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This thesis describes the work performed at the Quantum Optics lab at UNAM,Mexico City. Third order spontaneous parametric down conversion (TOSPDC) isa quantum optical process where an incoming photon is annihilated and generatesthree quantum entangled photons, so called photon triplets, under energy and mo-mentum conservation. This TOSPDC process was experimentally realized using afused silica optical fiber as nonlinear source. The spectra of the emitted signal weremeasured and coincidence counts measurements were performed in order to verifythe generation of these triplets. An average of 0.8 triplets per second were detected,which is the first sign of a realized TOSPDC process to our knowledge. At thispoint, the signal was too low for any spectra to be recorded. There is a lot of roomfor improvements, especially regarding the equipment used due to the heavy signalloss throughout the experimental setup, and more experiments will be performed toproperly verify the production and entanglement of the triplet photons.

A single spin confined to a semiconductor quantum dot is a system of significant interest for quantum information science, as a potential optically-addressable qubit. In many respects, a quantum dot behaves like a single atom with high quality single photon emission. By controlling the light-matter coupling in such a system, it is possible to generate highly non-classical states of light and coherently control a single spin confined to the quantum dot. A departure from the ideal atomic picture appears once we consider the mesoscopic environment with which the quantum dot interacts. Charge fluctuations in the surroundings of the quantum dot affect the photon emission frequency leading to inhomogeneous broadening. Further broadening of the emission is caused by coupling to phonon modes of the host semiconductor material. Finally, coupling between the spin of a confined electron and a large bath of nuclear spins residing in the quantum dot leads to fast dephasing of the electron spin. All of these effects are typically considered detrimental to the potential use of quantum dots for quantum technologies. In this thesis, we develop the environmental coupling of a negatively charged quantum dot as a resource for quantum optics and spin control. First, the phonon-assisted fluorescence is shown to be a useful independent channel for feedback stabilisation of the quantum dot emission frequency, without requiring a measurement of the indistinguishable zero-phonon line. With stabilisation, the corresponding frequency broadening is drastically improved, and the sub-Hz frequency fluctuations are no longer resolved. Next, we show low-power resonance fluorescence emission spectra of the negatively charged trion transition. In the low power regime of resonance fluorescence, the excited state is not populated and most of the emission is coherent. In addition to elastic Rayleigh scattering, we observe coherent Raman sidebands, linked to an effective magnetic field created by the hyperfine interaction, the Overhauser field. This fluctuating effective field lifts the electron spin degeneracy in the absence of a magnetic field, and dictates the optical selection rules of the trion system. These spectra therefore allow for a measurement of the time-averaged distributions of in-plane and out-of-plane Overhauser field components. In the final part of the thesis, we use this hyperfine-generated ? -scheme to optically create electron spin superpositions through two-colour excitation and coherent population trapping. We then show that rapid shifts in the relative phase of the lasers lead to initialisation of the electron spin into a rotated dark state.

L'optique quantique réalisée à l'échelle du nanometer est un défit crucial, surtout pour la caractérisation d'émetteur de photon unique. Ces émetteurs sont des défauts ponctuels dans des matériaux (quelques angströms) ou des structures confinées de quelques nanomètres. Une façon d'atteindre cette échelle est d'utiliser la cathodoluminescence (CL) dans un microscope électronique à transmission à balayage (CL-STEM) [1]. Cependant, lorsque l'on cherche à étudier les propriétés statistique d'émission de la lumière sortant d'une expérience de CL, ce qui est nécessaire pour étudier par exemple la nature quantique d'émetteur de photon unique (SPE), une expérience dédiée s'ajoutant à l'expérience de CL-STEM doit être réalisée. Quelques mois avant mon arrivé dans le groupe STEM du LPS, une expérience d'interférence des intensités (HBT) qui mesure la fonction d'autocorrélation g(2)(τ) du signal de CL a été construit [2]. Il est bien connu que la signature univoque d'un SPE en photoluminescence (PL) est l'antibunching, c'est à dire que le g(2)(τ) est toujours inférieur à un. Il a été récemment démontré que lorsque seulement un SPE est excité la CL-STEM est similaire à la PL sur un célèbre SPE, le centre NV dans le diamant. Dans cette thèse nous montrerons comment la CL-STEM a permis de caractériser un nouveau défaut ponctuel dans le h-BN, montrant la pertinence de l'expérience HBT dans un CL-STEM pour découvrir et caractériser de nouveaux SPE. Cependant, en étudiant l'excitation de multiple SPE en CL, on a découvert un nouveau phénomène d'émission, caractérisé par un grand effet de regroupement (bunching) dans la fonction g(2) (g(2)(0) > 35), en complète contradiction avec les mesures de PL et ce que l'on pourrait attendre (g(2)(0)< 1). Dans mon manuscrit de thèse, cet effet surprenant a été expérimentalement étudié, expliqué théoriquement et appliqué à la mesure de temps de vie à l'échelle du nanomètre. Parce que l'optique quantique est souvent liée à la plasmonique quantique, je présenterai pour conclure une proposition théorique en collaboration avec Javier Garcia de Abajo pour étudier la plasmonique quantique dans un microscope électronique à transmission à balayage. / Quantum optics performed at the nanometer scale is an important challenge, especially for quantum emitters characterization. They can be point defects in material (few ang- ströms) or confined structures of a few nanometers. A way to reach this scale is by using cathodoluminescence (CL) performed in a scanning transmission electron microscope (CL- STEM), which has only recently been done [1]. However, when aiming at studying the statistical properties of the light coming out of a CL experiment, which is necessary to e. g. study the quantum nature of Single Photon Emitters (SPE) emission, dedicated expe- riments on top of regular CL ones have to be designed. Few months before my arrival in the STEM-group of the LPS, an intensity interferometry experiment (HBT) that measures the autocorrelation function g(2) of the CL signal intensity was built [2]. It is well known that the clear signature of SPE as measured in photoluminescence (PL) is antibunching in the g(2)(τ), namely that the autocorrelation function is always less than one. It was re- cently demonstrated on a famous SPE, the Nitrogen vacancy (NV) defect in diamond, that CL-STEM is similar to PL when only one SPE is involved. In this thesis we will see how CL-STEM allowed to characterize a new point defect in h-BN, showing the relevance of HBT experiments in a CL-STEM for discovering and characterizing new SPE. However, by studying the excitation of multiple SPE in CL, we discovered a new emission phenomenon, characterized by a huge bunching effect of the g(2)(τ) function (g(2)(0) > 35), in complete contradiction to PL measurements and expectations (g(2)(0)<1). In my thesis manuscript, this surprising effect will be experimentally investigated, theoretically explained and applied to lifetime measurement at the nanometer scale. Because quantum optics is often linked to quantum plasmonics, I will present, to conclude, a theoretical proposal, in collaboration with J. Garcia de Abajo, about quantum plasmonics measurement in a STEM.

