Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 100-103).

In this thesis regimes of quantum degeneracy of electrons and holes in semiconductor quantum wells in a strong magnetic field are studied theoretically. The coherent pairing of electrons and holes results in the formation of Bose-Einstein condensate of magnetic excitons in a single-particle state with wave vector <b>K</b>. We show that correlation effects due to coherent excitations drastically change the properties of excitonic gas, making possible the formation of a novel metastable state of dielectric liquid phase with positive compressibility consisting of condensed magnetoexcitons with finite momentum. On the other hand, virtual transitions to excited Landau levels cause a repulsive interaction between excitons with zero momentum, and the ground state of the system in this case is a Bose condensed gas of weakly repulsive excitons. We introduce explicitly the damping rate of the exciton level and show that three different phases can be realized in a single quantum well depending on the exciton density: excitonic dielectric liquid surrounded by weakly interacting gas of condensed excitons versus metallic electron-hole liquid. In the double quantum well system the phase transition from the excitonic dielectric liquid phase to the crystalline state of electrons and holes is predicted with the increase of the interwell separation and damping rate. We used a framework of Green's function to investigate the collective elementary excitations of the system in the presence of Bose-Einstein condensate, introducing "anomalous" two-particle Green's functions and symmetry breaking terms into the Hamiltonian. The analytical solution of secular equation was obtained in the Hartree-Fock approximation and energy spectra were calculated. The Coulomb interactions in the system results in a multiple-branch structure of the collective excitations energy spectrum. Systematic classification of the branches is proposed, and the condition of the stability of the condensed excitonic phase is discussed.

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In this thesis, both experimental studies and numerical simulations of ultracold atoms in optical potentials are presented in a collection of nine scientific papers. In particular, noise-induced transport in dissipative optical lattices and superfluid properties of Bose-Einstein condensates have been studied. Noise is usually regarded as a complication to most systems and as something that needs to be minimized. However, in a series of experiments at Umeå University, noise has been shown to play a key role for laser-cooled cesium atoms trapped in dissipative optical lattices. By using a combination of two dissipative optical lattices, where the relative spatial phase between them can be controlled, a so-called Brownian motor can be realized, where energy can be extracted from the inherent noise. In the experiment, this energy is used to control the transport of the laser-cooled atoms in real time and along pre-designed paths. This thesis also presents a way to characterize this system in terms of energy conversion efficiency and coherence of the transport, which may allow for a more straightforward comparison with other systems that rely on noise rectification. In the studies, it is also shown that the noise triggers a downward drift due to gravity, even though the optical potential should support the atoms. Further investigation of this might help to understand the underlying principles of laser cooling, as well as showing that the system might be suitable as a flexible test bed for statistical physics. In close relation to the experimental system, two numerical simulations are also presented, one in which different ways to induce asymmetries between two periodic potentials are investigated, and one in which a proposal for detecting quantum walks is explored. In the second part of the thesis, a work from the Joint Quantum Institute is presented, where a long-lived persistent current in a toroidal Bose-Einstein condensate, held in an all-optical trap, is created. The critical velocity of the superflow is measured in the presence of a tunable barrier. The system can be seen as a first realization of an elementary closed-loop atom circuit. Finally a theoretical study of the crossover between one- and two-dimensional systems is presented, in particular the transition between a two-dimensional superfluid to a one-dimensional Mott insulator is investigated. / Medelst nio vetenskapliga artiklar presenteras i denna avhandling experimentella och teoretiska studier av ultrakalla atomer fångade i optiska potentialer. Framförallt har brusinducerade transporter och supraytande egenskaper hos Bose-Einstein-kondensat studerats.     För de flesta system betraktas brus som något negativt som bör minimeras, men i en serie experiment som redovisas i denna avhandling spelar bruset istället en avgörande positiv roll. I ett system där laserkylda atomer genom växelverkan med laserstrålar fångas i två individuella optiska kristallgitter, kan atomernas kollektiva rörelse styras genom att energi utvinns ur det inneboende bruset. I denna avhandling, genom att kontrollera de optiska potentialerna i realtid, visas att atomernas kollektiva rörelse kan styras längs förutbestämda banor med en så kallade Brownska motor. I ett annat experiment mäts verkningsgraden i omvandligen mellan brus och arbete, samt koherensen i atomtransporten. En sådan karakterisering gör att systemet blir enklare att jämföra med andra system som bygger på liknande principer. I avhandlingen presenteras också en studie där det visas att det inneboende bruset i systemet, tillsammans med en svag kraft, i detta fall från gravitation, kan skapa drifter trots att de optiska potentialerna borde vara tillräckligt djupa för att atomerna ska vara fångade. Denna upptäckt kan leda till ökad grundläggande kundskap om laserkylning. Dessutom visar det att systemet kan beskrivas med modeller från statistisk fysik. I relation till det experimentella systemet i Umeå redovisas även två teoretiska studier, en för två symmetriska periodiska potentialer och deras sätt att möjliggöra inducerade drifter med olika typ av asymmetrier, samt en annan för möjligheten att genomföra och detektera kvantvandringar.     I avhandlingen presenteras också ett experimentellt arbete utfört vid Joint Quantum Institute, där en långlivad ihållande ström i ett torusformat Bose-Einstein-kondensat har skapats i en optisk fälla. Den kritiska hastigheten på strömmen har mätts i närvaron av en ställbar optisk barriär. Detta system kan ses som en första realisation av en grundläggande atomkrets. Slutligen presenteras även en teoretisk studie av övergången mellan en- och tvådimensionella system, där fasövergången mellan superytande och Mottisolation studeras.

