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AIP conference proceedings

Matter-Wave Solitons In Optical Superlattices

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

Published Jan 1, 2006• 1 citation
Publisher

Abstract

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.

DOI
10.1063/1.2354602

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•Jan 1, 2004•11 citations
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.
We present a numerical study of dispersion manipulation and formation of matter-wave gap solitons in a Bose-Einstein condensate trapped in an optical superlattice. We demonstrate a method for controlled generation of matter-wave gap solitons in a stationary lattice by using an interference pattern of two condensate wave packets, which mimics the structure of the gap soliton near the edge of a spectral band. The efficiency of this method is compared to that of gap soliton generation in a moving lattice recently demonstrated experimentally by Eiermann et al. [Phys. Rev. Lett., 92, 230401 (2004)]. We show that, by changing the relative depths of the superlattice wells, one can fine-tune the effective dispersion of the matter waves at the edges of the minigaps of the superlattice Bloch-wave spectrum and, therefore, effectively control both the peak density and the spatial width of the emerging gap solitons.
We study the pumping of matter-wave solitons formed in Bose-Einstein condensates (BECs) with attractive atomic interactions that are loaded into optical superlattices in which one of the lattices is moving with respect to the other. We find that solitons exhibit the remarkably similar pumping properties in both shallow and deep lattices, and that for exactly the same soliton initially excited, switching between integer (fractional) pumping and trapping can be achieved by simply adjusting the lattice parameters. In addition, we find that the gap solitons, which bifurcate from the lowest energy band in a semi-infinite band gap, also exhibit this lattice-parameter-dependent pumping and trapping. The treatment of solitons as classical particles with effective centre-of-mass equations of motion provides a good description of this parameter-dependent integer (fractional) pumping and trapping of solitons.
We study the mobility and interaction of gap solitons in a Bose–Einstein condensate (BEC) confined by an optical lattice potential. Such localized wavepackets can exist only in the gaps of the matter-wave band-gap spectrum and their interaction properties are shown to serve as a measure of the discreteness imposed on a BEC by the lattice potential. We show that inelastic collisions of two weakly localized near-band-edge gap solitons provide a simple and effective means for generating strongly localized in-gap solitons through soliton fusion.
Bose–Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years—particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes—gap solitons and soliton clusters—are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.
Abstract. We study mobility and interaction of gap solitons in a Bose-Einstein condensate (BEC) confined by an optical lattice potential. Such localized wavepackets can exist only in the gaps of the matter-wave band-gap spectrum and their interaction properties are shown to serve as a measure of discreteness imposed onto a BEC by the lattice potential. We show that inelastic collisions of two weakly localized nearthe-band-edge gap solitons provide simple and effective means for generating strongly localized in-gap solitons through soliton fusion.