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:0912.1470 · Physical Review A

Two-dimensional discrete solitons in dipolar Bose-Einstein condensates

Goran Gligorić, Aleksandra Maluckov, Milutin Stepić, Ljupčo R. Hadžievski, Boris A. Malomed

Published Jan 29, 2010• 46 citations
arXivHTMLPDF

Abstract

We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disk's plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, which differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying three-dimensional Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on the effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site, and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial.

DOI
10.1103/physreva.81.013633

Related papers

Discrete vortex solitons in dipolar Bose–Einstein condensates

Goran Gligorić, Aleksandra Maluckov, Milutin Stepić +2 more

We analyse the existence, stability and dynamics of localized discrete modes with intrinsic vorticity S = 1 and S = 2 in the disc-shaped dipolar Bose-Einstein condensate loaded into a deep two-dimensional optical lattice. The condensate, which features the interplay of local contact and nonlocal dipole-dipole (DD) interactions between atoms, is modelled by the 2D discrete Gross-Pitaevskii equation which includes the long-range DD term. Various species of discrete vortex solitons, which are known in the model of the condensate with local interactions, are found to exist in the presence of the DD interaction too. In locally self-attractive condensates, the isotropic DD repulsion, which corresponds to the orientation of atomic dipoles perpendicular to the confinement plane, helps to extend the region of the vortex stability, while in the case of anisotropic DD interactions, corresponding to the in-plane orientation of the dipoles, vortices are unstable. In the former case, those vortices which are unstable may evolve into robust ring-shaped breathers. The attractive isotropic DD interaction can create localized vortices in the condensate with the local self-repulsion, but they all are unstable, evolving into single-peak asymmetric structures.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 16, 2010•23 citations

Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions

Goran Gligorić, Aleksandra Maluckov, Ljupčo R. Hadžievski +1 more

A model of the Bose-Einstein condensate of dipolar atoms, confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction, is introduced, taking into regard the dipole-dipole (DD) and contact interactions. The model is based on the discrete nonlinear Schr\"odinger equation with an additional nonlocal term accounting for the DD interactions. The existence and stability of fundamental unstaggered solitons are studied for attractive and repulsive signs of both the local and nonlocal interactions. The DD forces strongly affect the shape and stability of on-site and intersite discrete solitons. The corresponding existence and stability regions in the parametric space are summarized in the form of diagrams, which feature a multiple stability exchange between the on-site and intersite families; in the limit of the dominating DD attraction, the on-site solitons are stable, while their intersite counterparts are not. We also demonstrate that the DD interactions reduce the Peierls-Nabarro barrier and enhance the mobility of the discrete solitons.

Physical Review A•Dec 22, 2008•63 citations

Vortical and fundamental solitons in dipolar Bose–Einstein condensates trapped in isotropic and anisotropic nonlinear potentials

R Kishor Kumar, P Muruganandam, Boris A. Malomed

We predict the existence of stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipole interactions (DDI). The condensate is trapped in the 2D plane with the help of the repulsive contact interactions whose local strength grows $\sim r^{4}$ from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons and solitary vortices in the pseudopotential, which is induced by the repulsive local nonlinearity with the strength growing from the center to periphery, to the case when the trapping mechanism competes with the long-range repulsive DDI. Another objective is to extend the analysis for elliptic vortices and solitons in an anisotropic nonlinear pseudopotential. Using the variational approximation (VA) and numerical simulations, we construct families of self-trapped modes with vorticities $\ell =0$ (fundamental solitons), $\ell =1$, and $\ell =2$. The fundamental solitons and vortices with $\ell =1$ exist up to respective critical values of the eccentricity of the anisotropic pseudopotential, being stable in the entire existence regions. The vortices with $\ell =2$ are stable solely in the isotropic model.

arXiv:1308.0468•Journal of Physics B Atomic Molecular and Optical Physics•Aug 22, 2013•7 citations

Dipolar matter-wave solitons in two-dimensional anisotropic discrete lattices

Huaiyu Chen, Yan Liu, Qiang Zhang +3 more

We numerically demonstrate two-dimensional (2D) matter-wave solitons in the disk-shaped dipolar Bose-Einstein condensates (BECs) trapped in strongly anisotropic optical lattices (OLs) in a disk's plane. The considered OLs are square lattices which can be formed by interfering two pairs of plane waves with different intensities. The hopping rates of the condensates between two adjacent lattices in the orthogonal directions are different, which gives rise to a linearly anisotropic system. We find that when the polarized orientation of the dipoles is parallel to disk's plane with the same direction, the combined effects of the linearly anisotropy and the nonlocal nonlinear anisotropy strongly influence the formations, as well as the dynamics of the lattice solitons. Particularly, the isotropy-pattern solitons (IPSs) are found when these combined effects reach a balance. Motion, collision, and rotation of the IPSs are also studied in detail by means of systematic simulations. We further find that these IPSs can move freely in the 2D anisotropic discrete system, hence giving rise to an anisotropic effective mass. Four types of collisions between the IPSs are identified. By rotating an external magnetic field up to a critical angular velocity, the IPSs can still remain localized and play as a breather. Finally, the influences from the combined effects between the linear and the nonlocal nonlinear anisotropy with consideration of the contact and/or local nonlinearity are discussed too.