Thesis (Ph.D.); Submitted to Iowa State Univ., Ames, IA (US); 12 Dec 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "IS-T 2605" Chang-Hwan Kim. 12/12/2003. Report is also available in paper and microfiche from NTIS.

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Orientador: Silvio A. S. Vitiello / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-11T05:46:23Z (GMT). No. of bitstreams: 1 Reis_MarceloAugustodos_M.pdf: 11400954 bytes, checksum: da0c111de1e988997b785a1a91546049 (MD5) Previous issue date: 2008 / Resumo: Este trabalho propõe duas funções de onda variacionais baseadas no conceito de partículas sombra e que descrevem a fase sólida dos sistemas formados por átomos de 4He. Uma delas, denominada Função de Onda Sombra Livre e Periódica (PFS) fornece bons resultados para esta fase aferidos pelas suas propriedades, entre elas as energias do sistema e a distribuição radial de pares que se mostraram em bom acordo com outros resultados da literatura. A outra, denominada Função de Onda Sombra Periódica (PS) além de fornecer bons resultados para as propriedades de interesse, se destaca por conseguir descrever a fase supersólida e desse modo predizer uma Condensação de Bose-Einstein na fase sólida. Todos os resultados que obtivemos foram decorrentes de nossas próprias implementações numéricas através do método Monte Carlo Variacional / Abstract: This work proposes two variational wave functions based on the concept of shadow particles that describes the solid phase of systems formed by atoms of 4He. One of them, called Periodic Free Shadow Wave Function (PFS) provides good results for this phase like the energies of the system and the Radial Distribution Function that proved to be in good agreement with other results of the literature. The other, called the Periodic Shadow Wave Function (PS) in addition to providing good results for these properties, describes the supersolid phase and thus predicts a Bose-Einstein Condensation of the solid phase. All the results that have been obtained are due to our own numerical implementations of the Variational Monte Carlo method / Mestrado / Física da Matéria Condensada / Mestre em Física

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste trabalho, estudamos numericamente a formaÃÃo e a dinÃmica de defeitos topolÃgicos do tipo parede de domÃnio em superfluidos em um modelo (3+1)-dimensional do tipo Maxwell-Higgs abeliano, no contexto da correspondÃncia AdS/CFT. Obtemos os propagadores bulk-fronteira, assim como as funÃÃes de correlaÃÃo na fronteira, para um campo escalar nos casos massivo e nÃo-massivo. Se impusermos que os campos dependem apenas da coordenada radial no bulk e de uma coordenada na fronteira, conseguimos obter na teoria dual as soluÃÃes do tipo parede de domÃnio encontradas na literatura. A partir dessas soluÃÃes, estudamos suas propriedades, verificando que o superfluido à caracterizado por duas escalas de comprimento, uma para o parÃmetro de ordem e outra para a densidade de carga. Estudamos tambÃm a variaÃÃo da densidade de carga na regiÃo prÃxima à interface do defeito, e por fim, investigamos as modificaÃÃes necessÃrias na teoria para se estudar a dinÃmica dessas soluÃÃes. / We numerically study the formation and dynamics of domain-wall-like topological defects in superfluids, using a (3+1)-dimensional abelian Maxwell-Higgs model, under the AdS/CFT correspondence. We obtain the bulk-boundary propagators, as well as the correlation functions on the boundary for a scalar field, both in massive and non-massive cases. If we impose that the fields depends only on a boundary coordinate and the bulk radial coordinate, we obtain in the dual theory the domain wall solutions found in literature. From these solutions we found that the superfluid is characterized by two length scales, one for the order parameter and other for the charge density. We also study the change of charge density in the region near the interface of the defect, and finally we investigate the modifications needed in theory to study the dynamics of these solutions.

