Dumb holes (also known as acoustic black holes) are fluid flows which include an "acoustic horizon:" a surface, analogous to a gravitational horizon, beyond which sound may pass but never classically return. Soundwaves in these flows will therefore experience "effective geometries" which are identical to black hole spacetimes up to a conformal factor. By adjusting the parameters of the fluid flow, it is possible to create an effective geometry which is conformal to the Anti-de Sitter black hole spacetime- a geometry which has recieved a great deal of attention in recent years due to its conjectured holographic duality to Conformal Field Theories. While we would not expect an acoustic analogue of the AdS-CFT correspondence to exist, this dumb hole provides a means, at least in principle, of experimentally testing the theoretical properties of the AdS spacetime. In particular, I have calculated the quasinormal mode spectrum of this acoustic geometry. / Graduate / 0986 / 0753 / jpbabb@yahoo.ca

In this thesis we numerically compute the scattering lengths and bound states for sodium-rubidium collisions at low energy. This work was motivated by experiments which aim to produce Bose-Einstein condensates (BEC) mixtures of sodium-rubidium. Elastic collision properties are important for the rethermalization of the atoms during the evaporative cooling process. Inelastic processes, which we also discuss to some extent, cause trap losses in those experiments. In order to reach the required temperature and density the elastic collision rates should be sufficiently large compared to the inelastic rates. The scattering lengths, which completely specify the elastic collision parameters at low energy, determine the miscibility and phase diagram of the sodium-rubidium condensate mixture. We calculate the scattering lengths approximately and find agreement with previous calculations indicating that miscible phases of sodium and rubidium condensates do not appear to be feasible in the absence of external fields.

Made available in DSpace on 2010-04-20T20:51:12Z (GMT). No. of bitstreams: 3 127144.pdf.jpg: 22926 bytes, checksum: f0072844d69084281a9c7092f970dac1 (MD5) 127144.pdf: 1287076 bytes, checksum: 7e0f27092b752813a38b17f36c8acaeb (MD5) 127144.pdf.txt: 218017 bytes, checksum: a230d57f4715dacbd3f269641e43f092 (MD5) Previous issue date: 2004-09-01T00:00:00Z / Ones of most important strategical decision that are placed for the Brazilian hospitals is how expand its activities for other markets which the same still not been covering. Several strategies are being adopted, and the opening of Satellites Units is one of them and has been adopted by a private hospital in São Paulo. Considering this fact, the objective of this study was to carry through a case study on one of these units, analysing the financial and marketing impacts caused by the implantation of the satellite unit. For this analysis, internal information of the unit had been raised and interviews had been carried through with some managers or people who had relationship with the process of implantation and management of the unit. Futhermore, usuaries had been also interviewed, with the aim to detect theirs perceptions of the unit. The results showed that the users are very satisfied with the Unit. However, there is a clear dissatisfaction in relation to the covering of the supplementary assistance sector. By this fact, it has an important restriction in the access to the unit, that is the main explanation for the negative financial results that the Unit is presenting since its implantation. Due to this results, the unit needs to improve the relationship between the hospital adminsitration and the supplementary health assistance companies in order to revert such situation. / Umas das importantes mais importantes decisões estratégicas que está sendo colocada para os hospitais brasileiros diz respeito à decisão de como expandir sua atuação para outros mercados-alvos no qual o mesmo ainda não tem uma boa cobertura. Diversas estratégias estão sendo adotadas, sendo que a abertura de Unidades Satélites é uma delas e que foi adotada por um hospital privado de grande porte do Estado de São Paulo. Sendo assim, o objetivo do trabalho foi realizar um estudo de caso sobre uma dessas unidades, procurando verificar os impactos financeiros e mercadológicos causados pela implantação da mesma. Para isso, foram levantadas informações internas da unidade e entrevistas foram realizadas com alguns gestores ou pessoas que de algumas forma estiveram relacionadas com o processo de implantação e gerenciamento. Além disso, também foram entrevistados usuários, procurando detectar a percepção dos mesmos sobre a Unidade. Os resultados mostraram que os usuários de modo geral estão muito satisfeitos com a Unidade em termos de atendimento. Entretanto, existe uma clara insatisfação com relação à cobertura do setor de assistência supletiva na Unidade. Em virtude desse fato, há uma restrição importante quanto ao acesso à mesma, o que é uma das mais fortes explicações para os resultados financeiros negativos que a Unidade vêm obtendo desde a sua implantação. Dessa forma, fazem-se necessárias melhorias no relacionamento hospital-operadoras a fim de reverter tal situação.

