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Master's Dissertation
DOI
https://doi.org/10.11606/D.76.2020.tde-15052020-104917
Document
Author
Full name
Pedro de Castro Diniz
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2020
Supervisor
Committee
Henn, Emanuel Alves de Lima (President)
Adhikari, Sadhan Kumar
Gammal, Arnaldo
Title in Portuguese
Estado fundamental e modos coletivos de um condensado de Bose-Einstein dipolar aprisionado em uma casca esférica
Keywords in Portuguese
Armadilha tipo bolha
Condensado de Bose-Einstein
Física atômica
Interação dipolar
Abstract in Portuguese
Consideramos o estado fundamental e as excitações colectivas de um condensado de Bose-Einstein dipolar numa armadilha tipo bolha, isto é, um potencial de confinamento esfericamente simetrico em forma de casca. Por meio de um ansatz gaussiano para a parte radial da função de onda e uma expansão em harmônicos esféricos para a parte angular, fomos capazes de obter expressões analíticas para a energia total do sistema, que foram minimizadas em relação aos parâmetros variacionais. Determinamos as propriedades do estado fundamental no caso em que as partículas interagem por interação de contato isotrópica de curto alcance e também por interações dipolares anisotrópicas de longo alcance no limite de casca fina, demonstrando a existência de perfis de densidade anisotrópicos em regimes fortemente dipolares. Ademais, com o estado fundamental em mãos, empregamos a abordagem de Sum Rules para estudar os modos de monopolo, quadrupolo bidimensional, tridimensional e dipolo. Encontramos desvios significativos em relação aos casos não dipolares, identificando assim traços úteis para a detecção experimental das propriedades de excitação do sistema e da interação de dipolo-dipolo.
Title in English
Ground state and collective modes of a dipolar Bose-Einstein condensate trapped in a spherical shell
Keywords in English
Atomic physics
Bose-Einstein condensate
Bubble Trap
Dipolar interactions
Abstract in English
We consider the ground state and collective excitations of a dipolar Bose-Einstein condensate in a bubble trap, i.e., a potential for spherically symmetric shell-shaped confinement. By means of a gaussian ansatz for the radial part of the wave function and an expansion in spherical harmonics for the angular part, we were able to obtain analytical expressions for the total energy of the system, which were minimized in relation to the variational parameters. We determined the properties of the ground state in the case where particles interact by short range isotropic contact interaction and also by long range anisotropic dipolar interactions at the thin shell limit, demonstrating the existence of anisotropic density profiles in strongly dipolar regimes. In addition, with the ground state at hand, we employ the Sum Rules approach in order to study the monopole, two-dimensional, three-dimensional quadrupole and dipole modes. We found significant deviations from non-dipolar cases, thus identifying useful features for the experimental detection of the excitation properties of the system and the dipole-dipole interaction.
 
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Publishing Date
2020-05-21
 
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