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

Abstract

Ultracold atoms in the combined potential of a parabolic trap and an optical lattice is considered a promising tool for coherent manipulation of matter wave packets. The recent Aarhus experiment[P. L. Pedersen et al., Phys. Rev. A. 88, 023620 (2013)] produced wave packets by applying the optical lattice's amplitude modulation to a Bose-Einstein condensate (BEC) of ${}^{87}$Rb. The present paper renders a theoretical account with single-particle analysis of this experimental production of the wave packets and their subsequent time-evolution. We focus on the one-dimensional non-interacting bosonic system as a fundamental starting point for accurate quantum analysis and for further investigation of similar experiments. We show that a simple Rabi-oscillation model gives a good description of the wave packet production in terms of the inter-band transition while the first-order perturbation theory proves inadequate, that is the recent experiment already reached the realm of high-order couplings. As a natural extension, we demonstrate enhancement of the wave packet production by the two-step Rabi-oscillation method using either single frequency or dual frequencies. We assess the high-order Bragg reflection and Landau-Zener transition at a band gap with the aid of rigorous quantum time-propagation as well as the semi-classical theory exploited earlier by the Hamburg experiment [J. Heinze et al., PRL 107, 135303(2011)]. Complicated reflections and splittings of the wave packet during free evolution may be largely attributed to the intertwining of these two effects.

29 pages, 11 figures

References in corpus (8)

• Probing nearest-neighbor correlations of ultracold fermions in an optical lattice
• Making ultracold molecules in a two color pump-dump photoassociation scheme using chirped pulses
• Single-atom density of states of an optical lattice
• Intrinsic Photoconductivity of Ultracold Fermions in Optical Lattices
• Quantum dynamics of one and two bosonic atoms in a combined tight-binding periodic and weak parabolic potential
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• Dynamical control of matter wave splitting using time-dependent optical lattices
• Quantum vortices in optical lattices

Cited by in corpus (1)

• Emission of particles from a parametrically driven condensate in a one-dimensional lattice