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Ultracold atoms in the combined potential of a parabolic trap and an opticallattice is considered a promising tool for coherent manipulation of matter wavepackets. The recent Aarhus experiment[P. L. Pedersen et al., Phys. Rev. A. 88,023620 (2013)] produced wave packets by applying the optical lattice'samplitude modulation to a Bose-Einstein condensate (BEC) of $^{87}$Rb. Thepresent paper renders a theoretical account with single-particle analysis ofthis experimental production of the wave packets and their subsequenttime-evolution. We focus on the one-dimensional non-interacting bosonic systemas a fundamental starting point for accurate quantum analysis and for furtherinvestigation of similar experiments. We show that a simple Rabi-oscillationmodel gives a good description of the wave packet production in terms of theinter-band transition while the first-order perturbation theory provesinadequate, that is the recent experiment already reached the realm ofhigh-order couplings. As a natural extension, we demonstrate enhancement of thewave packet production by the two-step Rabi-oscillation method using eithersingle frequency or dual frequencies. We assess the high-order Bragg reflectionand Landau-Zener transition at a band gap with the aid of rigorous quantumtime-propagation as well as the semi-classical theory exploited earlier by theHamburg experiment [J. Heinze et al., PRL 107, 135303(2011)]. Complicatedreflections and splittings of the wave packet during free evolution may belargely attributed to the intertwining of these two effects.

Single-particle Analysis of Non-interacting Ultracold Bosons in Amplitude Modulated Parabolic Optical Lattice