Spatiotemporal properties of classical coupled nonlinear oscillators are investigated in this thesis. Chapter 1 gives an introduction to nonlinear lattices and to the concept of breathers, that are spatially localized and temporally periodic excitation in nonlinear lattices. The concept of anti-continuous limit that provides the basic methodology in probing spatiotemporal breather properties is discussed. In Chapter 2, the general approach for finding exact breather solutions from the anti-continuous limit is examined, and the rotating wave approximation(RWA) is applied to probe the spatial structure of static breathers. Numerical evidence reveals that the RWA relates the spatial structure of stable multi-breathers to a single breather of the same frequency. Chapter 3 presents linear stability analysis of static breathers and gives a systematic way to construct mobile breathers. Formation and collision properties of this moving breathers are also studied. Chapter 4 discusses dynamics of kinks and anti-kinks in hydrogen-bonded chains in the context of two-component soliton model. From molecular dynamics simulations with finite temperature, it is observed that, in a real system (eg. ice), a pair of kink and anti-kink can evolve into a moving-breather-like excitation. Chapter 5 is devoted to the understand of the effects of disorder in the Holstein model. The summary is given in Chapter 6.

The gauge-invariant formulation of quantum mechanics is compared to the conventional approach for the case of a one-dimensional charged harmonic oscillator in an electromagnetic field in the electric dipole approximation. The probability of finding the oscillator in the ground state or excited states as a function of time is calculated, and the two approaches give different results. On the basis of gauge invariance, the gauge-invariant formulation of quantum mechanics gives the correct probability, while the conventional approach is incorrect for this problem. Therefore, expansion coefficients or a wave function cannot always be interpreted as probability amplitudes. For a physical interpretation as probability amplitudes the expansion coefficients must be gauge invariant.

La structure traditionnelle d'un oscillateur optoélectronique (OEO) s'appuie sur une boucle de fibre optique très longue, servant de ligne à retard et lui conférant la grande pureté spectrale, ou le très faible bruit de phase de l'oscillateur. Un tel oscillateur fonctionnant à la fréquence de 8 GHz a été mis en œuvre aux laboratoires SATIE/LPQM de l'ENS Cachan. Néanmoins un tel système présente des inconvénients comme les dimensions un peu grandes, la difficulté de contrôler la température et un large peigne de fréquences parmi lequel il est difficile d'extraire un seule mode. Il est en fait possible d'éliminer ses inconvénients en remplaçant la boucle de fibre par un micro-résonateur optique de grand facteur de qualité. Dans cette thèse deux types résonateurs ont été fabriqués et étudiés. Des microsphères ont été fabriquées à partir de fibres optiques de fibres optiques monomodes. Les modes de galeries de ces résonateurs sont caractérisés grâce à couplage avec une fibre effilée. L'étude expérimentale met en évidence un facteur de qualité pouvant atteindre une valeur de 106 et un intervalle spectral libre (FSR) dépendant du diamètre de la sphère. Ainsi pour un diamètre de 300 µm on obtient un FSR de 0,2 nm soit 25 GHz en fréquence. Mais pour un OEO fonctionnant à la fréquence de 8 GHz il faudrait un FSR plus petit et donc une sphère dont le diamètre serait de taille millimétrique, donc très difficile à fabriquer. Un autre type de résonateur, en forme d'hippodrome, a été conçu et étudié. L'étude expérimentale a été conduite par un couplage avec de fibres lentillées. Le spectre en transmission présente des pics de résonances avec un facteur de qualité moyen de 0,050 ± 0.003 nm (correspondant en fait à 6 GHz) sur une plage de longueurs d'onde allant de 1534 nm à 1610 nm. Les caractéristiques les plus intéressantes de ce résonateur en forme d'hippodrome sont un facteur de qualité élevé et un intervalle spectral libre tout à fait en accord avec les besoins de l'OEO étudié. Néanmoins le couplage avec les fibres lentillées induit des pertes optiques trop importantes pour satisfaire aux conditions d'oscillations. Les travaux futurs devront porter sur l'amélioration du couplage ainsi que sur l'asservissement des pics de résonnance du micro-résonateur sur la longueur d'onde du laser employé dans l'OEO. / The classical structure of an Opto-Electronic Oscillator (OEO) is based on a long fiber loop acting as a delay line and leading to the high spectral purity, or very low phase noise, of the oscillator. Such an OEO has been developed in SATIE/LPQM laboratory at ENS Cachan, operating at 8 GHz frequency. However, this system has some main disadvantages such as a bulky size, the difficulty to control temperature and a wide range of peaks among which it is difficult to select only one mode. In order to eliminate these disadvantages, high quality factor optical resonator can be used instead of the optical fiber loop. In this thesis, two resonator structures are produced and investigated. Microspheres are fabricated based on optical single mode fiber. Whispering gallery modes of these resonators are characterized by tapered fiber –resonator coupling. The experimental results show that the quality factor of the microsphere is up to 106 and FSR depends on the diameter of the resonator. A microsphere with a diameter of 300 µm, presents a FSR of 0.2 nm corresponding to a frequency of 25 GHz. However, for an OEO system which should work at 8 GHz, microsphere with a smaller FSR or with diameter of some millimeters should be fabricated- that is really difficult to obtain. Another add/drop racetrack resonator is designed and investigated. Optical experimental behavior of racetrack is characterized via fiber micro-lens coupling. The transmission spectrum shows resonance dips with average quality factor of 105 and a small FSR of 0.050 ± 0.003 nm (actually corresponding to 6 GHz) for a scanning wavelength range from 1534 nm to 1610 nm. The most promising features of the racetrack resonator are its high quality factor, and its free spectral range, which give it the high suitability for being used in the OEO system. Nevertheless the coupling with fiber lens leads to high losses and it is not possible to fulfill the oscillation conditions. Future work should be conducted for improving the coupling and for controlling the resonance dips position in agreement with the wavelength of the laser used in the OEO.

