Excited Bose-Einstein Condensates: Dark Solitons and Quadrupole Oscillations

Excited Bose-Einstein Condensates: Dark Solitons and Quadrupole Oscillations

Theodoros Horikis
Department of Mathematics
University of Ioannina, Greece

We study the dynamics of atomic Bose-Einstein condensates (BECs), when the quadrupole mode is excited. Within the Thomas-Fermi approximation, we derive an exact first order system of differential equations that describe the parameters of the BEC wave function. Using perturbation theory arguments, we derive analytical expressions for the phase, density and width of the condensate. The observed oscillatory dynamics of the BEC density can even reach a quasi-resonance state when the trap strength is varying according to a time-periodic driving term. Finally, the dynamics of a dark soliton on top of a breathing BEC is also briefly discussed.