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We theoretically investigate quadrupolar collective excitations intwo-component Bose-Einstein condensates and their nonlinear dynamics associatedwith harmonic generation and mode coupling. Under the Thomas-Fermiapproximation and the quadratic polynomial ansatz for density fluctuations, thelinear analysis of the superfluid hydrodynamic equations predicts excitationfrequencies of three normal modes constituted from monopole and quadrupoleoscillations, and those of three scissors modes. We obtain analytically theresonance conditions for the second harmonic generation in terms of the trapaspect ratio and the strength of intercomponent interaction. The numericalsimulation of the coupled Gross-Pitaevskii equations vindicates the validity ofthe analytical results and reveals the dynamics of the second harmonicgeneration and nonlinear mode coupling that lead to nonlinear oscillations ofthe condensate with damping and recurrence reminiscent of the Fermi-Pasta-Ulamproblem.Comment: 10 pages, 5 figures, revtex

Quadrupole and scissors modes and nonlinear mode coupling in trapped two-component Bose-Einstein condensates