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DINIZ, P. Ground state and collective modes of a dipolar Bose-Einstein condensate trapped in a spherical shell. 2020. 87p. Dissertação (Mestrado em Ciências) Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, 2020. 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.

Estado fundamental e modos coletivos de um condensado de Bose-Einstein dipolar aprisionado em uma casca esférica