Quadrupole Collective Modes in Trapped Finite-Temperature Bose-Einstein Condensates

Finite-temperature simulations are used to study quadrupole excitations of a trapped Bose-Einstein condensate. We focus specifically on the $m=0\mathrm{}$ mode, where a long-standing theoretical problem is to account for an anomalous variation of the mode frequency with temperature. We explain this behavior in terms of the excitation of two separate modes, corresponding to the coupled motion of the condensate and the thermal cloud. The relative amplitude of the modes depends sensitively on the temperature and on the frequency of the harmonic drive used to excite them. Good agreement with experiment is found for appropriate drive frequencies.