Thesis (M.S.)--Miami University, Dept. of Physics, 2005. / Title from first page of PDF document. Document formatted into pages; contains [1], v, 296 p. : ill. Includes bibliographical references (p. 393-396).

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xxiii, 261 p.; also includes graphics. Includes bibliographical references (p. 256-261). Available online via OhioLINK's ETD Center

The past three decades have seen extraordinary progress in the manipulation of neutral atoms with laser light, to the point where it is now routine to trap and cool both individual atoms and entire atomic clouds to temperatures of only a few tens of nanoKelvin in a controlled and repeatable fashion. In this thesis we study several applications of Rydberg atoms - atoms with an electron in a highly excited state - within such ultracold atomic systems. Due to their highly-excited electron, Rydberg atoms have a number of exaggerated properties: in addition to being physically large, they have long radiative lifetimes, and interact strongly both with one another and with applied external fields. Rydberg atoms consequently find many interesting applications within ultracold atomic physics. We begin this thesis by analysing the way in which a rubidium atom prepared in an excited Rydberg state decays to the ground state. Using quantum defect theory to model the wavefunction of the excited electron, we compute branching ratios for the various decay channels that lead out of the Rydberg states of rubidium. By using these results to carry out detailed simulations of the radiative cascade process, we show that the dynamics of spontaneous emission from Rydberg states cannot be adequately described by a truncated atomic level structure. We then investigate the stability of ultra-large diatomic molecules formed by pairs of Rydberg atoms. Using quantum defect theory to model the electronic wavefunctions, we apply molecular integral techniques to calculate the equilibrium distance and binding energy of these molecular Rydberg states. Our results indicate that these Ryberg macro-dimers are predicted to show a potential minimum, with equilibrium distances of up to several hundred nanometres. In the second half of this thesis, we present a new method of symbolically evaluating functions of matrices. This method, which we term the method of path-sums, has applications to the simulation of strongly-correlated many-body Rydberg systems, and is based on the combination of a mapping between matrix multiplications and walks on weighted directed graphs with a universal result on the structure of such walks. After presenting and proving this universal graph theoretic result, we develop the path-sum approach to matrix functions. We discuss the application of path-sums to the simulation of strongly-correlated many-body quantum systems, and indicate future directions for the method.

We study the atom-light interaction in the fully quantum regime, with the focus on off-resonant light scattering into a cavity from ultracold atoms trapped in an optical lattice. Because of the global coupling between the atoms and the light modes, observing the photons leaking from the cavity allows the quantum nondemolition (QND) measurement of quantum correlations of the atomic ensemble, distinguishing between different quantum states. Moreover, the detection of the photons perturbs the quantum state of the atoms via the so-called measurement backaction. This effect constitutes an unusual additional dynamical source in a many-body strongly correlated system and it is able to efficiently compete with its intrinsic short-range dynamics. This competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period, without the need of single site addressing. We demonstrate nontrivial dynamical effects such as large-scale multimode oscillations, breakup and protection of strongly interacting fermion pairs. We show that measurement backaction can be exploited for realizing quantum states with spatial modulations of the density and magnetization, thus overcoming usual requirement for a strong interatomic interactions. We propose detection schemes for implementing antiferromagnetic states and density waves and we demonstrate that such long-range correlations cannot be realized with local addressing. Finally, we describe how to stabilize these emerging phases with the aid of quantum feedback. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems and it is easily extendable to other systems promising for quantum technologies.

