Collective excitations of a trapped dilute Bose gas for harmonic and anharmonic trapping potentials

Abstract

We theoretically investigate the effects of different forms of trapping potentials and interatomic interactions of Bose gases at ultra-cold temperatures on their dynamics. We explore topological modes, collective excitations and their dynamic phase transitions due to external perturbations. The Gross-Pitaevskii equation (GPE) is used to analyze these excitations analytically. The stationary state solutions to GPE refer to topological modes that require external resonant fields for the excitations of particular modes. While the reduction of GPE to parametric equations of motion by using variational analysis lead to dynamical description of collective excitations. The types of trapping potentials considered include magnetic traps, harmonic, anharmonic potential with cubic and quartic distortions. The magnetic traps require an external bias magnetic field that is tuned near resonance point. These traps along with interatomic interactions set oscillations in Bose-Einstein condensate (BEC), the excitation spectrum of these oscillations about their mean positions is investigated for each type of perturbation. A comparison is made for the equilibrium points and excitation spectrums of both internal and external perturbations in BEC. The excitation spectrum for the collective excitations in ground state of topological modes is lowered with addition of anharmonicity in the trap. The three-body interactions and external bias magnetic field also exhibit similar effects. Unlike anharmonic trapping potential system, the condensate center for harmonic system oscillates independently with the natural frequency of the trap. The Kohn theorem is not valid for all the cases of anharmonic potential leading to symmetry breaking while it sustains for the harmonic cases unless an external perturbation is added in the trap. We reveal the role of both external and internal perturbations in BEC, this can help to control the dynamic behavior of these ultra-cold bosons in formation of effective devices that involve BEC.