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

Chinese Physics B

Three-dimensional Bose—Einstein condensate vortex solitons under optical lattice and harmonic confinements

Ying Wang, Feng-De Zong, Feng-Bo Li

Published Mar 1, 2013• 3 citations
Publisher

Abstract

We predict three-dimensional vortex solitons in a Bose—Einstein condensate under a complex potential, which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction. The vortex solitons are built in the form of a layer-chain structure made of several fundamental vortices along the optical-lattice direction. This has not been reported before in the three-dimensional Bose—Einstein condensate. By using a combination of the energy density functional method with direct numerical simulation, we find three-dimensional vortex solitons with topological charges χ = 1, χ = 2, and χ = 3. Moreover, the macroscopic quantum tunneling and chirp phenomena of the vortex solitons are shown in the evolution. Therein, the occurrence of macroscopic quantum tunneling provides the possibility for the experimental realization of quantum tunneling. Specifically, we successfully manipulate the vortex solitons along the optical lattice direction. The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.

DOI
10.1088/1674-1056/22/3/030315

Related papers

Vortical Solitons of Three-Dimensional Bose—Einstein Condensates under Both a Bichromatic Optical Lattice and Anharmonic Potentials

Li Fengbo, Feng-De Zong, Ying Wang

We study Bose—Einstein condensate vortical solitons under both a bichromatic optical lattice and anharmonic potential. The vortical solitons are built in the form of a layer-chain structure made up of two fundamental vortices along the bichromatic optical lattice direction, which have not been reported before in the three-dimensional Bose—Einstein condensate. A variation approach is applied to find the optimum initial solutions of vortical solitons. The stabilities of the vortical solitons are confirmed by the numerical simulation of the time-dependent Gross—Pitaevskii equation. In particular, stable Bose—Einstein condensate vortical solitons with fundamental vortices of different atomic numbers in the external potential within a range of experimentally achievable timescales are found. We further manipulate the vortical solitons to an arbitrary position by steadily moving the bichromatic optical lattice, and find a stable region for the successful manipulation of vortical solitons without collapse. These results provide insight into controlling and manipulating the Bose—Einstein condensate vortical solitons for macroscopic quantum applications.

Chinese Physics Letters•Jun 1, 2013•2 citations

Effect of soliton and vortex geometry on the transport of Bose-Einstein condensates in optical lattices

R. G. Scott, A. Martin, T. M. Fromhold

We investigate the effect of solitons and vortices, with a range of different topologies, on the dynamics of Bose-Einstein condensates in a one-dimensional optical lattice and a three-dimensional harmonic trap. The solitons and vortices are imposed on the initial state of the atom cloud, which is set in oscillatory motion by a sudden displacement of the harmonic trap. We study this motion using both quantum-mechanical calculations, based on the nonlinear Schr\"odinger equation, and a semiclassical model for transport through the lowest energy band of the optical lattice. We demonstrate that the geometry of the vortices and solitons in the initial state plays a crucial role in the evolution of the atom cloud. In particular, we find that the center-of-mass motion of a condensate containing a vortex is only weakly damped if the vortex core lies parallel to the optical lattice direction, but is strongly damped when the core is orientated perpendicular to the lattice direction. Severe damping is observed for a condensate containing a soliton whose nodal plane is perpendicular to the optical lattice.

Physical Review A•Jun 11, 2004•1 citation

Vortex chains in rotating two-dimensional Bose-Einstein condensate in a harmonic plus optical lattices potential

Zhiqiang Zhang

Bose-Einstein condensate (BEC) is essentially a macroscopic quantum effect with quantum volatility, macroscopic quantum coherence and artificial controllability. Owing to its unique controllability, it becomes a new ideal platform for quantum simulations and studies of interacting quantum systems. In this paper, the generation of vortices and the formation of vortex chains, as well as characteristics of vortex chains in rotating two-dimensional BEC in a potential composed of harmonic potential and optical lattice are studied numerically. Firstly, the generation of vortices, the formation and distribution of vortex chains and the effects of different physical parameters on the vortex chains in two-dimensional BEC are investigated by using the multigrid preconditioned conjugate gradient method. Secondly, the evolution of the vortex chains with time is studied by using the time-splitting spectral method. The results show that the generation of vortices in BEC trapped in the compound potential corresponds to the minimum value of the potential. When the depth of the optical lattice increases to a certain value, vortex chains are formed in the BEC. With the further increase of the depth of the optical lattice, the vortex depth in the vortex chain in the BEC decreases continuously, and finally the vortex chain disappears completely. When the interaction strength between atoms increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the interaction strength between atoms increases to a certain value, the symmetry of the vortex chains is broken. As the rotation frequency of the condensate increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the rotation frequency is close to the external trapping potential frequency, the linear alignment of the vortex chains is disrupted. It is also found that there are three stages in the evolution of the vortex chains in the BEC: in the first stage, vortex chains rotate together with the condensate, and the original chain distribution keeps unchanged; in the second stage, the phenomenon of vortex space extrusion appears, and the vortex chain is destroyed; in the third stage, the phenomenon of vortex space expansion occurs, and finally the vortex chains disappear. The results above show that the depth of the optical lattice, the interaction strength between atoms, and the rotation frequency of the condensate have important effects on the vortices and vortex chains in the condensate. By adjusting these physical quantities, the number of vortices and the shape of vortex chains in the BEC can be effectively manipulated. This may provide some theoretical reference and guidance for future experiments and applications.