No description available.

A study of magnetization dynamics experiments in nanostructured materials using the rf susceptibility tunnel diode oscillator (TDO) method is presented along with a extensive theoretical analysis. An original, computer controlled experimental setup that measures the change in susceptibility with the variation in external magnetic field and sample temperature was constructed. The TDO-based experiment design and construction is explained in detail, showing all the elements of originality. This experimental technique has proven reliable for characterizing samples with uncoupled magnetic structure and various magnetic anisotropies like: CrO2 , FeCo/IrMn and Co/SiO2 thin films. The TDO was subsequently used to explore the magnetization switching in coupled magnetic systems, like synthetic antiferromagnet (SAF) structures. Magnetoresistive random access memory (MRAM) is an important example of devices where the use of SAF structure is essential. To support the understanding of the SAF magnetic behavior, its configuration and application are reviewed and more details are provided in an appendix. Current problems in increasing the scalability and decreasing the error rate of MRAM devices are closely connected to the switching properties of the SAF structures. Several theoretical studies that were devoted to the understanding of the concepts of SAF critical curve are reviewed. As one can notice, there was no experimental determination of SAF critical curve, due to the difficulties in characterizing a magnetic coupled structure. Depending of the coupling strength between the two ferromagnetic layers, on the SAF critical curve one distinguishes several new features, inexistent in the case of uncoupled systems. Knowing the configuration of the SAF critical curve is of great importance in order to control its switching characteristics. For the first time a method of experimentally recording the critical curve for SAF is proposed in this work. In order to overcome technological limitations, a new way of recording the critical curve by using an additional magnetic bias field was explored.

