Palestrante
Descrição
The study of Bose-Einstein condensates basically happens inside conservative traps. An important feature of these systems is that the trap strongly determines the properties of the cloud of atoms, therefore the investigation of the Bose-Einstein condensates in diverse geometries of trapped atoms is a very rich and interesting area of research. A possible geometry is the ”bubble”(1), which corresponds to a trap that confines the atoms in a spherical surface. Recently, this geometry has been observed and studied in the spacial station. The reason why these experiments must take place in space is because the influence of gravity makes it impracticable to produce a bubble shaped condensate. In addition to the geometrical aspect there is also the possibility of making Bose-Einstein condensates from atoms with high magnetic dipole moment. This is interesting because the dipole-dipole interaction is anisotropic and long ranged, in contrast with the usual mean field interaction that appears in the Gross-Pitaewiski equation which is isotropic and short ranged. Consequently, BECs made of dipolar atoms present different and more complex behavior when compared with those that have pure contact interaction. Our work consists in a theoretical investigation of a dipolar Bose-Einstein condensate in a bubble trap with all the dipoles alligned in one spacial direction. We were able to obtain the density distribution and energy of the ground state for many different values of the relevant parameters as well as the frequencies of collective modes of vibration of the condensate. The strategy used to obtain the ground state was to calculate the total energy of the system and minimize it. In order to calculate the energy we first needed to make some assumptions about the wave function. For the radial behavior a gaussian dependence was chosen so the atoms would always be confined in a very thin spherical shell with fixed radius and thickness. Having the radial dependence fixed we left the angular distribution completely arbitrary expressing it as a spherical harmonics expansion, and with this ansatz the total energy was calculated. The final expression for the energy ended up being a polynomial of the angular expansion coefficients, so we proceeded with the minimization proccess using those as the variational parameters. This procedure was repeated for many different dipolar interaction "strengths". Our results showed that as the dipolar interaction increases the atoms tend to concentrate around the equator of the bubble with vanishing density at the poles. Having the ground state at hand we were then able to calculate the frequencies of some collective modes of excitation. The method we used to obtain these frequecies is called "sume rule approach", wich is very convenient since the only thing we need in order to apply it is the ground state. We obtained the dependence of the monopole, dipole and two quadrupole excitations upon the dipolar interaction and observed that the dipole excitation presents interesting features.
Referências
1 SUN, K. Static and dynamic properties of shell-shaped condensates. Physical Review A, v. 98, n. 1, p. 013609-1-013609-24, July 2018.
| Subárea | Física Atômica e Molecular |
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