Regular Article

Transport through degenerate tori and quantum-to-classical crossover in a driven Aubry-Andre model^★

Laboratory of Nonlinear Dynamical Systems, V.I.Il’ichev Pacific Oceanological Institute of the Far-Eastern Branch of the Russian Academy of Sciences, 43 Baltiyskaya St., 690041 Vladivostok, Russia

^a e-mail: makarov@poi.dvo.ru

Received: 16 October 2019
Received in final form: 9 December 2019
Published online: 20 January 2020

Abstract

Dynamics of ultracold atoms in a one-dimensional incommensurate quasiperiodic optical lattice is considered. The lattice is created as superposition of a large-amplitude primary lattice and a small-amplitude secondary lattice. In the tight-binding approximation motion of atoms is described by the Aubry-Andre model. Attention is focused on atom delocalization caused by amplitude modulation of the secondary lattice. We consider the semiclassical regime that is realized if the lattice spacing of the primary lattice is small compared to that of the secondary one. It is shown that efficient delocalization occurs if frequency of the modulation corresponds to resonant influence on degenerate tori in classical phase space. Inclusion of the next-to-nearest tunneling into the Aubry-Andre model leads to shift of the corresponding resonance to the lower frequency range. As ratio of primary and secondary lattice periods increases, effect of the resonance ceases.