O presente trabalho apresenta o estudo das propriedades da condensação de Bose-Einstein e da superfluidez em um sistema bosônico disposto em um arranjo unidimensional de potenciais periódicos em formato de anel. O Hamiltoniano efetivo usual em termos dos operadores de campo é implementado na representação construída em termos das funções de Bloch da primeira banda e o problema é resolvido por meio da sua diagonalização através de métodos numéricos. No limite de hopping pequeno, este modelo é essencialmente equivalente à representação usual do modelo de Bose-Hubbard, mas incorpora efeitos adicionais através das energias de Bloch de partícula independente e dos elementos da matriz de dois corpos na situação em que o hopping é grande [19]. Através da inclusão de rotação no sistema, as energias de partícula independente são forçadas a depender da velocidade angular. Isto implica, correspondentemente, uma dependência da velocidade angular nas funções de onda de partícula independente e nos resultados de muitos corpos obtidos através da diagonalização do Hamiltoniano. Com o objetivo de estudar a superfluidez, o critério de dois fluidos é empregado e através de resultados numéricos obtêm-se a variação da fração de superfluido com o quadrado da velocidade angular. Ainda, considera-se aqui uma expressão perturbativa para o parâmetro inercial do sistema expresso em termos das excitações do sistema sem rotação, o que permite relacionar as energias do sistema com rotação com aquelas do sistema sem rotação. Isto é particularmente interessante para obter a fração de superfluido em termos da informação espectral do sistema sem rotação. Resultados semelhantes podem ser encontrados através da definição de superfluido baseada na resposta do sistema a uma variação de fase, imposta através de condições de contorno torcidas [30, 33], mas com a diferença de que os desenvolvimentos aqui não fazem uso da hipótese do modo condensado. De maneira geral, os resultados numéricos obtidos indicam, que pelo menos para este sistema, as frações de superfluido e condensado são quantidades sem relação direta, sugerindo então que mesmo para sistemas gasosos diluídos a idéia de que a superfluidez é uma consequência da condensação de Bose-Einstein deve ser considerada com mais cuidado. / In this work we study the properties of Bose-Einstein condensation and superfluidity in a finite bosonic system in a 1-dimensional ring with a periodic potential under rotation. The usual field effective Hamiltonian is implemented in a representation constructed in terms of the first band Bloch functions and the problem is solved by numeric diagonalization. In the limit of small hopping, this model is essentially equivalent to the quasi-momentum representation of the usual Bose-Hubbard model but incorporates additional effects via Bloch single particle energies and two-body matrix elements in the case of large hopping [19]. By including rotation in the system we force the single particle energies to be a function of the angular velocity. This implies a corresponding angular velocity dependence of the single particle wavefunctions and many-body diagonalization results. In order to study superfluidity, we consider the two fluid criterion. Numerical results for the superfluid fraction involving the change of in rinsic ground state energy with the square of the angular velocity are obtained. We also consider a perturbative expression for the system inertial parameter expressed in terms of the excitation spectrum of the non rotating system, which enables us to relate the energies in the rotating system to the ones in the system without rotation. This is particularly interesting for obtaining superfluid fraction in terms of spectral information of the non rotating system. Similar results can be found by using the definition of superfluid fraction based on the response of the system to a phase variation imposed by means of twisted boundary conditions [30, 33], but with the difference that our developments do not assume the hypothesis of a condensate mode. Our numerical results indicate that in this system condensate and superfluid fractions are quite unrelated in terms of parameter values, indicating that even for dilute gases the concept that superfluidity is a consequence of Bose-Einstein condensation should be considered more carefully.