Abstract
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.
Highlights
Photonic band-gap materials [1] – artificial periodic structures fabricated in a dielectric medium with a high refractive index contrast – offer new possibilities for the control and manipulation of coherent light waves
The study of nonlinear photonic crystals made of a Kerr nonlinear material [2, 3], has revealed that such structures can support self-trapped localized modes of the electromagnetic field in the form of optical gap solitons [4] with the energies inside the photonic gaps of a periodic structure
In this paper we describe the structure and stability properties of nonlinear localized states of Bose-Einstein condensates (BECs) in one- and two-dimensional optical lattices, and make links to parallel studies in nonlinear optics of periodic photonic structures such as nonlinear photonic crystals and optically-induced photonic lattices
Summary
Photonic band-gap materials [1] – artificial periodic structures fabricated in a dielectric medium with a high refractive index contrast – offer new possibilities for the control and manipulation of coherent light waves. Many recent experimental studies of Bose-Einstein condensates (BECs) in periodic potentials of optical lattices [8, 9, 10] demonstrate an unprecedented level of control and manipulation of coherent matter waves in the reconfigurable crystal-like structures created by light. Due to the inherent nonlinearity of coherent matter waves which is introduced by the interactions between atoms, BEC in a lattice potential forms a periodic nonlinear system which is expected to display rich and complex dynamics The modelling of both nonlinear optical and nonlinear matter-wave dynamics is often based on the nonlinear Schrodinger equation, which is used to describe both the electromagnetic field envelope and the BEC macroscopic wavefunction (mean-field).
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