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We present results of calculations on Bose-Einstein condensed $^{87}$Rb atomssubjected to a moving standing-wave light-potential of the form $V_L(z,t) =V_0(t) \cos(q z-\omega t)$. We calculate the mean-field dynamics (the orderparamter) of the condensate and determine the resulting condensate momentum inthe $z$ direction, $P_z(q,\omega,V_0,t_p)$, where $V_0$ is the peak opticalpotential strength and $t_p$ is the pulse duration. Although the local densityapproximation for the Bogoliubov excitation spectral distribution is a goodapproximation for very low optical intensities, long pulse duration andsufficiently large values of the wavevector $q$ of the light-potential, forsmall $q$, short duration pulses, or for not-so-low intensities, the localdensity perturbative description of the excitation spectrum breaks down badly,as shown by our results.Comment: 8 pages, 7 figure

Momentum transfer to and elementary excitations of a Bose-Einstein condensate by a time-dependent optical potential