Strong-field driving of a dilute atomic Bose-Einstein condensate

Abstract

A hydrodynamical version of the time-dependent Gross-Pitaevskii equation has been formulated and applied to the description of a Bose-Einstein condensate (BEC) of ${}^{87}$Rb atoms in the JILA time-averaged orbiting potential (TOP) trap. The response of the BEC to time-dependent modulations of the trap potential is computed and the characteristic frequencies of a BEC oscillation agree well with those observed in recent experiments. For the axially symmetric $m=0\mathrm{}$ mode of the TOP trap, we find a weak dependence of the oscillatory frequency on the strength of the driving amplitude under conditions comparable to those of current experiments. The free ringing of the BEC that is induced by a transient change in the potential is found to be periodic, in agreement with the predictions of Thomas-Fermi theory. We analyze the harmonic content of the spectral response and consider possibilities for high-harmonic generation in the context of nonlinear atom optics.