The newly discovered iron based superconductors have captivated the attention of the scientific community due to the unusual mechanism behind their superconductivity and their promise as the next generation high temperature superconductors. After a century of superconductor research, the physical mechanism behind high temperature superconductivity is still not understood. These new materials bring renewed hope in elucidating the pairing mechanism responsible with high temperature superconductors and achieving the ultimate goal of the field, room temperature superconductivity. Consequently, a deeper understanding of the intriguing properties of iron based materials is essential. A great deal about the pairing mechanism of Cooper electron pairs can be inferred from the symmetry of their pairing wave function or order parameter. One of the most involved probes for studying the pairing symmetry is the London penetration depth. The low temperature behavior of London penetration depth in superconductors is directly related to the density of states and provides a powerful tool for investigating low-lying quasiparticle energy and, for this very reason, can give valuable hints on superconducting gap symmetry. The work presented focuses on investigating the pairing symmetry in the Fe1+y(Te1−xSex) system using a radio-frequency tunnel diode oscillator (TDO) technique for precise measurements of the temperature dependence of their in-plane penetration depth. The TDO technique, based on an original concept involving the use of planar inductors in an novel configuration, was implemented on a dilution refrigerator to investigate a significant number of single crystal samples, with nominal Se concentrations of 36%, 40%, 43% and 45% respectively, down to temperatures as low as 50 mK. A systematic study together with a comprehensive analysis regarding the order parameter symmetry in the Fe1+y(Te1−xSex) system is presented. In many cases we found that London penetration depth shows an upturn below at low temperatures, indicative of a paramagnetic-type contribution. Also the low-temperature behavior of penetration depth is best described by a quadratic power law with no systematic dependence on the Se concentration. Most importantly, in the limit of T → 0, in some samples we observed a narrow region of linear temperature dependence, suggestive of nodes in the superconducting gap of Fe1+y(Te1−xSex).

Nesta dissertação, descreveremos as primeiras medidas de ruído quântico em um oscilador paramétrico ótico (OPO) bombeado em 780 nm, construído no nosso laboratório. Esse OPO servirá de fonte de estados não clássicos da luz para interação com átomos de rubídio. Faremos uma revisão da teoria clássica do OPO: o bombeamento de um cristal não linear inserido dentro de uma cavidade ótica, produzindo dois feixes intensos de luz (sinal e complementar) com cores distintas. Calcularemos as expressões para o limiar de oscilação, potências de saída dos feixes convertidos e compararemos as principais diferenças entre OPOs com cristais do tipo I e tipo II. Analisaremos a descrição quântica do OPO, calcularemos os espectros de ruído para as quadraturas do bombeio refletido e para as quadraturas dos feixes gêmeos. Veremos que o OPO gera feixes com correlações quânticas, como o emaranhamento tripartido, entres os três feixes envolvidos no processo não linear. O cristal não linear utilizado no nosso experimento é um PPKTP tipo I. Ajustando a temperatura do cristal, podemos gerar feixes próximos da degenerescência até uma diferença de comprimentos de onda de aproximadamente 350 nm. A compressão de ruído quântico observado na diferença das amplitudes dos feixes sinal e complementar é 44%(-2.5 dB). O próximo passo é a implementação da técnica da rotação da elipse de ruído por cavidades óticas, para medir os ruídos de fase dos três campos . Fazendo a verificação do emaranhamento tripartido e determinando a sua dependência com o ruído de fônons inserido pelo cristal, a caracterização do OPO estará completa. A caracterização deste OPO é um passo importante nos objetivos do LMCAL, que é realizar a troca de informação entre luz e átomos em uma rede quântica. / In this dissertation, we will describe the first measurements of quantum noise in an optical parametric oscillator (OPO) pumped at 780 nm, built at our laboratory. This OPO will be the source of nonclassical states of light to interact with rubidium atoms. We will review the classical OPO theory: the pumping of a nonlinear crystal inside a cavity producing two bright light beams (signal and idler) with different colors. We will calculate the power threshold, output power of the converted beams and compare the main differences between type-I and type-II OPO.We will analyze the quantum description of the OPO, and calculate the noise spectrum of the reflected pump quadratures and for the twin beams quadratures. We will observe that the OPO generates beams with quantum correlations, for example, the tripartite entanglement among the three fields involved in the nonlinear phenomena. The nonlinear crystal used in our experiment is a PPKTP type-I. By adjusting the temperature of the crystal, we can generate beams from close to degenerate regime to a difference between them of 350 nm. The squeezing of quantum noise measured in the amplitude quadratures subtraction for signal and idler is 44%(-2.5 dB). The next step is to implement the method of ellipse noise rotation by an optical cavity, to be able to measure phase quadratures of the three different fields. By verifying the tripartite entanglement and determining the phonon noise due to the crystal, our source characterization will be complete. The characterization of this OPO is an important step in LMCAL goals, which is to realize exchange of information between light and atoms in a quantum network.