Ce manuscrit est consacré à la caractérisation de structures cristallines pour des applications de technologie quantique. Il est composé de deux parties.Dans un premier projet, nous étudions la transition d'une particule d'un état étendu à un état localisé dans un cristal artificiel quasipériodique, dont le potentiel dépend de la position de la particule. Nous considérons un atome ultrafroid, confiné par un réseau optique et incorporé dans une cavité optique. Le dipôle atomique est en interaction forte avec le champ électrique dans la cavité, ce qui mène à un deuxième potentiel optique pour l'atome. La position de l'atome dans la cavité influence notamment le champ intracavité~: le mouvement de l'atome a donc un effet rétroactif sur le potentiel dans lequel il est confiné. Pour des longueurs d'onde incommensurables, nous montrons que la compétition entre les deux réseaux optiques donne lieu à un potentiel quasipériodique pour l'atome. Nous déterminons les paramètres pour lesquels nous reproduisons le modèle Aubry-André et nous discutons les effets de la rétroaction de la cavité sur la transition de localisation.Le deuxième projet est une proposition pour générer une radiation THz, en utilisant le couplage entre excitons et phonons dans un cristal semi-conducteur. Nous proposons un schéma de conversion de fréquence, basé sur une chaîne d'interactions naturellement présentes dans une cavité semi-conductrice pompée. La partie cruciale du schéma de conversion de fréquence est l'interaction faible entre des excitons et des phonons transverses optiques. Nous la dérivons en commençant avec l'interaction électron-phonon via le potentiel de déformation et en prenant en compte les propriétés de symétrie du cristal. Nous identifions les conditions nécessaires pour générer une radiation THz, nous estimons la puissance de l'émission et nous montrons que l'interaction entre excitons et phonons transverses optiques fournit une susceptibilité non linéaire d'ordre deux. / This thesis is devoted to the characterization of crystalline structures for quantum technological applications. It is composed of two parts.In a first project we study the localization transition of one particle in an one-dimensional artificial quasiperiodic crystal, whose potential depends on the particle position. We consider an ultracold atom in an optical lattice, embedded in an optical cavity. The atom strongly couples to the cavity, leading to a second optical potential. The position of the atom within the cavity affects the cavity field, thus the atomic motion backacts on the potential it is subjected to. For incommensurate wavelengths, we show that the competition between the two potentials yields a quasiperiodic potential. We determine the parameters for which we reproduce the Aubry-Andr'e model and discuss the effects of the backaction on the localization transition.In the second project we propose a frequency down-conversion scheme to generate THz radiation using the exciton-phonon coupling in a semiconductor crystal. Our idea is based on a chain of interactions that are naturally present in a pumped semiconductor microcavity. We derive the crucial exciton-phonon coupling, starting from the electron-phonon interaction via the deformation potential and taking into account the crystal symmetry properties. We identify conditions necessary for THz emission, estimate the emission power and show that the exciton-phonon interaction provides a second-order susceptibility.

Cette thèse s’inscrit dans le domaine de l'opto-mécanique et propose l'utilisation de différentes techniques de mesure et de manipulation des propriétés mécaniques de nano-structures.La première partie de ce travail est dédiée aux fils photoniques. Ces objets sont des structures en GaAs en forme de cône inversé, avec une longueur d’une dizaine de µm et un diamètre inférieur au µm, contenant une couche de boîtes quantiques à l'intérieur. Nous avons démontré une méthode de réglage statique du spectre de photoluminescence de ces boîtes quantiques sensibles à la contrainte, en utilisant des nano-manipulateurs pour contraindre mécaniquement les fils. De plus, grâce à la dépendance spatiale du décalage spectral, il est possible d’établir une carte de la position des boîtes quantiques.La deuxième partie de ce travail concerne la mise en mouvement de ces fils photoniques à l’aide d’un faisceau laser modulé à la fréquence de résonance mécanique. Les mécanismes physiques à l’origine de ces effets sont présentés et discutés.Dans la troisième partie, nous présentons une méthode permettant l’observation d'oscillations mécaniques de nano-fils fins (moins de 50 nm de diamètre) en utilisant un microscope électronique à balayage. Cette méthode originale offre la possibilité de contrôler de nombreux types de structures micro et nano-électromécaniques, dont la détection du mouvement n’est pas possible optiquement en raison de la limite de diffraction de la lumière. De plus, cette méthode permet également d'agir sur les propriétés mécaniques des structures via une force de contre-réaction qui devient non négligeable pour ces structures très légères. Cela ouvre la possibilité d'études fondamentales complémentaires liées au refroidissement du mouvement mécanique. / This thesis is related to the field of opto-mechanics and the use of different techniques for the measurement and manipulation of mechanical properties of nano-structures.First part of the work is dedicated to the photonic wires. These objects are GaAs structures with an inverted conical shape of length of the order of 10 µm and diameter of less than 1 µm, containing a layer of InAs quantum dots inside. Wide-range static stress-tuning of quantum dots photoluminescence spectrum was demonstrated using nano-manipulators to bend the wires. Additionally, owing to the spatial dependence of the spectral shift, this technique offers the possibility of QD positions mapping.The second part of this work concerns the optical actuation of these photonic wires. A laser beam focused on the wire and modulated at the mechanical resonance frequency can set the wire in motion. The physical mechanisms responsible for these effects are presented and discussed.In the third part is presented a method enabling the detection of mechanical oscillations of small (less than 50 nm in diameter) nanowires with the use of a Scanning Electron Microscope. This original method offers a possibility to detect the motion of many types of micro- and nano-electromechanical devices which are too small to be detected optically owing to light diffraction limit.Moreover, this method also affects the mechanical properties of the structures via a back-action force that becomes non-negligible for such small devices. It opens up the possibility for further fundamental studies related to cooling of the mechanical motion.

