This thesis describes the design, construction and optimisation of a new apparatus to produce Bose-Einstein condensates (BECs) of 87Rb atoms. The main aim in building this system was to include a high resolution imaging system capable of resolving single atoms. Optical access for the imaging system was created by including a stage of atom transport in which the atoms are magnetically transferred ~50 cm from a magneto-optical trap (MOT), where they are initially collected, to a glass science cell where experiments are carried out and imaging takes place. Two magnetic transport schemes have been demonstrated, based on approaches first used in other laboratories. First, a scheme in which the atoms are transferred in a moving pair of magnetic trapping coils. Second, a hybrid scheme where the atoms are translated part of the distance in the moving coils, and the rest of the way by switching the current in a chain of fixed coils. This second scheme was designed to allow optical access for a high numerical aperture microscope objective to be placed immediately next to the science cell for high resolution imaging. The atoms were first collected in a large pyramid MOT which can be loaded with 3 × 10^9 atoms in a time of 20 s. Around half of these atoms – those in the |F = 1, mF = −1> magnetic substate – were then magnetically trapped prior to transport. The typical fraction of the trapped atoms transferred to the science cell was ~30% and ~18% for the moving coils and hybrid schemes respectively. Evaporative cooling was carried out on the atom cloud following transport with the moving coils and loading into a time-orbiting potential trap. The optimised cooling sequence lasted for 28 s and consistently produced a pure condensate with 5 × 10^5 atoms. A BEC has also been produced by evaporative cooling following hybrid transport. The next experimental steps will be to optimise the hybrid transfer approach further and install the high resolution imaging system. The system is well-placed to continue an ongoing series of experiments in which ultracold atoms are trapped in RF-dressed potentials. These potentials will be used to study low-dimensional quantum gases as well as in experiments where small atom number BECs are rapidly rotated to enter the fractional quantum Hall regime.

It has been shown that the cosmic censorship conjecture holds for polarized Gowdy spacetimes. In the more general, unpolarized case, however, the question remains open. It is known that cylindrically symmetric dust can collapse to form a naked singularity. Since Gowdy universes comprise gravitational waves that are locally cylindrically symmetric, perhaps these waves can collapse onto a symmetry axis and create a naked singularity. It is known that in the case of cylindrical symmetry, event horizons will not form under gravitational collapse, so the formation of a singularity on the symmetry axis would be a violation of the cosmic censorship conjecture.To search for cosmic censorship violation in Gowdy spacetimes, we must have a better understanding of their singularities. It is known that far from the symmetry axes, the spacetimes are asymptotically velocity term dominated, but this property is not known to hold near the axes. In this thesis, we take the first steps toward understanding on and near axis behavior of Gowdy spacetimes with space-sections that have the topology of the three-sphere. Null geodesic behavior on the symmetry axes is studied, and it is found that in some cases, a photon will wrap around the universe infinitely many times on its way back toward the initial singularity.

Einstein's equations in vacuum spacetimes with two spacelike killing vectors are explored using affine projection tensor geometry. By doing a semi-conformal transformation on the metric, a new "fiducial" geometry is constructed using a projection tensor fields. This fiducial geometry provides coordinate independent information about the underlying structure of the spacetime without the use of an explicit form of the metric tensor.

Busca soluciones exactas para las ecuaciones de Einstein se ha desenvuelto en dos direcciones diferentes por un lado, el estudio de objetos masivos aislados cuyo campo gravitacional externo es modelado por soluciones asintóticamente planas (métrica de Schwarzschikl); y por otro lado, el estudio a gran escala del universo, en forma global, para predecir su evolución, origen y su destino final (métrica FLRW). Pero hay un tercer camino que trata de mantener estos dos aspectos juntos, se trata de la métrica de McVittie, la cual nos presenta la posibilidad de estudiar los sistemas locales influenciados por la evolución a gran escala del espacio en el que están inmersos. Motivados por este enfoque, realizamos un estudio de la métrica de McVittie en dos etapas. En la primera etapa, analizamos el espacio-tiempo de McVittie para una partícula cargada y a partir de ello, mediante una construcción matemática adecuada, introducimos la constante de Hubble. Posteriormente haciendo uso de las ecuaciones de campo de Einstein, se resuelve la ecuación de McVittie cargada con constante cosmológica negativa. En la segunda etapa, partimos del agujero de gusano atravesable de MorrisThorne, la función de desplazamiento al rojo se hace nula y se realiza un cambio de variable adecuado para la función de forma, se construye una métrica para un agujero de gusano atravesable en el universo de FLRW; posteriormente, se analiza el caso de un agujero de gusano más general, se utiliza la métrica de McVittie, donde el agujero de gusano está modelado por una delgada capa esférica que acrecenta el fluido de quinta esencia, finalmente, se encuentra la evuación dinámica de dicha capa delgada y el radio comoving de la misma. / Tesis

