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Journal of Optics B Quantum and Semiclassical Optics

Matter-wave dark solitons in optical lattices

Pearl J. Y. Louis, Elena A. Ostrovskaya, Yuri S. Kivshar

Published May 1, 2004• 38 citations
Publisher

Abstract

We analyse the Floquet–Bloch spectrum of matter waves in Bose–Einstein condensates loaded into single-periodic optical lattices and double-periodic superlattices. In the framework of the Gross–Pitaevskii equation, we describe the structure and analyse the mobility properties of matter-wave dark solitons residing on backgrounds of extended nonlinear Bloch-type states. We demonstrate that interactions between dark solitons can be effectively controlled in optical superlattices.

DOI
10.1088/1464-4266/6/5/020

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We analyse the Floquet–Bloch spectrum of matter waves in Bose–Einstein condensates loaded into single-periodic optical lattices and double-periodic superlattices. In the framework of the Gross–Pitaevskii equation, we describe the structure and analyse the mobility properties of matter-wave dark solitons residing on backgrounds of extended nonlinear Bloch-type states. We demonstrate that interactions between dark solitons can be effectively controlled in optical superlattices.
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We present two families analytical solutions to the extended Gross-Pitaevskii equation (GPE), which describe the dynamics of bright and dark solitons in Bose-Einstein condensations(BECs) with varying coefficients of two and three-body interactions in a parabolic and complex potential. The properties of the dynamical evolutions of the bright and dark matter-wave solitons are investigated. It is interesting that the matter-wave can be controlled by applying the external magnetic field and a background.
We overview our recent theoretical studies on nonlinear atom optics of the Bose-Einstein condensates (BECs) loaded into optical lattices. In particular, we describe the band-gap spectrum and nonlinear localization of BECs in one- and two-dimensional optical lattices. We discuss the structure and stability properties of spatially localized states (matter-wave solitons) in 1D lattices, as well as trivial and vortex-like bound states of 2D gap solitons. To highlight similarities between the behavior of coherent light and matter waves in periodic potentials, we draw useful parallels with the physics of coherent light waves in nonlinear photonic crystals and optically-induced photonic lattices.
In this work we show that the properties of both bright and dark Bose‐Einstein condensate (BEC) solitons trapped in optical superlattices can be controlled by changing the shape of the trapping potential whilst maintaining a constant periodicity and lattice height. Using this method we can control the properties of bright gap solitons by dispersion management. We can also control the interactions between dark lattice solitons. In addition we demonstrate a method for controlled generation of matter‐wave gap solitons in stationary optical lattices by interfering two condensate wavepackets, producing a single wavepacket at a gap edge with properties similar to a gap soliton. As this wavepacket evolves, it forms a bright gap soliton.
Optical lattices have been used as a versatile toolbox to control Bose-Einstein condensates (BECs) in recent years, and a wealth of emergent nonlinear phenomena have been found, including bright gap solitons and dark ones, among which the former has been realized in experiments. The latter, however, has only theoretical results and its fundamental properties are still not well understood. Here we theoretically and numerically explore an open issue of creating stable matter-wave dark gap solitons in a one-dimensional optical lattice, onto which the BECs with self-defocusing quintic nonlinearity are loaded. Using linear-stability analysis and direct simulations, the formation, structures, and properties of dark gap solitons in quintic nonlinearity have been compared to those upheld by cubic Kerr nonlinearity. In particular, we uncover that the dark gap solitons and soliton clusters are robustly stable in the first finite band gap of the underlying linear spectrum, and are hard to be stabilized in the second gap. The predicted dark gap solitons are observable in current experiments on dense ultracold atoms, using an optical lattice technique, and in the optics domain for nonlinear light propagation in periodic optical media with quintic nonlinearity.