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

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Three-dimensional matter-wave vortices in optical lattices

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

Published Jan 25, 2006• 2 citations
Publisher

Abstract

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

DOI
10.1109/cleoe.2005.1568483

Related papers

Matter-wave gap vortices in optical lattices

Elena A. Ostrovskaya, Yuri S. Kivshar

We describe the band-gap spectrum and localized coherent-matter waves in twodimensional optical lattices, and predict the existence of novel types of soliton bound states with a vortex-like phase, the gap vortices.

Conference on Lasers and Electro-Optics•Jan 1, 2004•3 citations

Matter-Wave Gap Vortices in Optical Lattices

Elena A. Ostrovskaya, Yuri S. Kivshar

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.

arXiv:cond-mat/0404714•Physical Review Letters•Oct 13, 2004•107 citations

Three-dimensional matter-wave vortices in optical lattices

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

We reveal that a repulsive Bose-Einstein condensate confined in a three-dimensional (3D) optical lattice supports vortex states which are spatially localized in all three dimensions and possess highly nontrivial particle flow. We demonstrate that the lattice stabilizes extended vortex lines that are normally unstable to transverse modulations, and show that stable vortices localized inside the 3D lattice may be easily generated via a nonadiabatic loading process.

arXiv:cond-mat/0501590•Physical Review A•Oct 10, 2005•22 citations

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

Matter-Wave Gap Solitons and Vortices in Three-Dimensional Parity-Time-Symmetric Optical Lattices

Jiawei Li, Yanpeng Zhang, Jianhua Zeng

Past decades have witnessed the emergence and increasing expansion of parity-time (PT )-symmetric systems in diverse physical fields and beyond as they license entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT -symmetric non-Hermitian systems have recently been explored broadly, whose understanding in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional PT optical lattices with emphasis on multidimensional gap solitons and vortices. Relying on direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linearband gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems.

iScience•Jan 1, 2021•20 citations

Gap solitons and vortices in two-dimensional spin-orbit-coupled Bose-Einstein condensates loaded onto moiré optical lattices

Li Wang, Zhenya Yan, Yi Zhu +1 more

Abstract In ultracold atomic gases, optical lattices and spin-orbit coupling are two important and useful linear means to study and control the nonlinear and quantum dynamics of matter waves, and both have been well realized in experiments. Here, nonlinear localization of spin-orbit-coupled Bose-Einstein condensates in moiré optical lattices is revealed theoretically, stressing the existence and stability of localized modes of diverse types including fundamental, half-vortex matter-wave gap solitons, and full-vortex ones (of both components). Notably, to our knowledge, a new type of vector vortex gap solitons, which is composed of a gap vortex soliton (singular mode) and a rhombic-array gap vortex (quadruple mode), is predicted in our two-component theoretical framework. It is also found that the model exhibits unique linear Bloch band structures including band splitting and extremely-flat bands, because of which all the predicted localized modes tend to be robustly stable, backed by our direct perturbed simulations. Our results demonstrate that the moiré pattern (and its joint cooperation with spin-orbit coupling) provides great possibilities to explore flat-band and moiré physics in ultracold atoms, and to further investigate the nonlinear dynamics.

Quantum Frontiers•Jul 11, 2025•6 citations
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
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.
Past decades have witnessed the emergence and increasing expansion of parity-time (PT )-symmetric systems in diverse physical fields and beyond as they license entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT -symmetric non-Hermitian systems have recently been explored broadly, whose understanding in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional PT optical lattices with emphasis on multidimensional gap solitons and vortices. Relying on direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linearband gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems.
Abstract In ultracold atomic gases, optical lattices and spin-orbit coupling are two important and useful linear means to study and control the nonlinear and quantum dynamics of matter waves, and both have been well realized in experiments. Here, nonlinear localization of spin-orbit-coupled Bose-Einstein condensates in moiré optical lattices is revealed theoretically, stressing the existence and stability of localized modes of diverse types including fundamental, half-vortex matter-wave gap solitons, and full-vortex ones (of both components). Notably, to our knowledge, a new type of vector vortex gap solitons, which is composed of a gap vortex soliton (singular mode) and a rhombic-array gap vortex (quadruple mode), is predicted in our two-component theoretical framework. It is also found that the model exhibits unique linear Bloch band structures including band splitting and extremely-flat bands, because of which all the predicted localized modes tend to be robustly stable, backed by our direct perturbed simulations. Our results demonstrate that the moiré pattern (and its joint cooperation with spin-orbit coupling) provides great possibilities to explore flat-band and moiré physics in ultracold atoms, and to further investigate the nonlinear dynamics.