Realizamos neste trabalho a construção de um Oscilador Paramétrico Ótico triplamente ressonante bombeado por um laser de Titânio Safira sintonizável na faixa entre 730 nm e 800 nm com potencial de extensão. Os feixes emitidos possuem comprimento de onda em torno de 1560 nm que estão na janela de transmissão das fibras óticas, com potência de saída máxima em torno de 420 mW e um limiar de oscilação mínimo de 53(3) mW quando bombeado por 780.126(0.03) nm. Para os feixes gêmeos a finesse da cavidade vale F=155 e as perdas intracavidade 0.05(0.1)%, permitindo, em tese, uma compressão de ruído próxima a 97(6)%. Esse OPO foi construído com o propósito de que o utilizemos como fonte geradora de estados triplamente emaranhados em um sistema de armazenamento e transferência de informação quântica quando em interação com um sistema atômico de rubídio. Medimos a potência de limiar e a eficiência de conversão para cada comprimento de onda do feixe de bombeio utilizado para caracterizar o sistema. / At the present work we conducted the construction of a triply resonant Optical Parametric Oscillator pumped by a Titanium-Sapphire laser, which is tunable between 730 nm to 800 nm. The emitted beams have wavelength around 1560 nm, in the optical fibers transmission window, maximum output of 420 mW and minimum oscillation threshold of 53(3) mW. For the twin beams, the cavity finesse is F=155 mW and the intracavity losses are 0.05(0.10)%, allowing, in principle, a noise compression close to 97(5)%. The present OPO was built having the purpose of being used as source of triply entangled states in a system for quantum information storage and transfer, while interacting with an atomic rubidium system. We measured the power threshold and conversion efficiency for each pump beam wavelength that we used to characterize the system.

Apresentamos nesta tese a primeira geração direta de emaranhamento tripartite entre feixes intensos de luz. Medimos o emaranhamento entre os feixes sinal, complementar e bombeio refletido, produzidos por um Oscilador Paramétrico Ótico (OPO) operando acima do limiar de oscilação. A principal característica do nosso sistema é a diferença entre os comprimentos de onda dos campos (l0 = 532.251 nm, l1 = 1062.102 nm, e l2 = 1066.915 nm). Esta é a primeira medida de emaranhamento entre mais de dois subsistemas produzidos por uma única fonte no âmbito de variáveis contínuas. Para investigar a existência emaranhamento, utilizamos o critério de positividade sob transposição parcial (PPT). Este critério, aplicado a sistemas compostos por estados gaussianos, dispostos em bipartições do tipo 1×(N 1), torna-se necessário e suficiente na demonstração do emaranhamento. Realizamos também a caracterização do emaranhamento produzido quando submetemos os campos a perdas, identificando regiões de parâmetros onde os estados apresentam emaranhamento frágil ou robusto. A fim de garantir que estamos lidando com estados gaussianos, investigamos a estatística das flutuações dos campos, mostrando excelente acordo entre os valores dos momentos de ordem mais alta da fotocorrente medida e os valores esperados para uma distribuição gaussiana. O estudo que apresentamos é um passo importante para a elaboração de uma rede de informação quântica que possibilitará a comunicação entre diferentes sistemas físicos. / We present in this thesis the first direct generation of tripartite entanglement among bright beams of light. We measured the entanglement among signal, idler and reflected pump beams, produced by an Optical Parametric Oscillator (OPO) operating above the threshold. The main feature of our system is the difference between the wavelengths of the fields (l0 = 532.251 nm, l1 = 1062.102 nm, e l2 = 1066.915 nm). This is the first measurement of entanglement among more than two subsystems produced by a single source, in a continuous variable system. In order to investigate the existence of entanglement, we applied the criterion of positivity under partial transposition (PPT). This criterion, applied to systems composed of Gaussian states, arranged in 1×(N1) bipartition, becomes necessary and sufficient to demonstrate entanglement. We also characterized the entanglement when the fields are submitted to losses, identifying regions of parameters where the states have fragile or robust entanglement. To ensure that we are dealing with Gaussian states, we investigate the statistics of the fields, showing excelent agreement among values of higher order moments of the photocurrent measured and expected values for a Gaussian distribution. The present study is an important step in the development of a quantum information network formed by different physical systems.

