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

Physical Review A

Two-component Bose-Einstein condensates in D -dimensional optical lattices

Jianjun Wang, Ai‐Xia Zhang, Kezhi Zhang, Juan Ma, Ju-Kui Xue

Published Mar 12, 2010• 9 citations
Publisher

Abstract

The impurity-induced self-trapping and stable moving soliton and breather of two-component Bose-Einstein condensates (BEC's) in deep $D$-dimensional optical lattices are discussed both analytically and numerically. Under the tight-binding approximation and within a time-dependent variational approach, analytical criteria for occurrences of a self-trapping, moving soliton and breather in the system are obtained. The analytical results are confirmed by direct numerical simulation. It is shown that the dynamics of the condensates can be modified significantly by a minor admixture of an impurity (the second component). The diffusion state of the single-component BEC will transit to the self-trapped state due to the minor admixture of an impurity, even if the two condensates are only with marginal spatial overlap. Furthermore, we find that, in certain conditions, a stable moving soliton can exist in high-dimensional lattices for the two-component BEC's, which is very different from the single-component BEC (where a moving soliton cannot be stabilized in high-dimensional lattices). On the other hand, the impurity can play a crucial role in causing important coherence-decoherence and localization-delocalization phase transitions.

DOI
10.1103/physreva.81.033607

Related papers

Impurity-induced localization of Bose-Einstein condensates in one-dimensional optical lattices

Jianjun Wang, Ai‐Xia Zhang, Ju-Kui Xue

The impurity-induced localization of two-component Bose-Einstein condensates loaded into deep one-dimensional optical lattices is studied both analytically and numerically. It is shown that, the analytical criteria for self-trapping and moving soliton/breather of the primary-component condensate are modified significantly by an admixture of an impurity component (the second component). The realization of the self-trapped state and the moving soliton/breather states of the primary-component becomes more easy with the minor admixture of the impurity-component, even if the two components are partly overlapped.

Chinese Physics B•Aug 1, 2011•5 citations

Self-trapping of Bose-Einstein condensates in optical lattices: The effect of the lattice dimension

Ju-Kui Xue, Ai‐Xia Zhang, Jie Liu

In the present paper, we analytically and numerically investigate the dynamics of Bose-Einstein condensates (BECs) loaded into deep optical lattices of one dimension (1D), 2D, and 3D. We focus on the self-trapped state and the effect of the lattice dimension. Under the tight-binding approximation, we obtain an analytical criterion for the self-trapped state of BEC using the time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of a BEC cloud is obtained accordingly and verified by directly solving a discrete Gross-Pitaevskii equation numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the optical lattices.

arXiv:0708.2128•Physical Review A•Jan 2, 2008•36 citations

Dynamical self-trapping of two-dimensional binary solitons in cross-combined linear and nonlinear optical lattices

K. K. Ismailov, Golam Ali Sekh, Mario Salerno

Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-Einstein condensates in cross-combined lattices, consisting of a one-dimensional (1D) linear optical lattice (LOL) in the x direction for the first component and a 1D nonlinear optical lattice (NOL) in the y direction for the second component, are analytically and numerically investigated. The existence and stability of 2D binary matter wave solitons in these settings are demonstrated both by variational analysis and by direct numerical integration of the coupled Gross-Pitaevskii equations. We find that in the absence of the NOL, binary solitons, stabilized by the action of the 1D LOL and by the attractive intercomponent interaction, can freely move in the y direction. In the presence of the NOL, we find, quite remarkably, the existence of threshold curves in the parameter space separating regions where solitons can move from regions where the solitons become dynamically self-trapped. The mechanism underlying the dynamical self-trapping phenomenon (DSTP) is qualitatively understood in terms of a dynamical barrier induced by the NOL, similar to the Peirls-Nabarro barrier of solitons in discrete lattices. DSTP is numerically demonstrated for binary solitons that are put in motion both by phase imprinting and by the action of external potentials applied in the y direction. In the latter case, we show that the trapping action of the NOL allows one to maintain a 2D binary soliton at rest in a nonequilibrium position of a parabolic trap or to prevent it from falling under the action of gravity. Possible applications of the results are also briefly discussed.

arXiv:2305.03438•Physical review. E•Nov 20, 2023•6 citations

Superfluid Fermi Gas in Optical Lattices: Self-Trapping, Stable, Moving Solitons and Breathers

Ju-Kui Xue, Ai‐Xia Zhang

We predict the existence of self-trapping, stable, moving solitons and breathers of Fermi wave packets along the Bose-Einstein condensation (BEC)-BCS crossover in one dimension (1D), 2D, and 3D optical lattices. The dynamical phase diagrams for self-trapping, solitons, and breathers of the Fermi matter waves along the BEC-BCS crossover are presented analytically and verified numerically by directly solving a discrete nonlinear Schrödinger equation. We find that the phase diagrams vary greatly along the BEC-BCS crossover; the dynamics of Fermi wave packet are different from that of Bose wave packet.

Physical Review Letters•Oct 28, 2008•55 citations

Localization and spin dynamics of spin-orbit-coupled Bose-Einstein condensates in deep optical lattices

Ai-Xia Zhang, Xiao-Wen Hu, Yan-Fang Jiang +4 more

We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.

Physical review. E•Dec 28, 2021•1 citation

Variational dynamics of Bose-Einstein condensates in deep optical lattices

Andrea Trombettoni, Augusto Smerzi

We study the dynamics of a Bose-Einstein condensate wavepacket trapped in an optical lattice. In the tight-binding limit, the system maps onto a discrete nonlinear Schrödinger equation. Using a collective coordinate approximation, we investigate different dynamical regimes: diffusive (in which the boson wavepacket spreads out), self-trapped (with a self-induced pinning), breathing (where the centre of mass of the wavepacket moves with an oscillating width), and solitonic (in which the wavepacket shape is exactly preserved during the dynamics).

Journal of Physics B Atomic Molecular and Optical Physics•Nov 23, 2001•27 citations
The impurity-induced self-trapping and stable moving soliton and breather of two-component Bose-Einstein condensates (BEC's) in deep DDD-dimensional optical lattices are discussed both analytically and numerically. Under the tight-binding approximation and within a time-dependent variational approach, analytical criteria for occurrences of a self-trapping, moving soliton and breather in the system are obtained. The analytical results are confirmed by direct numerical simulation. It is shown that the dynamics of the condensates can be modified significantly by a minor admixture of an impurity (the second component). The diffusion state of the single-component BEC will transit to the self-trapped state due to the minor admixture of an impurity, even if the two condensates are only with marginal spatial overlap. Furthermore, we find that, in certain conditions, a stable moving soliton can exist in high-dimensional lattices for the two-component BEC's, which is very different from the single-component BEC (where a moving soliton cannot be stabilized in high-dimensional lattices). On the other hand, the impurity can play a crucial role in causing important coherence-decoherence and localization-delocalization phase transitions.
The impurity-induced localization of two-component Bose-Einstein condensates loaded into deep one-dimensional optical lattices is studied both analytically and numerically. It is shown that, the analytical criteria for self-trapping and moving soliton/breather of the primary-component condensate are modified significantly by an admixture of an impurity component (the second component). The realization of the self-trapped state and the moving soliton/breather states of the primary-component becomes more easy with the minor admixture of the impurity-component, even if the two components are partly overlapped.
In the present paper, we analytically and numerically investigate the dynamics of Bose-Einstein condensates (BECs) loaded into deep optical lattices of one dimension (1D), 2D, and 3D. We focus on the self-trapped state and the effect of the lattice dimension. Under the tight-binding approximation, we obtain an analytical criterion for the self-trapped state of BEC using the time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of a BEC cloud is obtained accordingly and verified by directly solving a discrete Gross-Pitaevskii equation numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the optical lattices.
Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-Einstein condensates in cross-combined lattices, consisting of a one-dimensional (1D) linear optical lattice (LOL) in the x direction for the first component and a 1D nonlinear optical lattice (NOL) in the y direction for the second component, are analytically and numerically investigated. The existence and stability of 2D binary matter wave solitons in these settings are demonstrated both by variational analysis and by direct numerical integration of the coupled Gross-Pitaevskii equations. We find that in the absence of the NOL, binary solitons, stabilized by the action of the 1D LOL and by the attractive intercomponent interaction, can freely move in the y direction. In the presence of the NOL, we find, quite remarkably, the existence of threshold curves in the parameter space separating regions where solitons can move from regions where the solitons become dynamically self-trapped. The mechanism underlying the dynamical self-trapping phenomenon (DSTP) is qualitatively understood in terms of a dynamical barrier induced by the NOL, similar to the Peirls-Nabarro barrier of solitons in discrete lattices. DSTP is numerically demonstrated for binary solitons that are put in motion both by phase imprinting and by the action of external potentials applied in the y direction. In the latter case, we show that the trapping action of the NOL allows one to maintain a 2D binary soliton at rest in a nonequilibrium position of a parabolic trap or to prevent it from falling under the action of gravity. Possible applications of the results are also briefly discussed.
We predict the existence of self-trapping, stable, moving solitons and breathers of Fermi wave packets along the Bose-Einstein condensation (BEC)-BCS crossover in one dimension (1D), 2D, and 3D optical lattices. The dynamical phase diagrams for self-trapping, solitons, and breathers of the Fermi matter waves along the BEC-BCS crossover are presented analytically and verified numerically by directly solving a discrete nonlinear Schrödinger equation. We find that the phase diagrams vary greatly along the BEC-BCS crossover; the dynamics of Fermi wave packet are different from that of Bose wave packet.
We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.
We study the dynamics of a Bose-Einstein condensate wavepacket trapped in an optical lattice. In the tight-binding limit, the system maps onto a discrete nonlinear Schrödinger equation. Using a collective coordinate approximation, we investigate different dynamical regimes: diffusive (in which the boson wavepacket spreads out), self-trapped (with a self-induced pinning), breathing (where the centre of mass of the wavepacket moves with an oscillating width), and solitonic (in which the wavepacket shape is exactly preserved during the dynamics).