Dans cette thèse nous étudions expérimentalement les propriétés magnétiques de condensats de sodium de spin 1 à l'équilibre. Dans ce système les atomes peuvent occuper chacun des trois états Zeeman caractérisés par la projection de leur spin sur l'axe de quantification m=+1,0,-1. Nous mesurons l'état de spin à N particules du système en fonction du champ magnétique appliqué et et de la magnétisation (différence entre les populations des états m=+1 et m=-1) du nuage atomique. Nos mesures sont en très bon accord avec la prédiction de la théorie de champ moyen, et nous identifions deux phases magnétiques résultant de la compétition entre les interactions de spin antiferromagnétiques et l'effet du champ magnétique. Nous décrivons ces deux phases en terme d'un ordre nématique de spin caractérisant la symétrie de l'état de spin à N particules. Dans une seconde partie nous nous concentrons sur les propriétés du condensat à très faible magnétisation et soumis à un faible champ magnétique. Dans ces conditions, la symétrie du système se manifeste à travers de très grandes fluctuations de spin. Ce phénomène n'est pas explicable par une théorie de champs moyen naïve, et nous développons une approche statistique plus élaborée pour décrire l'état de spin du condensat. Nous mesurons les fluctuations de spin et nous sommes capables de déduire de leur analyse la température caractérisant le degré de liberté de spin du condensat. Nous trouvons que cette température diffère de celle décrivant les atomes thermiques entourant le condensat. Nous interprétons cette différence comme une conséquence du faible couplage entre ces deux systèmes. / In this thesis we study experimentally the magnetic properties of spin-1 Bose-Einstein condensate of Sodium at equilibrium. In this system the atoms can occupy any of the three Zeeman states characterized by their spin projection on the quantization axis m=+1,0,-1. We measure the many-body spin state of the system as a function of the applied magnetic field and of the magnetization (difference between the populations of the spin states m=+1 and m=-1) of the atomic sample. We find that our measurements reproduce very well the mean-field prediction, and we identify two magnetic phases expressing the competition between the antiferromagnetic inter-particle interactions and the effect of the magnetic field. We describe these phases in terms of a spin nematic order characterizing the symmetry of the many-body spin state. In a second part we focus on the properties of condensates of very low magnetization under a weak magnetic field. In these conditions, the symmetry of the system manifests itself in huge spin fluctuations. This phenomenon is not explainable by a naive mean-field theory and we develop a more elaborate statistical approach to describe the spin state of the condensate. We measure the spin fluctuations and are able from their analysis to infer the temperature characterizing the spin degree of freedom of the condensate. We find that this temperature differs from the temperature of the thermal fraction surrounding the condensate. We interpret this difference as a consequence of the weak coupling between these two systems.

This thesis consists of three articles investigating the asymptotic behaviour of cosmological spacetimes with symmetries arising in Mathematical General Relativity. In Paper A and B, we consider spacetimes with Bianchi symmetry and where the matter model is that of a perfect fluid. We investigate the behaviour of such spacetimes close to the initial singularity ('Big Bang'). In Paper A, we prove that the Strong Cosmic Censorship conjecture holds in non-exceptional Bianchi class B spacetimes. Using expansion-normalised variables, we further show detailed asymptotic estimates. In Paper B, we prove similar estimates in the case of stiff fluids. In Paper C, we consider T2-symmetric spacetimes satisfying the Einstein equations for a non-linear scalar field. To given initial data, we show global existence and uniqueness of solutions to the corresponding differential equations for all future times. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we investigate in detail the asymptotic behaviour towards the future. We prove that the Cosmic No-Hair conjecture holds for solutions satisfying an additional a priori estimate, an estimate which we show to hold in T3-Gowdy symmetry. / Denna avhandling består av tre artiklar som undersöker det asymptotiska beteendet hos kosmologiska rumstider med symmetrier som uppstår i Matematisk Allmän Relativitetsteori. I Artikel A och B studerar vi rumstider med Bianchi symmetri och där materiemodellen är en ideal fluid. Vi undersöker beteendet av sådana rumstider nära ursprungssingulariteten ('Big Bang'). I Artikel A bevisar vi att den Starka Kosmiska Censur-förmodan håller för icke-exceptionella Bianchi klass B-rumstider. Med hjälp av expansions-normaliserade variabler visar vi detaljerade asymptotiska uppskattningar. I Artikel B visar vi liknande uppskattningar för stela fluider. I Artikel C betraktar vi T2-symmetriska rumstider som uppfyller Einsteins ekvationer för ett icke-linjärt skalärfält. För givna begynnelsedata visar vi global existens och entydighet av lösningar till motsvarande differentialekvationer för all framtid. I det speciella fallet med en konstant potential, en situation som motsvarar ett linjärt skalärfält på en bakgrund med en positiv kosmologisk konstant, undersöker vi i detalj det asymptotiska beteendet mot framtiden. Vi visar att den Kosmiska Inget-Hår-förmodan håller för lösningar som uppfyller en ytterligare a priori uppskattning, en uppskattning som vi visar gäller i T3-Gowdy-symmetri. / <p>QC 20171220</p>