Acta Physica Sinica•Jan 1, 2022•0 citations

Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices

Antonio Muñoz Mateo, V. Delgado, Boris A. Malomed

We study fundamental and compound gap solitons (GSs) of matter waves in one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D) weak-radial-confinement regime, which corresponds to realistic experimental conditions in Bose-Einstein condensates (BECs). In this regime GSs exhibit nontrivial radial structures. Associated with each 3D linear spectral band exists a family of fundamental gap solitons that share a similar transverse structure with the Bloch waves of the corresponding linear band. GSs with embedded vorticity $m$ may exist inside bands corresponding to other values of $m$. Stable GSs, both fundamental and compound ones (including vortex solitons), are those which originate from the bands with lowest axial and radial quantum numbers. These findings suggest a scenario for the experimental generation of robust GSs in 3D settings.

arXiv:1010.5271•Physical Review A•Nov 8, 2010•21 citations

Gap solitons in a dipolar Bose–Einstein condensate on a three-dimensional optical lattice

Paulsamy Muruganandam, S K Adhikari

We suggest and study the stable disc- and cigar-shaped gap solitons of a dipolar Bose–Einstein condensate of 52 Cr atoms localized in the lowest band gap by three optical-lattice (OL) potentials along orthogonal directions. The one-dimensional version of these solitons of experimental interest confined by an OL along the dipole moment direction and harmonic traps in transverse directions is also considered. Important dynamics of (i) the breathing oscillation of a gap soliton upon perturbation and (ii) the dragging of a gap soliton by a moving lattice along the axial z direction demonstrates the stability of gap solitons. A movie clip (available at http://stacks.iop.org/0953-4075/44/121001/mmedia ) of the dragging of the three-dimensional gap soliton is included.

arXiv:1105.2766•Journal of Physics B Atomic Molecular and Optical Physics•Jun 1, 2011•28 citations

Three-dimensional ring vortex solitons and their stabilities in Bose-Einstein condensates under magnetic confinement

Ji Li, Deng‐Shan Wang, Zhi-Yong Wu +2 more

A three-dimensional study of the ring vortex solitons is conducted for both attractive and repulsive Bose-Einstein condensates subject to harmonic potential confinement. A family of stationary ring vortex solitons, which is defined by the radial excitation number and the winding number of the intrinsic vorticity, are obtained numerically for a given atomic interaction strength. We find that stabilities of the ground and radially excited states of the ring vortex soliton are dependent on the winding number differently. The ground state of the ring vortex soliton with the large winding number is unstable dynamically against random perturbation. The radially excited state of the ring vortex soliton with large winding number corresponds to the increased collapse threshold and therefore can be made stable for sufficiently small atomic interaction strengths. The ground and radially excited states also demonstrate different dynamic evolutions under large atomic interaction strengths. The former exhibits simultaneous symmetric splitting in the transverse plane, while the latter displays periodic expand-merge cycles in the longitudinal direction.

