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.
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.
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 paper studies the modulational instability (MI), both theoretically and numerically, of the helicoidal spin-orbit coupled Bose-Bose mixture. An expression of the MI growth rate is found through the linear stability analysis of continuous wave, followed by a comprehensive parametric study of the MI regions, emphasizing the effects of the spin-orbit coupling, the helicoidal gauge potential, and interatomic interactions. Direct numerical simulations concur with the analytical predictions. Under suitable balance between nonlinear and dispersive effects, trains of solitonlike objects are obtained, and their behaviors are very sensitive to parameter variations. Attention is particularly paid to the impact of the left- and right-handed helicoidal spin-orbit couplings on the appearance of matter waves that have the form soliton molecules in the Bose-Bose mixture. Additionally, for qualitative support of the obtained structures, the formation of a bright solitons train is also reported numerically using two neighboring solitons subjected to a fixed phase difference. Their behavior under the action of the helicoidal spin-orbit coupling is also debated, especially when left- and right-handed helicoidal couplings are interchanged.
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.
We present a comprehensive study of modulational instability (MI) in a binary Bose-Einstein condensate with spin-orbit coupling, confined to a deep optical lattice. The system is modeled by a set of discrete Gross-Pitaevskii equations. Using linear stability analysis, we derive the explicit MI conditions for the system, elucidating the critical and distinct roles played by spin-orbit coupling, inter-species nonlinearity, and intra-species nonlinearity. Our analysis, conducted for both unstaggered and staggered fundamental modes, reveals markedly different instability landscapes for these two configurations. The analytical predictions are confirmed by extensive numerical simulations of the full nonlinear dynamics, which vividly illustrate the spatiotemporal evolution of wave amplitudes, phase coherence, and energy localization during the instability process. The numerical results, obtained via a fourth-order Runge-Kutta method, show excellent agreement with the linear stability theory and provide a complete picture of the MI-induced pattern formation.
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.
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.