternative treatment of the system, which allows us to investigate the resonant regime. In the low-feeding limit, we analytically derive the correlation function g^{left(2right)}left(tauright)for the transmitted and reflected lights, based on the factorization of the lowest perturbative order of operator product averages. We then propose an effective non-linear three-boson model for the coupled atom-cavity system. Finally, we investigate the resonant regime and observe novel features of the correlation function g^{left(2right)}showing the interplay of impedance matching conditions and dipole-dipole interactions. In chapter 4, we analyze the system in the Schwinger-Keldysh formalism. Applying Wick's theorem, we perturbatively expand correlation functions with respect to both, feeding and dipole-dipole interactions Hamiltonians and perform a complete resummation with respect to the latter. By this method we recover the results of Chap. 3 in an analytic form. We also go beyond and derive analytic expressions for the elastic and inelastic components of the cavity transmission spectrum. We identify a polaritonic resonance structure in this spectrum, to our knowledge unreported so far, that we physically interpret. In chapter 5, we describe a novel scheme for high fidelity photonic controlled-phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. This protocol can be implemented with cavities of moderate finesse allowing for highly efficient processing of quantum information encoded in photons.

Recent advances in linear quantum optics have involved the development of unbiased, multi-port optical elements for use with pairs of identical photons, or biphotons, for the design of novel quantum devices. The unbiased counterpart of a conventional 50:50 beam-splitter is a particularly useful multiport, thanks to its unique algebraic properties when acting on both classical and quantum states of light. Dubbed the “Grover coin” due to its utility in the Grover’s Search quantum algorithm, the unbiased four-port behaves as a conventional beam splitter, but with two additional ports to provide a photon amplitude with four, equally-probable, spatially distinct paths through which it may propagate. While the Grover coin has been realized in the laboratory in the form of bulk optical elements, the formation of a network of Grover coins is impractical due to the meticulous alignment and large number of elements required for a single component. Therefore, the development of a small, chip-integrated embodiment of the unbiased four-port would enable experimentation with novel quantum optics theories, through the interconnection of multiple Grover coins over a small footprint. This thesis details the design and fabrication of photonic waveguide-based integrated circuit elements through numerical simulation, topology optimization and CMOS-compatible manufacturing processes. / 2025-06-08T00:00:00Z

We investigate the influence of the pump and collection mode parameters on the collection efficiency of Type I down converted photons into single mode fibers. For best single and coincidence counting rates, we find that the mode sizes should be close to the same size and that the mode waists should be located near the down-conversion crystal. Larger collection waists give higher collection efficiencies, but lower singles counts.

In this dissertation, the prospect of a quantum technology based on a photonic crystal chip hosting a quantum network made of quantum dot spins interacting via single photons is investigated. The mathematical procedure to deal with the Liouville-Von Neumann equation, which describes the time-evolution of the density matrix, was derived for an arbitrary system, giving general equations. Using this theoretical groundwork, a numerical model was then developed to study the spatiotemporal dynamics of entanglement between various qubits produced in a controlled way over the entire quantum network. As a result, an efficient quantum interface was engineered allowing for storage qubits and traveling qubits to exchange information coherently while demonstrating little error and loss in the process; such interface is indispensable for the realization of a functional quantum network. Furthermore, a carefully orchestrated dynamic control over the propagation of the flying qubit showed high-efficiency capability for on-chip single-photon transfer. Using the optimized dispersion properties obtained quantum mechanically as design parameters, a possible physical structure for the photonic crystal chip was constructed using the Plane Wave Expansion and FiniteDifference Time-Domain numerical techniques, exhibiting almost identical transfer efficiencies in terms of normalized energy densities of the classical electromagnetic field. These promising results bring us one step closer to the physical realization of an integrated quantum technology combining both semiconductor quantum dots and subwavelength photonic structures.

Models of the spontaneous emission and absorption of photons coupled to the electronic states of quantum dots, molecules, N-V (single nitrogen vacancy) centers in diamond, that can be modeled as artificial few level atoms, are important to the development of quantum computers and quantum networks. A quantum source modeled after an effective few level system is strongly dependent on the type and coupling strength the allowed transitions. These selection rules are subject to the Wigner-Eckert theorem which specifies the possible transitions during the spontaneous creation of a photonic state and its subsequent emission. The model presented in this dissertation describes the spatio-temporal evolution of photonic states by means of a Dirac-like equation for the photonic wave function within the region of interaction of a quantum source. As part of this aim, we describe the possibility to shift from traditional electrodynamics and quantum electrodynamics, in terms of electric and magnetic fields, to one in terms of a photonic wave function and its operators. The mapping between these will also be presented herein. It is further shown that the results of this model can be experimentally verified. The suggested method of verification relies on the direct comparison of the calculated density matrix or Wigner function, associated with the quantum state of a photon, to ones that are experimentally reconstructed through optical homodyne tomography techniques. In this non-perturbative model we describe the spontaneous creation of photonic state in a non-Markovian limit which does not implement the Weisskopf-Wigner approximation. We further show that this limit is important for the description of how a single photonic mode is created from the possibly infinite set of photonic frequencies νk that can be excited in a dielectric-cavity from the vacuum state. We use discretized central-difference approximations to the space and time partial derivatives, similar to finite-difference time domain models, to compute these results. The results presented herein show that near field effects need considered when describing adjacent quantum sources that are separated by distances that are small with respect to the wavelength of iii their spontaneously created photonic states. Additionally, within the future scope of this model, we seek results in the Purcell and Rabi regimes to describe enhanced spontaneous emission events from these few-level systems, as embedded in dielectric cavities. A final goal of this dissertation is to create novel computational and theoretical models that describe single and multiple photon states via single photon creation and annihilation operators.

<p dir="ltr">This thesis discusses the use of a fiber optic system to synchronize GHz frequency radio-frequency signals over distances of up to 5 km and its future applications in quantum communications. The stability of the synchronization is assessed by an ‘identity gate’, where each radio-frequency signal drives a phase modulator, and the frequency profile of a continuous wave laser sent through both modulators indicates the stability of the RF signals relative to one another. Experimental results indicate that 19 GHz signals synchronized over 5.5 km drifted less than 1 ps over 30 minutes. This is superior to the radio-frequency synthesizers’ built in synchronization method and to other commonly used protocols. To illustrate an application, the system was employed in a quantum nonlocal modulation cancellation experiment. Joint spectral characterization of the biphotons shows that this synchronization scheme can be used for nodes in a quantum communications network. More specifically, possible future applications of this technology include use in a photonic quantum local area network at Oak Ridge National Laboratories.</p>

We present a theoretical study that investigates the applicability of a graph theoretical approach to realize various quantum experiments. Crucially, we may represent quantum optical experiments involving tabletop optical elements in terms of highly interpretable, coloured, weighted multi-graphs. We introduce the formalism behind this approach; then through the digital discovery framework PyTheus, we uncover over 100 different quantum experiments which realizes complex, novel quantum states. Towards enhancing our interpretation of the AI-based framework's solutions, we also leverage eXplainable-AI (XAI) techniques from computer vision to investigate what a trained neural network learns about quantum experiments. Crucially, we find that we are able to conceptualize the learned strategies which the neural network applies to optimize for a target quantum property, and discover how the network conceives of its solution. We conclude by presenting an experimental proposal which yields realizable solutions that, for the first time, solves high-dimensional variants of a quantum retrodiction puzzle known as the Mean King's Problem. We, therefore, present a case study which investigates the potential for new scientific discoveries through a joint collaboration between human and artificial intelligence.