Cette thèse est consacrée à de nouveaux phénomènes en physique liées au spin et à la topologie des quasi-particules lumière-matière dans des hétérostructures. Elle est divisée en quatre parties. Chapitre 1 donne un fond nécessaire et introduit les propriétés fondamentales des polaritons et des excitons indirects dans des puits quantiques couplés. Chapitre 2 est concentré sur la dynamique de spin et sur formation de défauts topologiques dans des systèmes aux excitons indirects. Les 2 derniers chapitres considèrent les structures basées sur les microcavités. Chapitre 3 est consacré à la dynamique de spin des polaritons dans des oscillateurs paramétriques optiques. Finalement, chapitre 4 étudie les réseaux des microcavités en forme des piliers et introduit l’isolant topologique polaritonique. / The present thesis manuscript is devoted to new phenomena in physics of light-matter quasiparticles in heterostructures, related to spin and topology. It is divided into four parts. Chapter 1 gives a necessary background, introducing basic properties of microcavity polaritons and indirect excitons in coupled quantum wells. Chapter 2 is focused on spin dynamics and topological defects formation in indirect exciton many-body systems. The last 2 chapters are related to microcavity-based structures. Chapter 3 is devoted to polariton spin dynamics in optical parametric oscillators. Finally, Chapter 4 studies pillar microcavity lattices and introduces the polariton topological insulator.

Masters thesis of Liam Farrell, under the supervision of Dr. Duncan O'Dell. Successfully defended on August 26, 2021. / Caustics are regions created by the natural focusing of waves. Some examples include rainbows, spherical aberration, and sonic booms. The intensity of a caustic is singular in the classical ray theory, but can be smoothed out by taking into account the interference of waves. Caustics are generic in nature and are universally described by the mathematical theory known as catastrophe theory, which has successfully been applied to physically describe a wide variety of phenomena. Interestingly, caustics can exist in quantum mechanical systems in the form of phase singularities. Since phase is such a central concept in wave theory, this heralds the breakdown of the wave description of quantum mechanics and is in fact an example of a quantum catastrophe. Similarly to classical catastrophes, quantum catastrophes require some previously ignored property or degree of freedom to be taken into account in order to smooth the phase divergence. Different forms of spontaneous pair-production appear to suffer logarithmic phase singularities, specifically Hawking radiation from gravitational black holes. This is known as the trans-Planckian problem. We will investigate Hawking radiation formed in an analogue black hole consisting of a flowing ultra-cold Bose-Einstein condensate. By moving from an approximate hydrodynamical continuum description to a quantum mechanical discrete theory, the phase singularity is cured. We describe this process, and make connections to a new theory of logarithmic catastrophes. We show that our analogue Hawking radiation is mathematically described by a logarithmic Airy catastrophe, which further establishes the plausibility of pair-production being a quantum catastrophe / Thesis / Master of Science (MSc)