Physical Review A•Aug 22, 2012•17 citations
We predict three-dimensional vortex solitons in a Bose—Einstein condensate under a complex potential, which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction. The vortex solitons are built in the form of a layer-chain structure made of several fundamental vortices along the optical-lattice direction. This has not been reported before in the three-dimensional Bose—Einstein condensate. By using a combination of the energy density functional method with direct numerical simulation, we find three-dimensional vortex solitons with topological charges χ = 1, χ = 2, and χ = 3. Moreover, the macroscopic quantum tunneling and chirp phenomena of the vortex solitons are shown in the evolution. Therein, the occurrence of macroscopic quantum tunneling provides the possibility for the experimental realization of quantum tunneling. Specifically, we successfully manipulate the vortex solitons along the optical lattice direction. The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.
We study Bose—Einstein condensate vortical solitons under both a bichromatic optical lattice and anharmonic potential. The vortical solitons are built in the form of a layer-chain structure made up of two fundamental vortices along the bichromatic optical lattice direction, which have not been reported before in the three-dimensional Bose—Einstein condensate. A variation approach is applied to find the optimum initial solutions of vortical solitons. The stabilities of the vortical solitons are confirmed by the numerical simulation of the time-dependent Gross—Pitaevskii equation. In particular, stable Bose—Einstein condensate vortical solitons with fundamental vortices of different atomic numbers in the external potential within a range of experimentally achievable timescales are found. We further manipulate the vortical solitons to an arbitrary position by steadily moving the bichromatic optical lattice, and find a stable region for the successful manipulation of vortical solitons without collapse. These results provide insight into controlling and manipulating the Bose—Einstein condensate vortical solitons for macroscopic quantum applications.
We investigate the effect of solitons and vortices, with a range of different topologies, on the dynamics of Bose-Einstein condensates in a one-dimensional optical lattice and a three-dimensional harmonic trap. The solitons and vortices are imposed on the initial state of the atom cloud, which is set in oscillatory motion by a sudden displacement of the harmonic trap. We study this motion using both quantum-mechanical calculations, based on the nonlinear Schr\"odinger equation, and a semiclassical model for transport through the lowest energy band of the optical lattice. We demonstrate that the geometry of the vortices and solitons in the initial state plays a crucial role in the evolution of the atom cloud. In particular, we find that the center-of-mass motion of a condensate containing a vortex is only weakly damped if the vortex core lies parallel to the optical lattice direction, but is strongly damped when the core is orientated perpendicular to the lattice direction. Severe damping is observed for a condensate containing a soliton whose nodal plane is perpendicular to the optical lattice.
Bose-Einstein condensate (BEC) is essentially a macroscopic quantum effect with quantum volatility, macroscopic quantum coherence and artificial controllability. Owing to its unique controllability, it becomes a new ideal platform for quantum simulations and studies of interacting quantum systems. In this paper, the generation of vortices and the formation of vortex chains, as well as characteristics of vortex chains in rotating two-dimensional BEC in a potential composed of harmonic potential and optical lattice are studied numerically. Firstly, the generation of vortices, the formation and distribution of vortex chains and the effects of different physical parameters on the vortex chains in two-dimensional BEC are investigated by using the multigrid preconditioned conjugate gradient method. Secondly, the evolution of the vortex chains with time is studied by using the time-splitting spectral method. The results show that the generation of vortices in BEC trapped in the compound potential corresponds to the minimum value of the potential. When the depth of the optical lattice increases to a certain value, vortex chains are formed in the BEC. With the further increase of the depth of the optical lattice, the vortex depth in the vortex chain in the BEC decreases continuously, and finally the vortex chain disappears completely. When the interaction strength between atoms increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the interaction strength between atoms increases to a certain value, the symmetry of the vortex chains is broken. As the rotation frequency of the condensate increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the rotation frequency is close to the external trapping potential frequency, the linear alignment of the vortex chains is disrupted. It is also found that there are three stages in the evolution of the vortex chains in the BEC: in the first stage, vortex chains rotate together with the condensate, and the original chain distribution keeps unchanged; in the second stage, the phenomenon of vortex space extrusion appears, and the vortex chain is destroyed; in the third stage, the phenomenon of vortex space expansion occurs, and finally the vortex chains disappear. The results above show that the depth of the optical lattice, the interaction strength between atoms, and the rotation frequency of the condensate have important effects on the vortices and vortex chains in the condensate. By adjusting these physical quantities, the number of vortices and the shape of vortex chains in the BEC can be effectively manipulated. This may provide some theoretical reference and guidance for future experiments and applications.
We study fundamental and compound gap solitons (GSs) of matter waves in one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D) weak-radial-confinement regime, which corresponds to realistic experimental conditions in Bose-Einstein condensates (BECs). In this regime GSs exhibit nontrivial radial structures. Associated with each 3D linear spectral band exists a family of fundamental gap solitons that share a similar transverse structure with the Bloch waves of the corresponding linear band. GSs with embedded vorticity mmm may exist inside bands corresponding to other values of mmm. Stable GSs, both fundamental and compound ones (including vortex solitons), are those which originate from the bands with lowest axial and radial quantum numbers. These findings suggest a scenario for the experimental generation of robust GSs in 3D settings.
We suggest and study the stable disc- and cigar-shaped gap solitons of a dipolar Bose–Einstein condensate of 52 Cr atoms localized in the lowest band gap by three optical-lattice (OL) potentials along orthogonal directions. The one-dimensional version of these solitons of experimental interest confined by an OL along the dipole moment direction and harmonic traps in transverse directions is also considered. Important dynamics of (i) the breathing oscillation of a gap soliton upon perturbation and (ii) the dragging of a gap soliton by a moving lattice along the axial z direction demonstrates the stability of gap solitons. A movie clip (available at http://stacks.iop.org/0953-4075/44/121001/mmedia ) of the dragging of the three-dimensional gap soliton is included.
A three-dimensional study of the ring vortex solitons is conducted for both attractive and repulsive Bose-Einstein condensates subject to harmonic potential confinement. A family of stationary ring vortex solitons, which is defined by the radial excitation number and the winding number of the intrinsic vorticity, are obtained numerically for a given atomic interaction strength. We find that stabilities of the ground and radially excited states of the ring vortex soliton are dependent on the winding number differently. The ground state of the ring vortex soliton with the large winding number is unstable dynamically against random perturbation. The radially excited state of the ring vortex soliton with large winding number corresponds to the increased collapse threshold and therefore can be made stable for sufficiently small atomic interaction strengths. The ground and radially excited states also demonstrate different dynamic evolutions under large atomic interaction strengths. The former exhibits simultaneous symmetric splitting in the transverse plane, while the latter displays periodic expand-merge cycles in the longitudinal direction.