Collective modes of ground and dark-soliton states of Bose-Einstein condensates in anisotropic traps

Collective modes of the ground and excited states of Bose-Einstein condensates are studied by numerical solution of the time-dependent Gross-Pitaevskii equation in three spatial dimensions. Scissors modes are studied by quadrupole excitation of the ground and excited states of Na-23 condensates in a fully anisotropic magnetic trap. The frequencies of the collective modes for the ground state condensates are found to be in good agreement with previous linear response theory. New results are presented for the frequencies of the collective modes for excited state condensates which exhibit solitary density depressions. A key to the proper characterization of the wide variety of dark-soliton states in atomic condensates is the experimental observation of collective modes.