La thermodynamique a été développée au XIXe siècle pour décrire la physique des moteurs et autres machines thermiques macroscopiques. Depuis lors, le progrès des nanotechnologies a rendu nécessaire d'étendre ces lois, initialement pensées pour des systèmes classiques, aux systèmes obéissant à la mécanique quantique. Durant cette thèse, j'ai mis en place un formalisme pour étudier la thermodynamique stochastique des systèmes quantiques, dans lequel la mesure quantique occupe une place centrale: à l'instar du bain thermique de la thermodynamique statistique classique, la mesure est ici la source première d'aléatoire dans la dynamique. Dans un premier temps, j'ai étudié la mesure projective comme une transformation thermodynamique à part entière. J'ai montré que la mesure cause un changement incontrôlé de l'énergie du système quantique étudié, que j'ai appelé chaleur quantique, ainsi qu'une production d'entropie. Comme application de ces concepts, j'ai proposé un moteur qui extrait du travail à partir des fluctuations quantiques induites par la mesure. Ensuite, j'ai étudié les mesures généralisées, ce qui a permis de décrire des systèmes quantiques ouverts. J'ai défini les notions de travail, de chaleur, et de production d'entropie pour une réalisation unique d'une transformation thermodynamique, et retrouvé que ces quantités obéissent à des théorèmes de fluctuation. Ce formalisme m'a permis d'analyser le comportement thermodynamique de la situation canonique de l'optique quantique : un atome à deux niveaux en couplé à un laser et au vide électromagnétique. Enfin, j'ai étudié une plate-forme prometteuse pour tester la thermodynamique d'un Qubit : un système hybride optomécanique.Le formalisme développé dans cette thèse peut être d'un grand intérêt pour la communauté de thermodynamique quantique car il permet de caractériser les performances des machines thermiques quantiques et de les comparer à leurs analogues classiques. En outre, en caractérisant la mesure quantique comme un processus thermodynamique, il ouvre la voie à de nouveaux types de machines thermiques, exploitant d'une manière inédite les spécificités du monde quantique. / Thermodynamics was developed in the XIXth century to provide a physical description to engines and other macroscopic thermal machines. Since then, progress in nanotechnologies urged to extend these formalism, initially designed for classical systems, to the quantum world. During this thesis, I have built a formalism to study the stochastic thermodynamics of quantum systems, in which quantum measurement plays a central role : like the thermal reservoir of standard stochastic thermodynamics, it is the primary source of randomness in the system's dynamics. I first studied projective measurement as a thermodynamic process. I evidenced that measurement is responsible for an uncontroled variation of the system's energy that I called quantum heat, and also a production of entropy. As a proof of concept, I proposed an engine extracting work from the measurement-induced quantum fluctuations. Then, I extended this formalism to generalized measurements, which allowed to describe open quantum systems (i.e. in contact with reservoirs). I defined work, heat and entropy production for single realizations of thermodynamic protocols, and retrieved that these quantities obey fluctuation theorems. I applied this formalism to the canonical situation of quantum optics, i.e. a Qubit coupled to a laser and a the vacuum. Finally, I studied a promising platform to test Qubit's thermodynamics: a hybrid optomechanical system.The formalism developed in this thesis could be of interest for the quantum thermodynamics community as it enables to characterize quantum heat engines and compare their performances to their classical analogs. Furthermore, as it sets quantum measurement as a thermodynamic process, it pave the ways to a new kind of thermodynamic machines, exploiting the specificities of quantum realm in an unprecedented way.

