Eur. Phys. J. D 33, 253-263 (2005)
https://doi.org/10.1140/epjd/e2005-00040-x

Dynamics of Bose-Einstein condensates in one-dimensional optical lattices in the presence of transverse resonances

¹ Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
² Fachbereich Physik der Universität Konstanz, Fach M674, 78457 Konstanz, Germany
³ Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
⁴ Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

Corresponding author: ^a pmarzlin@qis.ucalgary.ca

Received: 8 October 2004
Revised: 11 February 2005
Published online: 12 April 2005

Abstract

The dynamics of Bose-Einstein condensates in the lowest energy band of a one-dimensional optical lattice is generally disturbed by the presence of transversally excited resonant states. We propose an effective one-dimensional theory which takes these resonant modes into account and derive variational equations for large-scale dynamics. Several applications of the theory are discussed and a novel type of “triple soliton” is proposed, which consists of a superposition of a wavepacket at the upper band edge and two transversally excited wavepackets which are displaced in quasi-momentum space.