We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in $4$-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in $7$-level atoms near nanoparticles. This could be used as a prototype to study any $n-$level atomic system experimentally in the presence of ensembles of quantum emitters. In the last chapter, we suggested a variant of a pulse-shaping technique applicable in stimulated Raman spectroscopy (SRS) for detection of atoms and molecules in multiscattering media. We used discrete-dipole approximation to obtain the fields created by the nanoparticles.

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archives@tulane.edu / With the advent of lasers the spatial shape of paraxial light also became an avenue for information processing and transfer applications. The light sources that support multiple of these spatial modes as separate, multiplexed information channels are readily used through classical optical implementations such as free-space optical communication, and to enhance the capacity of these channels. Recently, the hot atomic vapour based non-linear optical systems showed promise for the usage of paraxial multiple spatial modes of light for quantum information applications such as quantum communication, quantum networking, quantum computation and various other quantum technologies. In this dissertation, we use analytical, numerical, statistical and experimental techniques to model the propagation of multi-spatial light through various classical and non-linear systems to be able to steer, optimize and control the quantum states generated for quantum technologies applications. In the first chapter, we give a general introduction to classical (both linear & non-linear) and quantum (both linear \& non-linear) optical systems we are going to analyze. In the second chapter, we use a numerical, Fourier transform based beam propagation technique to examine the self-healing of a generic beam that is generated through an atomic process. In the third chapter, we analyzed our hot atomic vapour four-wave mixing experiment that uses a special type of multiple paraxial spatial mode to drive the non-linear optical process through numerical modeling of Fraunhofer diffraction. In the fourth chapter, we devise a coherent, analytically and quantum mechanically motivated beam propagation method based on decomposing the paraxial beam into its constituent multiple spatial modes. We calibrate this method by using the numerical, experimental and theoretical results of the previous chapters to model how the multiple spatial modes propagate through spatial masks that represent apertures, obstructions, atmospheric turbulence. In the fifth chapter, we extend the beam decomposition formalism into semi-classical and full quantum mechanical optical systems to model seeded hot-atomic vapour four-wave mixing experiments. We again calibrate our numerical models of intensity difference squeezing using the previous experimental results. Next, we use these calibrated models to devise a scheme to optimally generate multi-mode squeezed states. Lastly, in the sixth chapter, we turn our attention into estimating the quantum state of discrete variable, polarization qubit systems using machine learning and various other stochastic techniques. We improve these well studied systems to detect the quantum states in real time, in the presence of noise, and in the absence of various measurements using machine learning. We study these discrete variable, polarization qubit systems both as a gateway and a complement to study the tomographic reconstruction of continuous variable quantum optical systems of the previous chapters, in order to achieve our general goal of having a general estimation, steering and control methodology for quantum networking applications. / 1 / ONUR DANACI

archives@tulane.edu / Quantum nonlinear optics has opened up avenues to defy the measurement, sensing, and amplification limits inherent in classical physics. Separately, the use of multimode or spatially structured states in light-based communications allows for remarkable increases in the amount of information that may be transferred by an individual communication or light pulse. In this dissertation, we apply these two boundary-pushing concepts to several experimental projects, with a primary goal to hasten and facilitate the implementation of quantum and classical free-space optical communications schemes into real-life scenarios. We start by applying neural networks to the optimization of spatially-structured and pulsed light communications in Chapter 2, wherein our networks successfully learn to predict distorted optical pulses and classify noisy light patterns carrying non-zero orbital angular momentum. Chapter 3 focuses on four-wave mixing, a nonlinear light-matter interaction in atomic vapor that we use to construct quantum-correlated light beams with nontrivial structures as well as a novel phase-sensitive amplifier. Finally, we continue to take advantage of the complex nonlinear response of atomic vapor in Chapter 4, this time to create "self-regenerating" light beams whose cross-sections resemble Bessel-Gauss functions. / 1 / Erin Knutson

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