arXiv:1604.05798•Physical Review A•May 10, 2016•17 citations

Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole-dipole interactions

Goran Gligorić, Aleksandra Maluckov

Abstract. A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE) with additional terms describing long-range dipoledipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially as concerns their collapseinduced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions. Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole-dipole interactions2 1

•Dec 4, 2012•19 citations

Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole–dipole interactions

G Gligorić, A Maluckov, Ljupčo R. Hadžievski +1 more

A model of the Bose–Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE) with additional terms describing long-range dipole–dipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially concerning their collapse-induced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions.

arXiv:0905.3660•Journal of Physics B Atomic Molecular and Optical Physics•Jun 16, 2009•18 citations
We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disk's plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, which differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying three-dimensional Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on the effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site, and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial.
We analyse the existence, stability and dynamics of localized discrete modes with intrinsic vorticity S = 1 and S = 2 in the disc-shaped dipolar Bose-Einstein condensate loaded into a deep two-dimensional optical lattice. The condensate, which features the interplay of local contact and nonlocal dipole-dipole (DD) interactions between atoms, is modelled by the 2D discrete Gross-Pitaevskii equation which includes the long-range DD term. Various species of discrete vortex solitons, which are known in the model of the condensate with local interactions, are found to exist in the presence of the DD interaction too. In locally self-attractive condensates, the isotropic DD repulsion, which corresponds to the orientation of atomic dipoles perpendicular to the confinement plane, helps to extend the region of the vortex stability, while in the case of anisotropic DD interactions, corresponding to the in-plane orientation of the dipoles, vortices are unstable. In the former case, those vortices which are unstable may evolve into robust ring-shaped breathers. The attractive isotropic DD interaction can create localized vortices in the condensate with the local self-repulsion, but they all are unstable, evolving into single-peak asymmetric structures.
A model of the Bose-Einstein condensate of dipolar atoms, confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction, is introduced, taking into regard the dipole-dipole (DD) and contact interactions. The model is based on the discrete nonlinear Schr\"odinger equation with an additional nonlocal term accounting for the DD interactions. The existence and stability of fundamental unstaggered solitons are studied for attractive and repulsive signs of both the local and nonlocal interactions. The DD forces strongly affect the shape and stability of on-site and intersite discrete solitons. The corresponding existence and stability regions in the parametric space are summarized in the form of diagrams, which feature a multiple stability exchange between the on-site and intersite families; in the limit of the dominating DD attraction, the on-site solitons are stable, while their intersite counterparts are not. We also demonstrate that the DD interactions reduce the Peierls-Nabarro barrier and enhance the mobility of the discrete solitons.
We predict the existence of stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipole interactions (DDI). The condensate is trapped in the 2D plane with the help of the repulsive contact interactions whose local strength grows ∼r4\sim r^{4}∼r4 from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons and solitary vortices in the pseudopotential, which is induced by the repulsive local nonlinearity with the strength growing from the center to periphery, to the case when the trapping mechanism competes with the long-range repulsive DDI. Another objective is to extend the analysis for elliptic vortices and solitons in an anisotropic nonlinear pseudopotential. Using the variational approximation (VA) and numerical simulations, we construct families of self-trapped modes with vorticities ℓ=0\ell =0ℓ=0 (fundamental solitons), ℓ=1\ell =1ℓ=1, and ℓ=2\ell =2ℓ=2. The fundamental solitons and vortices with ℓ=1\ell =1ℓ=1 exist up to respective critical values of the eccentricity of the anisotropic pseudopotential, being stable in the entire existence regions. The vortices with ℓ=2\ell =2ℓ=2 are stable solely in the isotropic model.
We numerically demonstrate two-dimensional (2D) matter-wave solitons in the disk-shaped dipolar Bose-Einstein condensates (BECs) trapped in strongly anisotropic optical lattices (OLs) in a disk's plane. The considered OLs are square lattices which can be formed by interfering two pairs of plane waves with different intensities. The hopping rates of the condensates between two adjacent lattices in the orthogonal directions are different, which gives rise to a linearly anisotropic system. We find that when the polarized orientation of the dipoles is parallel to disk's plane with the same direction, the combined effects of the linearly anisotropy and the nonlocal nonlinear anisotropy strongly influence the formations, as well as the dynamics of the lattice solitons. Particularly, the isotropy-pattern solitons (IPSs) are found when these combined effects reach a balance. Motion, collision, and rotation of the IPSs are also studied in detail by means of systematic simulations. We further find that these IPSs can move freely in the 2D anisotropic discrete system, hence giving rise to an anisotropic effective mass. Four types of collisions between the IPSs are identified. By rotating an external magnetic field up to a critical angular velocity, the IPSs can still remain localized and play as a breather. Finally, the influences from the combined effects between the linear and the nonlocal nonlinear anisotropy with consideration of the contact and/or local nonlinearity are discussed too.
Abstract. A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE) with additional terms describing long-range dipoledipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially as concerns their collapseinduced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions. Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole-dipole interactions2 1
A model of the Bose–Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE) with additional terms describing long-range dipole–dipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially concerning their collapse-induced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions.