Collective excitations of a BEC under anharmonic trap position jittering

Collective excitations of a Bose-Einstein condensate under periodic oscillations of the position of a quadratic plus quartic trap have been studied. A coupled set of variational equations is derived for the width and the centre of the condensate wavefunction. Analytical expressions for the growth of oscillation amplitudes in the resonance case are derived. It is shown that jittering of the position of an anharmonic trap can cause double resonance in oscillations of the BEC width and centre of mass in a wide range of the BEC parameter values. The predictions of the variational approach are confirmed by full numerical simulations of the 1D Gross-Pitaevskii equation