Photonic quantum information processing has emerged as a powerful platform for realising quantum-enhanced technologies. In order to be scalable, many of these technologies depend on the availability of a suitable quantum memory for the coherent storage and on-demand retrieval of photonic quantum states. In this thesis, I investigate broadband light storage in a room-temperature Raman memory, implemented both in free space and, for the first time, inside a low-finesse optical cavity designed for low-noise operation. The ability of the Raman memory to preserve phase coherence was tested by storing coherent polarisation states in two spatially separate atomic ensembles. Polarisation storage with a fidelity of up to 97 ± 1% was demonstrated by performing full process tomography on the system. The Raman memory was then interfaced for the first time with a spontaneous parametric downconversion (SPDC) source of heralded, GHz-bandwidth single photons. The memory performance was characterised by measuring the second-order autocorrelation of the retrieved fields. While the SPDC input photon statistics showed a clear influence on the statistics of the retrieved field, four-wave mixing (FWM) noise, stimulated by spontaneous Raman scattering, prevented the preservation of non-classical photon statistics during read-out. Suppressing this source of noise represents the last remaining challenge for realising a broadband single-photon Raman memory suitable for quantum information applications. To this end, I demonstrate a novel cavity implementation of the Raman memory which reduces the FWM contribution relative to the signal field by re-distributing the density of states into which the noise photons can be scattered. Cavity-enhanced memory operation was investigated using weak coherent input states, showing a significant improvement of the signal-to-noise ratio compared to the free-space memory implementation. This proof-of-principle demonstration suggests that cavity Raman memories may offer a practical route towards low-noise, high-bandwidth quantum storage at room temperature.

xiii, 164 p. : ill. (some col.) / We explore the frequency translation of single-photon states of light and the creation of photon pairs by four-wave mixing in optical fiber. Frequency translation refers to changing the central frequency of a field, while photon pair creation refers to the creation of two individual photons at the same time. We demonstrate these effects in third-order nonlinear optical fiber. While both phenomena have previously been shown by three-wave mixing in second-order nonlinear media, there are compelling reasons to develop these tasks in third-order media. Most importantly, frequency translation in third-order material allows for the practical implementation of both small and large frequency shifts, while second-order material only practically allows for large shifts. Photon creation in third-order media often permits more flexible phase-matching conditions, allowing for the creation of a wider variety of quantum states than is often possible in second-order media. In our theoretical study of photon pair creation, we focus on the spectral correlations of the photon pairs. We pay particular attention to the creation of quantum states of high purity, where the photons are not spectrally correlated with one another. High purity photons are a requisite resource for several different quantum information processing applications, such as linear-optical quantum computing. We find that states with high purity can be realized with a minimal amount of spectral filtering. Experimentally, we study photon frequency translation in photonic crystal fiber. The central wavelength of the input photons was translated from 683 nm to 659 nm. We perform second-order intensity correlation measurements on both channels to demonstrate their quantum nature. This resulted in values of 0.21 ± 0.02 and 0.19 ± 0.05 for the 683-nm and 659-nm channels, respectively, demonstrating that those fields were dominated by their single-photon component. The efficiency at which the process occurred was 29 percent. Theoretically, we develop a Green function formalism to describe the translation process and develop a computational model to calculate the solution to the governing equations. Also, in a related experiment, we demonstrate classical frequency translation from 851 nm to 641 nm, a record translation in both wavelength and frequency, at an efficiency of 0.2 percent in a birefringent fiber. / Committee in charge: Dr. Daniel Steck, Chair; Dr. Michael Raymer, Advisor; Dr. Steven van Enk, Inside Member; Dr. Raghuveer Parthasarathy, Inside Member; Dr. Andrew Marcus, Outside Member

We study different phenomena associated with single-photon propagation in optical cavities coupled through optical fibers. We first address the issue of storing and delaying single-photon wavepackets in an array of microcavities. This has possible applications in developing reliable and efficient quantum repeaters that will be utilized in building long distance quantum networks. Second, we investigate a Hong-Ou-Mandel (HOM) type of interference between two photons that are produced in two coupled atom-cavity systems. The HOM effect in this setup can test the degree of indistinguishability between photons when they are stored inside cavities. This part of the dissertation also includes the study of entanglement between atoms, cavities and atom-cavity systems induced by the photons. Finally, we focus on single-photon interactions with a tiny movable mirror in the context of quantum optomechanics. We investigate how the mechanical motion of the mirror leaves its imprints on the optical spectrum of the photon This dissertation includes previously published and unpublished co-authored material. / 10000-01-01