Momentum-Transfer to and Elementary-Excitations of a Bose-Einstein Condensate by a Time-Dependent Optical Potential

We present results of calculations on Bose-Einstein condensed $^{87}$Rb atoms subjected 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 order paramter) of the condensate and determine the resulting condensate momentum in the $z$ direction, $P_z(q,\omega,V_0,t_p)$, where $V_0$ is the peak optical potential strength and $t_p$ is the pulse duration. Although the local density approximation for the Bogoliubov excitation spectral distribution is a good approximation for very low optical intensities, long pulse duration and sufficiently large values of the wavevector $q$ of the light-potential, for small $q$, short duration pulses, or for not-so-low intensities, the local density perturbative description of the excitation spectrum breaks down badly, as shown by our results.