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

The physics of ultracold atomic gases has been the subject of a long standing theoretical and experimental research over the last half century. The development of evaporative cooling techniques and the realization of the first Bose-Einstein Condensate (BEC) in 1995 gave a great advantage to the field. A great experimental knowledge of the fundamental properties of BECs, such as long-range coherence, superfluidity and topological excitations, has now been acquired. On top of these advances, current research on ultracold atoms is also focusing on quantum simulations, which aim at building analogue models of otherwise difficult to compute physical systems in the lab. In this context, BECs, with their enhanced coherence, many-body dynamics and superfluid character offer a powerful platform for advances in the field. Shortly after the first realization of a BEC, research started also investigating the physics of quantum mixtures of a BECs, either composed of different atomic species or isotopes, or of atoms occupying different hyperfine states. The latter are known as spin mixtures, or spinor condensates. The presence of multiple components interacting through mutual contact interactions enriches the physics of the condensate, introducing ground states with magnetic ordering as well as spin dynamics, which can be order of magnitudes less energetic than the density one. On top of this, hyperfine states can be coherently coupled with an external resonant radiation. Interesting physics arises when the strength of the coupling is comparable with the energy of spin excitations, an example of which is given by the emergence of the internal Josephson effect. This regime has been the subject of intense theoretical studies in the past twenty years, however its experimental realization on ultracold atomic platforms have been proven to be challenging, with experiments strongly limited by coherence times of few tens of milliseconds. In fact, the small energy scale of spin excitations reflects in a high sensitivity coupling to environmental magnetic noise, which affects the resonant condition. The experimental apparatus on which I worked during my Ph.D. solve this problem employing a magnetic shield that surrounds the science chamber, attenuating external magnetic fields by 6 orders of magnitudes. During my Ph.D., I investigated the properties of a coherently coupled mixture of BEC of Sodium 23, performing different experiments in two atomic configurations. The first configuration consist of a mixture of hyperfine states, namely the |F=1, mF = -1&gt; and |F=1, mF = +1&gt;, coupled by a two-photon transition, which is characterized by miscibility in the ground state. Another configuration was instead realized working with a strongly immiscible mixture of |F=1, mF=-1&gt; and |F=2, mF = -2&gt;, realized through with a one photon transition. My first experiment was devoted to the characterization of different methods of manipulation of the coupled miscible mixture in an elongated quasi-1D geometry. In Local Density Approximation (LDA), The dynamics of the system, depends on the atom number difference, the relative phase, and coupling to mean field energy ratio, can be fully described as an internal Josephson junction. We characterized this dynamics on a sample an inhomogeneous spatial profile, developing three different protocols for state manipulations. In a second experiment, I developed a protocol to generate Faraday waves in an unpolarized miscible mixture. Faraday waves are classical non-linear waves characterized by a regular pattern, that originate in classical and quantum fluids via a parametric excitation in the fluid. Interestingly enough, this process resembles the phase of reheating of the early universe, where the oscillation of the inflaton field is thought to have excited particles out of the vacuum. In analogy with this phenomenon, the oscillation of the inflaton field can be simulated with the periodic modulation of the trapping potential. On top of this, in a spin mixture, the parametric modulation can excite either in-phase (density) modes or out-of-phase (spin) modes, as two possible elementary excitations are present in the system. By extracting the spatial periodicity of the generated pattern at different modulation frequencies, I was then able to measure the dispersion relations for both density and spin modes of the system. In the presence of the coherent coupling, when spin excitations becomes gapped, we further demonstrate the scaling of the gap with the strength of the coupling radiation. The third experiment I realized concerned the characterization of the magnetic ground state of a spatially extended immiscible mixture in the presence of the coherent coupling. The Hamiltonian of such a system is formally equivalent to a continuous version of the transverse field Ising model, which describes magnetic materials at zero temperature. In this mapping, a nonlinear interaction term arises from the ratio between the self-interaction energy and the strength of the coupling, which acts as the transverse field. As the ratio between the two quantities is varied above and below one, the ground state of the system spontaneously changes from a paramagnetic phase to an ordered ferromagnetic phase, featuring two equivalent and opposite magnetizations, a signature of the occurrence of a second order quantum phase transition (QPT). Furthermore, in the magnetic model, the degeneracy between the two ferromagnetic ground states can be broken by introducing an additional longitudinal field. In the atomic case, the role of this additional field is taken by the detuning between the coupling radiation and the resonant transition frequency of non-interacting atoms. I characterized the QPT developing protocols to manipulate the spin mixture in its spatially extended ground state, varying the longitudinal field. Leveraging on the inhomogeneity of a BEC trapped in the harmonic potential, a smooth variation of the spin self-interaction energy occurs spontaneously in space, introducing different magnetic regimes at fixed coupling strength. These protocols gave access to a characterization of static properties typical of magnetic materials, such as the presence of an hysteresis cycle. The occurrence of the phase transition was instead validated by a measurement of the magnetic susceptibility and corresponding fluctuations, which both show a divergence when crossing the QPT critical point. At last, I developed a protocol to smoothly manipulate the position of magnetic domain walls, the least energetic excitations in a ferromagnet. While the previous study focused on static properties, the last experimental investigation presented in this thesis was devoted to the study of the dynamics of the metastable ferromagnetic region of the BEC. As a result of the presence of an hysteresis cycle, it is possible to engineer states of the ferromagnetic energy landscape that are homogeneously prepared either in the global minimum, with trivial dynamics, or in the metastable, higher energy, local minima. In the latter case, a classical system should eventually decay towards the global minimum, driven by temperature fluctuations which overtop the energy barrier separating the two minima. For a quantum system described by a field theory, such as a ferromagnetic BEC, the decay towards the global minimum occurs by tunneling through the barrier, triggered by quantum fluctuations. The event of tunneling is known as False Vacuum Decay (FVD), and is of outstanding relevance also for high energy physics and cosmology, were the first theoretical models were developed. In the FVD model, the decay towards the global minimum, the true vacuum, is a stochastic process that occurs only if a resonant bubble of true vacuum is formed. Once formed, the bubble will eventually expand throughout the whole system, as the true vacuum is energetically favorable. The probability for such a bubble to form can be approximately calculated analytically in 1D, and should depend exponentially on the height of the barrier the field has to tunnel through. Due to the exponentially long time scale of the process, experimental observations of FVD were still lacking. Thanks to the enhanced coherence time of the superfluid ferromagnetic mixture, and to the precise control of the barrier height through the detuning from atomic resonance, we were able to observe the event of bubble nucleation in a ferromagnetic BEC. To corroborate the observation, I measured the characteristic timescale of the decay for different values of the control parameters. Results were successfully compared first with numerical simulation, and then validated by instanton theory.