Neste trabalho estudamos um sistema bidimensional composto de duas espécies atômicas condensadas, uma delas contendo uma rede de vórtices. Analogamente ao modelo desenvolvido para tratar de átomos ultrafrios em redes ópticas, mapeamos o Hamiltoniano do nosso sistema com o Hamiltoniano do modelo Bose-Hubbard (BH), com o potencial periódico da rede advindo da interação de campo médio entre as duas espécies. A variação do comprimento de espalhamento atômico permite alterar as propriedades do potencial confinante, com a indução da transição de fase quântica na espécie aprisionada nos vórtices. O novo aspecto trazido pela rede de vórtices advém dos seus modos de excitação de baixa energia, os modos de Tkachenko. Consideramos os efeitos da dinâmica própria desse potencial sobre a espécie aprisonada através de um modelo BH efetivo, com novos valores para interação local e tunelamento, além de um termo adicional de interação de longo alcance, mediada pelos modos da rede. Além de complementar os estudos com redes ópticas estáticas, a proposta teórica desenvolvida apresenta grande viabilidade experimental no contexto das técnicas atuais para manipulação de átomos ultrafrios. / In this work we consider a two dimensional system composed of two condensed atomic species, one containing a vortex lattice. Analogously to the model used to describe ultracold atoms in optical lattices, we mapped our system Hamiltonian in the Hamiltonian of the Bose-Hubbard (BH) model, with the periodic lattice potential arising from the meanfield interaction between the two species. The variation of the atomic scattering length allow us to change the properties of the confining potential, to induce the quantum phase transition in the species trapped in the vortices. The new aspect brought by the vortex lattice comes with its low energy normal modes, the Tkachenko modes. We considered the effects of such dynamic potential over the confined species thought an effective BH model, with new values for the local interaction and tunneling parameters, besides an additional long-range interaction term mediated by the lattice modes. Our theoretical proposal goes beyond the studies with static optical lattice. Additionally, it has great feasibility in the current context of ultra-cold atoms experimental techniques.

Made available in DSpace on 2017-07-21T14:54:05Z (GMT). No. of bitstreams: 1 Jeverson Machado Nascimento.pdf: 937148 bytes, checksum: 8e7c59c82973d27a9601a4d6e2580e94 (MD5) Previous issue date: 2013-09-25 / The main goal of our work was to undertake a study of the novel Einstein's Dreams by Alan Lightman, in order to exploit its potential discourse regarding the meeting of the elements of the day and the night, which are corresponding, in Bachelard's beautiful metaphor, to the exercise of literary writing and the scientific activity. Therefore, the theoretical framework that guides us consists primarily of the works of Mikhail Bakhtin - particularly the philosophical theory contained in Toward a Philosophy of the Act (2010a) and his theory of aesthetics of the novel contained mainly in Questions of Literature and Aesthetics (2010b) - as well as the epistemological studies of Gaston Bachelard, especially the works The New Scientific Spirit (1988), The Philosophy of No (1991) and The poetics of reverie (1988b). Reading these authors we intended to understand concepts we consider as parallel, such as daydreaming and dreams, dialogism and philosophical epistemological plurality, dialectical pluralism; these concepts were vital so we could consider our object as a meeting between the daytime and nighttime, a discourse that walks along the horizon during dusk and dawn. Thus, we list some elements of the work that we understand as essential for the analysis, as the way the main character was built, the explicit context of the work, how the scientific and philosophical plurality of time presents itself. / O principal intuito de nosso trabalho é empreender um estudo do romance Sonhos de Einstein, de Alan Lightman, de modo a explorar seu potencial discursivo no que diz respeito ao encontro dos elementos do diurno e do noturno, correspondentes, na bela metáfora bachelardiana, ao exercício da escrita literária e da atividade científica. Para tanto, o referencial teórico que nos orienta compõem-se, primordialmente, das obras de Mikhail Bakhtin – principalmente a teoria filosófica que esboça em Para uma filosofia do ato responsável (2010a) e sua teoria da estética do romance contida principalmente em Questões de literatura e estética (2010b) – bem como os estudos epistemológicos de Gaston Bachelard, sobretudo as obras O novo espírito científico (1988), A filosofia do não (1991) e A poética do devaneio (1988b). Buscamos na leitura desses autores conceitos que entendemos serem paralelos, como, devaneio e sonhos, dialogia e pluralidade filosófica epistemológica, dialética do plural e polifilosofia; esses foram primordiais para que pudéssemos olhar nosso objeto como um encontro entre o diurno e o noturno, um discurso que vagueia pela horizonte durante o crepúsculo e o alvorecer. Elencamos,a partir daí, alguns elementos da obra que entendemos como primordiais para esse modelo de análise, como a forma construtiva do personagem principal, o contexto explícito na obra, a forma como a pluralidade cientifica e filosófica do tempo se apresenta.

This thesis details the design, construction and characterisation of an ultracold atoms system, developed in conjunction with a flexible optical trapping scheme which utilises a Liquid Crystal Spatial Light Modulator (LC SLM). The ultracold atoms system uses a hybrid trap formed of a quadrupole magnetic field and a focused far-detuned laser beam to form a Bose-Einstein Condensate of 2×105 87Rb atoms. Cold atoms confined in several arbitrary optical trapping geometries are created by overlaying the LC SLM trap on to the hybrid trap, where a simple feedback process using the atomic distribution as a metric is shown to be capable of compensating for optical aberrations. Two novel methods for creating flexible optical traps with the LC SLM are also detailed, the first of which is a multi-wavelength technique which allows several wavelengths of light to be smoothly shaped and applied to the atoms. The second method uses a computationally-efficient minimisation algorithm to create light patterns which are constrained in both amplitude and phase, where the extra phase constraint was shown to be crucial for controlling propagation effects of the LC SLM trapping beam.

Orientador: Sandro Silva e Costa. / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós Graduação em Física, 2010.

Orientador: Valery Shchesnavich / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós-Graduação em Física, 2012.

Orientador: Valery Shchesnovich / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós-Graduação em Física, 2014