Estabilidade de sólitons de ondas de matéria em condensados de Bose-Einstein atrativos aprisionados pelo potencial de Pöschl-Teller esfericamente simétrico.

Abstract

Bose-Einstein condensates are excellent macroscopic systems for observing the quantum behavior of matter. Since its experimental performance in weakly interacting atomic gases, trapped by external potentials, several non-linear phenomena related to this system have been intensively explored. In this thesis, we investigate the stability of matter-wave solitons in Bose-Einstein condensates with attractive interatomic interactions, confined by the spherically symmetrical Pöschl-Teller potential. For this purpose, we use the Gross-Pitaevskii equation, within the scope of the mean-field theory, to describe the Bose-Einstein condensate. In order to solve the Gross-Pitaevskii equation, we used two different approaches: one analytical (variational method) and the other numeric (split-step Crank-Nicolson method). In both approaches, we use the hyperbolic secant-tangent function to describe the macroscopic wave function for the Bose-Einstein condensate. The results, using the Vakhitov-Kolokov criterion, predicted the stability of three-dimensional solitons and, in addition, they predicted the behavior of the critical number of atoms as a function of the interatomic scattering length. From the perspective of possible applications, we believe that the results obtained may be relevant in the context of nonlinear optics and condensed matter physics.