Cette thèse décrit l'étude des gaz de fermions $^6$Li et de bosons<br />$^7$Li dans le régime quantique à très basse température. Le<br />refroidissement est obtenu par évaporation du $^7$Li dans un piège<br />magnétique très confinant. Puisque le refroidissement évaporatif<br />d'un gaz de fermion polarisé est quasiment impossible, le $^6$Li<br />est refroidi sympathiquement par contact thermique avec le $^7$Li.<br />Dans une première série d'expériences, les propriétés des gaz<br />quantiques dans les états hyperfins les plus élevés, piégés<br />magnétiquement, sont étudiées. Un gaz de $10^5$ fermions a une<br />température de 0.25(5) fois la température de Fermi ($T_F$) est<br />obtenu. L'instabilité du condensat pour plus de 300 atomes<br />condensés, à cause des interactions attractives, limite la<br />dégénérescence que l'on peut atteindre. Pour s'affranchir de cette<br />limite, une autre série d'expérience est menée dans les états<br />hyperfins bas, piégeable magnétiquement, où les interactions entre<br />bosons sont faiblement répulsives. Les collisions<br />inter-isotopiques permettent alors la thermalisation du mélange.<br />Le mélange d'un condensat de Bose-Einstein (CBE) de $^7$Li et d'un<br />mer de Fermi de $^6$Li est produit. Le condensat est quasi<br />unidimensionnel et la fraction thermique peut être négligeable. La<br />dégénérescence atteinte correspond à $T/T_C=T/T_F=0.2(1)$. La<br />température est mesurée à partir de la fraction thermique des<br />bosons qui disparaît aux plus basses températures, et limite notre<br />précision de mesure. Dans une troisième série d'expérience, les<br />bosons sont transférés dans un piège optique, et placé dans l'état<br />interne $|F=1,m_F=1\rangle$, l'état fondamental pour les bosons.<br />Une résonance de Feshbach est repérée puis exploitée pour former<br />un condensai où les interactions sont ajustables. Quand les<br />interactions effectives entre les atomes sont attractives, on<br />observe la formation d'un soliton brillant de matière. La<br />propagation de ce soliton sans dispersion sur une distance de<br />$1.1\,$mm est observée.