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Physica Scripta

Effects of residual nonlinearities on the modulational instability of three-component Bose–Einstein condensates

P. Mohanraj, R. Sivakumar

Published Jul 18, 2023• 2 citations
Publisher

Abstract

Abstract We study the modulation instability in a three-component Bose–Einstein condensate and the impact of higher-order interactions brought on by shape-dependent confinement. Using the modified Gross–Pitaevskii equation that accounts for the higher-order residual nonlinearity and the linear stability method, we analyze the dispersion relations and the gain spectrum for instability. In particular, we investigate the role of higher-order interactions over the MI in miscible and immiscible condensates. The observed MI spectrum shows a new regime for soliton generation in a ternary mixture of Bose–Einstein condensates. Our results show that the residual nonlinearity can effectively control the MI gain profile in both miscible and immiscible condensates. This allows one manipulate the MI in a ternary mixture of Bose–Einstein condensates to control the dynamics.

DOI
10.1088/1402-4896/ace854

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Abstract We study the modulation instability in a three-component Bose–Einstein condensate and the impact of higher-order interactions brought on by shape-dependent confinement. Using the modified Gross–Pitaevskii equation that accounts for the higher-order residual nonlinearity and the linear stability method, we analyze the dispersion relations and the gain spectrum for instability. In particular, we investigate the role of higher-order interactions over the MI in miscible and immiscible condensates. The observed MI spectrum shows a new regime for soliton generation in a ternary mixture of Bose–Einstein condensates. Our results show that the residual nonlinearity can effectively control the MI gain profile in both miscible and immiscible condensates. This allows one manipulate the MI in a ternary mixture of Bose–Einstein condensates to control the dynamics.
We investigate the effect of higher-order interactions induced by shape-dependent confinement in the modulational instability (MI) of a binary mixture of Bose-Einstein condensates. For this, we present and compute both analytically and numerically a system of coupled Gross-Pitaevskii equations with residual nonlinearity that rule the dynamics of the mixture. Using the linear stability approach, we obtain the instability criteria of the mixture and find that the MI can be excited in miscible condensates and altered in immiscible condensates due to the effect of residual nonlinearity. Direct numerical calculations are performed to support the analytical predictions, and a good agreement is found. The space-time evolution of the condensate density is displayed in both cases when the mixture is miscible and immiscible, showing the generation of bright solitons for modes predicted to be unstable.
We examine the instability characteristics in a three-body condensate and the effect of higher-order nonlinear effects caused by shape-dependent imprisonment and higher-order scattering coefficients such as S-wave scattering length and effective range for collisions. Using the linear stability technique, we study the spreading relations and gain profile of the adapted Gross–Pitaevskii equation with higher-order scattering coefficients and enduring nonlinearity. The role of higher-order interactions S-wave scattering length, residual nonlinearity, and effective range for collisions over the modulational instability in immiscible and miscible three-body Bose-Einstein condensates has been discussed in detail. Modulational instability (MI) can be excited in miscible condensates and changed in immiscible condensates because of residual nonlinearity, without taking into account higher-order nonlinearity and three-body condensates. However, the results of this work demonstrate that the influence of higher-order residual nonlinearity can cause the MI to change in both immiscible and immiscible condensates. The discovered MI spectrum reveals a new soliton production regime in three-body condensates. The results exhibit that higher-order scattering coefficient and remaining nonlinearity interplay can successfully switch the instability gain profile in miscible and immiscible condensates. This makes it possible to regulate the dynamics by varying the MI in a ternary combination of Bose-Einstein condensates. Received: 19 December 2023 | Revised: 13 June 2024 | Accepted: 23 September 2024 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement Data are available from the corresponding author upon reasonable request. Author Contribution Statement P. Mohanraj: Conceptualization, Methodology, Software, Writing – original draft. R. Sivakumar: Validation, Formal analysis, Investigation, Supervision. Jayaprakash Kaliyamurthy: Writing – review & editing, Visualization. V. Kamalakar: Writing – review & editing, Visualization. J. Gajendiran: Writing – review & editing, Visualization.
Abstract We demonstrate the existence of modulational instability (MI) in both trapped miscible and immiscible two component Bose–Einstein condensates. The study is addressed theoretically and numerically in the framework of one-dimensional coupled Gross–Pitaevskii equations incorporating intra- and interspecies cubic-quintic nonlinearities with higher-order ones. Using the time-dependent variational approach, we derive the new Euler-Langrange equations for the time evolution of the phase and amplitude of the modulational perturbation as well as the effective potential and the instability criteria of the system. We examine the effects of higher order nonlinearities on the instability dynamics of the condensates. We show that the modulational properties of the chosen wave numbers are significantly modified. Direct numerical simulations run by the split step Fourier method confirm the analytical predictions.
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 consider the modulational instability (MI) of Bose-Einstein condensate (BEC) described by a modified Gross-Pitaevskii (GP) equation with higher-order nonlinearity both analytically and numerically. A new explicit time-dependent criterion for exciting the MI is obtained. It is shown that the higher-order term can either suppress or enhance the MI, which is interesting for control of the system instability. Importantly, we predict that with the help of the higher-order nonlinearity, the MI can also take place in a BEC with repulsively contact interactions. The analytical results are confirmed by direct numerical simulations.
Beyond the mean-field theory, a new model of the Gross–Pitaevskii equation (GPE) that describes the dynamics of Bose–Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated.