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. E

Modulational instability of Bose-Einstein condensates with helicoidal spin-orbit coupling

X. X. Li, Rui-Jin Cheng, Ai‐Xia Zhang, Ju-Kui Xue

Published Sep 26, 2019• 25 citations
Publisher

Abstract

We theoretically study the modulation instability (MI) of the two-component helicoidal spin-orbit coupled Bose-Einstein condensates (BECs). The effects of spin-orbit coupling, the helicoidal gauge potential, and atomic interactions on MI are investigated. The results indicate that the presence of the helicoidal gauge potential breaks the symmetric properties of MI, strongly modifies the distribution of the MI region and the MI gain in parameters space, and the MI can be excited even when the miscibility condition for the atomic interactions is satisfied. Furthermore, the effect of the helicoidal gauge potential on MI is strongly coupled with the intra and intercomponent atomic interactions. Particularly, with the increase of the helical gauge potential, the MI gain increases for the repulsive atomic interaction case, however, the MI gain decreases for the attractive atomic interaction case. The direct numerical simulations are performed to support the analytical predictions, and a good agreement is found. Our results provide a potential way to manipulate the MI in BECs with helicoidal gauge potential.

DOI
10.1103/physreve.100.032220

Related papers

Interplay between spin-orbit couplings and residual interatomic interactions in the modulational instability of two-component Bose-Einstein condensates

Conrad Bertrand Tabi, Étienne Wamba, Emmanual Nare +1 more

The nonlinear dynamics induced by the modulation instability (MI) of a binary mixture in an atomic Bose-Einstein condensate (BEC) is investigated theoretically under the joint effects of higher-order residual nonlinearities and helicoidal spin-orbit (SO) coupling in a regime of unbalanced chemical potential. The analysis relies on a system of modified coupled Gross-Pitaevskii equations on which the linear stability analysis of plane-wave solutions is performed, from which an expression of the MI gain is obtained. A parametric analysis of regions of instability is carried out, where effects originating from the higher-order interactions and the helicoidal spin-orbit coupling are confronted under different combinations of the signs of the intra- and intercomponent interaction strengths. Direct numerical calculations on the generic model support our analytical predictions and show that the higher-order interspecies interaction and the SO coupling can balance each other suitably for stability to take place. Mainly, it is found that the residual nonlinearity preserves and reinforces the stability of miscible pairs of condensates with SO coupling. Additionally, when a miscible binary mixture of condensates with SO coupling is modulationally unstable, the presence of residual nonlinearity may help soften such instability. Our results finally suggest that MI-induced formation of stable solitons in mixtures of BECs with two-body attraction may be preserved by the residual nonlinearity even though the latter enhances the instability.

Physical review. E•Apr 17, 2023•15 citations

Stability control in a helicoidal spin–orbit-coupled open Bose–Bose mixture

Chao Kong, Bin Yin, Jiaxin Wu +4 more

Abstract In this article, the modulation instability (MI) of open Bose–Bose mixtures with helicoidal spin–orbit coupling (SOC) was studied. Unlike previous spin–orbit (SO)-coupled Bose–Einstein condensate system with helicoidal gauge potential, the purpose of this article to study the input of the helicoidal SOC in the emergence of MI in open Bose–Bose mixtures by taking into account the Lee–Huang–Yang corrections to the coupled Gross–Pitaevskii equations. We present the detailed analyses of system parameters on the characteristics of MI and analytically conclude the parameter conditions for MI occurrence. Our results provide a potential way to manipulate the MI in the helicoidal SO-coupled open Bose–Bose mixtures.

Open Physics•Jan 1, 2023•1 citation

Modulation instability in quasi-two-dimensional spin–orbit coupled Bose–Einstein condensates

S. Bhuvaneswari, K. Nithyanandan, Paulsamy Muruganandam +1 more

We theoretically investigate the dynamics of modulation instability (MI) in two-dimensional spin–orbit coupled Bose–Einstein condensates (BECs) with Rabi coupling. The analysis is performed for equal densities of pseudo-spin components. Different combination of the signs of intra- and intercomponent interaction strengths are considered, with a particular emphasis on repulsive interactions. We observe that the unstable modulation builds from originally miscible condensates, depending on the combination of the signs of the intra- and intercomponent interaction strengths. The repulsive intra- and intercomponent interactions admit instability and the MI immiscibility condition is no longer significant. The influence of interaction parameters such as spin–orbit and Rabi coupling on MI are also investigated. The spin–orbit coupling (SOC) inevitably contributes to instability regardless of the nature of the interaction. In the case of attractive interaction, SOC manifests in enhancing the MI. Thus, a comprehensive study of MI in two-dimensional spin–orbit coupled BECs of pseudo-spin components is presented.

arXiv:1606.04426•Journal of Physics B Atomic Molecular and Optical Physics•Nov 28, 2016•30 citations

Modulation instability in helicoidal spin-orbit coupled open Bose-Einstein condensates

Phelo Otlaadisa, Conrad Bertrand Tabi, Timoléon Crépin Kofané

We introduce a vector form of the cubic complex Ginzburg-Landau equation describing the dynamics of dissipative solitons in the two-component helicoidal spin-orbit coupled open Bose-Einstein condensates (BECs), where the addition of dissipative interactions is done through coupled rate equations. Furthermore, the standard linear stability analysis is used to investigate theoretically the stability of continuous-wave (cw) solutions and to obtain an expression for the modulational instability gain spectrum. Using direct simulations of the Fourier space, we numerically investigate the dynamics of the modulational instability in the presence of helicoidal spin-orbit coupling. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold for amplitude perturbations.

Physical review. E•May 5, 2021•47 citations

Influence of helicoidal spin-orbit coupling and Rabi coupling in dynamics of 2D Bose-Einstein Condensates

Sai Satyaprakash Biswal, S. Saravana Veni

This study explores the dynamics of Bose-Einstein condensates (BECs) with helicoidal spin-orbit coupling (SOC) and Rabi coupling, confined under a two-dimensional harmonic potential. The relationship between helicoidal SOC, non-linear interactions along with Rabi coupling and their impact on the stability and non linear trapped modes of the condensate is analyzed using a coupled Gross-Pitaevski (GP) framework. A linearized GP equation is used to investigate modulation instability (MI), demonstrating the impact of strong coupling effects and anisotropic confinement on the instability dynamics. It has been shown that the modulation instability in the condensate is predominantly governed by the competition between the attractive and repulsive mean-field interactions. Additionally, stability regimes are altered by the harmonic confinement, enhancing their susceptibility to SOC-induced asymmetry and intra- and intercomponent interactions. These results shed light on the possibility for unique quantum phases and emergent characteristics of helicoidal SOC-driven condensates.

arXiv:2605.26834•May 26, 2026•0 citations

Solitary matter wave in spin-orbit-coupled Bose-Einstein condensates with helicoidal gauge potential

X. X. Li, Rui-Jin Cheng, Ji-Li Ma +2 more

We analytically and numerically study the different types of solitary wave in the two-component helicoidal spin-orbit coupled Bose-Einstein condensates (BECs). Adopting the multiscale perturbation method, we derive the analytical bright and dark solitary wave solutions of the system, and the stationary and moving bright (dark) solitary waves are obtained. The effects of spin-orbit coupling, the helicoidal gauge potential, the momentum, the Zeeman splitting, and the atomic interactions on the solitary wave types are discussed, and it is found that the coupling of these physical parameters can manipulate different types of solitary waves in the system. The results indicate that the helicoidal gauge potential breaks the symmetric properties of the energy band of the system and adjusts the energy band structure, thus further effecting the solitary wave properties, i.e., stationary or moving solitary wave, bright, or dark solitary wave. Correspondingly, the analytical predictions for exciting stationary or moving bright (dark) solitary wave in parameter space are obtained. In particular, the helicoidal gauge potential changes the solitary wave types drastically for the weak spin-orbit coupling, i.e., in the absence of the helicoidal gauge potential, only dark (bright) solitary wave solutions exist in the system with repulsive (attractive) atomic interaction; however, in the presence of the helicoidal gauge potential, both dark and bright solitary waves can exist in the system regardless of whether the atomic interaction is repulsive or attractive. In addition, we investigate the stability of solitary waves and obtain the stability regions of different types of solitary waves by applying the linear stability analysis. The dynamic evolution results of the solitary waves by the direct numerical simulation not only validate the linear stability analysis but also confirm the analytical prediction of the solitary waves. Finally, the collision effects between solitary waves are also presented by the numerical simulation. It is shown that the interactions between solitary waves in the system have both elastic and inelastic collisions, which are closely related to the position of solitary wave states in the linear energy band. Our results provide a potential way to adjust the types of solitary waves in BECs with helicoidal gauge potential.

Physical review. E•Sep 21, 2021•13 citations
We theoretically study the modulation instability (MI) of the two-component helicoidal spin-orbit coupled Bose-Einstein condensates (BECs). The effects of spin-orbit coupling, the helicoidal gauge potential, and atomic interactions on MI are investigated. The results indicate that the presence of the helicoidal gauge potential breaks the symmetric properties of MI, strongly modifies the distribution of the MI region and the MI gain in parameters space, and the MI can be excited even when the miscibility condition for the atomic interactions is satisfied. Furthermore, the effect of the helicoidal gauge potential on MI is strongly coupled with the intra and intercomponent atomic interactions. Particularly, with the increase of the helical gauge potential, the MI gain increases for the repulsive atomic interaction case, however, the MI gain decreases for the attractive atomic interaction case. The direct numerical simulations are performed to support the analytical predictions, and a good agreement is found. Our results provide a potential way to manipulate the MI in BECs with helicoidal gauge potential.
The nonlinear dynamics induced by the modulation instability (MI) of a binary mixture in an atomic Bose-Einstein condensate (BEC) is investigated theoretically under the joint effects of higher-order residual nonlinearities and helicoidal spin-orbit (SO) coupling in a regime of unbalanced chemical potential. The analysis relies on a system of modified coupled Gross-Pitaevskii equations on which the linear stability analysis of plane-wave solutions is performed, from which an expression of the MI gain is obtained. A parametric analysis of regions of instability is carried out, where effects originating from the higher-order interactions and the helicoidal spin-orbit coupling are confronted under different combinations of the signs of the intra- and intercomponent interaction strengths. Direct numerical calculations on the generic model support our analytical predictions and show that the higher-order interspecies interaction and the SO coupling can balance each other suitably for stability to take place. Mainly, it is found that the residual nonlinearity preserves and reinforces the stability of miscible pairs of condensates with SO coupling. Additionally, when a miscible binary mixture of condensates with SO coupling is modulationally unstable, the presence of residual nonlinearity may help soften such instability. Our results finally suggest that MI-induced formation of stable solitons in mixtures of BECs with two-body attraction may be preserved by the residual nonlinearity even though the latter enhances the instability.
Abstract In this article, the modulation instability (MI) of open Bose–Bose mixtures with helicoidal spin–orbit coupling (SOC) was studied. Unlike previous spin–orbit (SO)-coupled Bose–Einstein condensate system with helicoidal gauge potential, the purpose of this article to study the input of the helicoidal SOC in the emergence of MI in open Bose–Bose mixtures by taking into account the Lee–Huang–Yang corrections to the coupled Gross–Pitaevskii equations. We present the detailed analyses of system parameters on the characteristics of MI and analytically conclude the parameter conditions for MI occurrence. Our results provide a potential way to manipulate the MI in the helicoidal SO-coupled open Bose–Bose mixtures.
We theoretically investigate the dynamics of modulation instability (MI) in two-dimensional spin–orbit coupled Bose–Einstein condensates (BECs) with Rabi coupling. The analysis is performed for equal densities of pseudo-spin components. Different combination of the signs of intra- and intercomponent interaction strengths are considered, with a particular emphasis on repulsive interactions. We observe that the unstable modulation builds from originally miscible condensates, depending on the combination of the signs of the intra- and intercomponent interaction strengths. The repulsive intra- and intercomponent interactions admit instability and the MI immiscibility condition is no longer significant. The influence of interaction parameters such as spin–orbit and Rabi coupling on MI are also investigated. The spin–orbit coupling (SOC) inevitably contributes to instability regardless of the nature of the interaction. In the case of attractive interaction, SOC manifests in enhancing the MI. Thus, a comprehensive study of MI in two-dimensional spin–orbit coupled BECs of pseudo-spin components is presented.
We introduce a vector form of the cubic complex Ginzburg-Landau equation describing the dynamics of dissipative solitons in the two-component helicoidal spin-orbit coupled open Bose-Einstein condensates (BECs), where the addition of dissipative interactions is done through coupled rate equations. Furthermore, the standard linear stability analysis is used to investigate theoretically the stability of continuous-wave (cw) solutions and to obtain an expression for the modulational instability gain spectrum. Using direct simulations of the Fourier space, we numerically investigate the dynamics of the modulational instability in the presence of helicoidal spin-orbit coupling. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold for amplitude perturbations.
This study explores the dynamics of Bose-Einstein condensates (BECs) with helicoidal spin-orbit coupling (SOC) and Rabi coupling, confined under a two-dimensional harmonic potential. The relationship between helicoidal SOC, non-linear interactions along with Rabi coupling and their impact on the stability and non linear trapped modes of the condensate is analyzed using a coupled Gross-Pitaevski (GP) framework. A linearized GP equation is used to investigate modulation instability (MI), demonstrating the impact of strong coupling effects and anisotropic confinement on the instability dynamics. It has been shown that the modulation instability in the condensate is predominantly governed by the competition between the attractive and repulsive mean-field interactions. Additionally, stability regimes are altered by the harmonic confinement, enhancing their susceptibility to SOC-induced asymmetry and intra- and intercomponent interactions. These results shed light on the possibility for unique quantum phases and emergent characteristics of helicoidal SOC-driven condensates.
We analytically and numerically study the different types of solitary wave in the two-component helicoidal spin-orbit coupled Bose-Einstein condensates (BECs). Adopting the multiscale perturbation method, we derive the analytical bright and dark solitary wave solutions of the system, and the stationary and moving bright (dark) solitary waves are obtained. The effects of spin-orbit coupling, the helicoidal gauge potential, the momentum, the Zeeman splitting, and the atomic interactions on the solitary wave types are discussed, and it is found that the coupling of these physical parameters can manipulate different types of solitary waves in the system. The results indicate that the helicoidal gauge potential breaks the symmetric properties of the energy band of the system and adjusts the energy band structure, thus further effecting the solitary wave properties, i.e., stationary or moving solitary wave, bright, or dark solitary wave. Correspondingly, the analytical predictions for exciting stationary or moving bright (dark) solitary wave in parameter space are obtained. In particular, the helicoidal gauge potential changes the solitary wave types drastically for the weak spin-orbit coupling, i.e., in the absence of the helicoidal gauge potential, only dark (bright) solitary wave solutions exist in the system with repulsive (attractive) atomic interaction; however, in the presence of the helicoidal gauge potential, both dark and bright solitary waves can exist in the system regardless of whether the atomic interaction is repulsive or attractive. In addition, we investigate the stability of solitary waves and obtain the stability regions of different types of solitary waves by applying the linear stability analysis. The dynamic evolution results of the solitary waves by the direct numerical simulation not only validate the linear stability analysis but also confirm the analytical prediction of the solitary waves. Finally, the collision effects between solitary waves are also presented by the numerical simulation. It is shown that the interactions between solitary waves in the system have both elastic and inelastic collisions, which are closely related to the position of solitary wave states in the linear energy band. Our results provide a potential way to adjust the types of solitary waves in BECs with helicoidal gauge potential.