This dissertation considers three related problems in distributed transmission and reception networks. Generally speaking, these types of networks have a transmit cluster with one or more transmit nodes and a receive cluster with one or more receive nodes. Nodes within a given cluster can communicate with each other using a wired or wireless local area network (LAN/WLAN). The overarching goal in this setting is typically to increase the efficiency of communication between the transmit and receive clusters through techniques such as distributed transmit beamforming, distributed reception, or other distributed versions of multi-input multi-output (MIMO) communication. More recently, the problem of wireless power transfer has also been considered in this setting. The first problem considered by this dissertation relates to distributed reception in a setting with a single transmit node and multiple receive nodes. Since exchanging lightly quantized versions of in-phase and quadrature samples results in high throughput requirements on the receive LAN/WLAN, previous work has considered an approach where nodes exchange hard decisions, along with channel magnitudes, to facilitate combining similar to an ideal receive beamformer. It has been shown that this approach leads to a small loss in SNR performance, with large reductions in required LAN/WLAN throughput. A shortcoming of this work, however, is that all of the prior work has assumed that each receive node has a perfect estimation of its channel to the transmitter. To address this shortcoming, the first part of this dissertation investigates the effect of channel estimation error on the SNR performance of distributed reception. Analytical expressions for these effects are obtained for two different modulation schemes, M-PSK and M2-QAM. The analysis shows the somewhat surprising result that channel estimation error causes the same amount of performance degradation in ideal beamforming and pseudo-beamforming systems despite the fact that the channel estimation errors manifests themselves quite differently in both systems. The second problem considered in this dissertation is related to oscillator stability and phase noise modeling. In distributed transmission systems with multiple transmitters in the transmit cluster, synchronization requirements are typically very strict, e.g., on the order of one picosecond, to maintain radio frequency phase alignment across transmitters. Therefore, being able to accurately model the behavior of the oscillators and their phase noise responses is of high importance. Previous approaches have typically relied on a two-state model, but this model is often not sufficiently rich to model low-cost oscillators. This dissertation develops a new three-state oscillator model and a method for estimating the parameters of this model from experimental data. Experimental results show that the proposed model provides up to 3 dB improvement in mean squared error (MSE) performance with respect to a two-state model. The last part of this work is dedicated to the problem of wireless power transfer in a setting with multiple nodes in the transmit cluster and multiple nodes in the receive cluster. The problem is to align the phases of the transmitters to achieve a certain power distribution across the nodes in the receive cluster. To find optimum transmit phases, we consider a iterative approach, similar to the prior work on one-bit feedback for distributed beamforming, in which each receive node sends a one-bit feedback to the transmit cluster indicating if the received power in that time slot for that node is increased. The transmitters then update their phases based on the feedback. What makes this problem particularly interesting is that, unlike the prior work on one-bit feedback for distributed beamforming, this is a multi-objective optimization problem where not every receive node can receive maximum power from the transmit array. Three different phase update decision rules, each based on the one-bit feedback signals, are analyzed. The effect of array sparsity is also investigated in this setting.