Wave-packet dynamics of noninteracting ultracold bosons in an amplitude-modulated parabolic optical lattice

The recent Aarhus experiment [Phys. Rev. A 88, 023620 (2013)] produced wave packets by applying amplitude modulation to a trapped Bose-Einstein condensate (BEC) of Rb-87 using an optical lattice. The present paper renders a theoretical account of this experimental production of wave packets and their subsequent time evolution, focusing on a one-dimensional noninteracting bosonic system as a fundamental starting point for accurate quantum analysis. Since experimental manipulation requires efficient wave-packet creation, we introduce the single-Q Rabi model to give a simple and reliable description of the interband transition. As a natural extension, we demonstrate enhancement of the wave-packet production by the two-step Rabi oscillation method using either one or two frequencies. The subsequent time evolution is affected by the intertwining of Bragg reflection and the Landau-Zener transition at each band gap, which is analyzed with the aid of a semiclassical theory [Phys. Rev. Lett. 110, 085302 (2013)].