Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0404714 · Physical Review Letters

Matter-Wave Gap Vortices in Optical Lattices

Elena A. Ostrovskaya, Yuri S. Kivshar

Published Oct 13, 2004• 107 citations
arXivHTMLPDF

Abstract

We predict the existence of spatially localized nontrivial topological states of a Bose-Einstein condensate with repulsive atomic interactions confined by an optical lattice. These nonlinear localized states, matter-wave gap vortices, carry a vortexlike phase dislocation and exist in the gaps of the matter-wave band-gap spectrum due to the Bragg scattering. We discuss the structure, stability, and formation dynamics of the gap vortices in the case of two-dimensional optical lattices.

DOI
10.1103/physrevlett.93.160405

Related papers

Generation and detection of matter-wave gap vortices in optical lattices

Elena A. Ostrovskaya, Tristram J. Alexander, Yuri S. Kivshar

We analyze numerically the process of dynamical generation of spatially localized vortices in Bose-Einstein condensates (BEC's) with repulsive atomic interactions confined by two-dimensional optical lattices. Akin to bright solitons in a repulsive condensate, these nonlinear localized states exist only within the gaps of the matter-wave band-gap spectrum imposed by the periodicity of the lattice potential. We discuss the complex structure of matter-wave phase singularities associated with different types of stationary gap vortices and suggest two different excitation methods. In one method, the condensate is adiabatically driven to the edge of the Brillouin zone where a vortex phase is subsequently imprinted onto the condensate wave packet. Alternatively, a vortex is created in a condensate confined in a harmonic trap and then is nonadiabatically released into the lattice potential. We find that only the latter method leads to robust and reliable generation of vortices within the gap of the matter-wave band-gap spectrum. Moreover, the nonadiabatic excitation can lead to the formation of broad gap vortices from the initial BEC wave packets with a large number of atoms. These broad vortices are intimately connected to self-trapped nonlinear states of the BEC recently demonstrated in experiments with a one-dimensional optical lattice. Our numerical simulations also confirm the feasibility of a homodyne interferometric detection of broad gap vortices.

Physical Review A•Aug 15, 2006•22 citations

Bose-Einstein condensates in optical lattices: Band-gap structure and solitons

Pearl J. Y. Louis, Elena A. Ostrovskaya, Craig M. Savage +1 more

We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.

arXiv:cond-mat/0208516•Physical Review A•Jan 9, 2003•269 citations

Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices

Elena A. Ostrovskaya, Yuri S. Kivshar

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.

Optics Express•Jan 1, 2004•90 citations

Matter-Wave Gap Solitons in Atomic Band-Gap Structures

Elena A. Ostrovskaya, Yuri S. Kivshar

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensional matter-wave gap solitons.

arXiv:cond-mat/0303190•Physical Review Letters•Apr 24, 2003•194 citations

Three-dimensional matter-wave vortices in optical lattices

Tristram J. Alexander, Elena A. Ostrovskaya, Andrey A. Sukhorukov +1 more

We study the localization of vortices in a three-dimensional band-gap. We report that not only planar, two-dimensional matter-wave gap vortices persist in the presence of the third dimension, but also the three-dimensional lattice may support novel types of quite unusual vortex-like structures which survive perturbations of both phase and atomic density. One remarkable result of the lattice geometry is that we may study coherent interactions of planar vortices, and even find stationary structures of an arbitrarily long stack of vortices. We find that the lattice stabilizes the vortex line, and leads to robust evolution of the perturbed state. The three-dimensional geometry also allows the existence of exotic vortex states which have no two-dimensional equivalent

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 25, 2006•2 citations

Bose-Einstein condensates in optical lattices: band-gap structure, solitons, and vortices

Elena A. Ostrovskaya

We give an overview of localization effects of Bose-Einstein condensates in optical lattices. In particular, we discuss the structure, dynamics, and feasibility of generation and detection of matter-wave solitons and vortices in two-dimensional lattices

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 25, 2006•0 citations
We predict the existence of spatially localized nontrivial topological states of a Bose-Einstein condensate with repulsive atomic interactions confined by an optical lattice. These nonlinear localized states, matter-wave gap vortices, carry a vortexlike phase dislocation and exist in the gaps of the matter-wave band-gap spectrum due to the Bragg scattering. We discuss the structure, stability, and formation dynamics of the gap vortices in the case of two-dimensional optical lattices.
We analyze numerically the process of dynamical generation of spatially localized vortices in Bose-Einstein condensates (BEC's) with repulsive atomic interactions confined by two-dimensional optical lattices. Akin to bright solitons in a repulsive condensate, these nonlinear localized states exist only within the gaps of the matter-wave band-gap spectrum imposed by the periodicity of the lattice potential. We discuss the complex structure of matter-wave phase singularities associated with different types of stationary gap vortices and suggest two different excitation methods. In one method, the condensate is adiabatically driven to the edge of the Brillouin zone where a vortex phase is subsequently imprinted onto the condensate wave packet. Alternatively, a vortex is created in a condensate confined in a harmonic trap and then is nonadiabatically released into the lattice potential. We find that only the latter method leads to robust and reliable generation of vortices within the gap of the matter-wave band-gap spectrum. Moreover, the nonadiabatic excitation can lead to the formation of broad gap vortices from the initial BEC wave packets with a large number of atoms. These broad vortices are intimately connected to self-trapped nonlinear states of the BEC recently demonstrated in experiments with a one-dimensional optical lattice. Our numerical simulations also confirm the feasibility of a homodyne interferometric detection of broad gap vortices.
We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.
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.
We study the localization of vortices in a three-dimensional band-gap. We report that not only planar, two-dimensional matter-wave gap vortices persist in the presence of the third dimension, but also the three-dimensional lattice may support novel types of quite unusual vortex-like structures which survive perturbations of both phase and atomic density. One remarkable result of the lattice geometry is that we may study coherent interactions of planar vortices, and even find stationary structures of an arbitrarily long stack of vortices. We find that the lattice stabilizes the vortex line, and leads to robust evolution of the perturbed state. The three-dimensional geometry also allows the existence of exotic vortex states which have no two-dimensional equivalent