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Physica Scripta

Modulational instability for a cubic-quintic model of coupled Gross–Pitaevskii equations with residual nonlinearities

Maïk Delon Mboumba, Marius Romuald Kamsap, A. B. Moubissi, Thierry Blanchard Ekogo, Timoléon Crépin Kofané

Published Nov 6, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ad8f77

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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.
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.
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 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.
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 investigate the modulational instability (MI) of trapped Bose–Einstein condensates with three-body and higher-order interactions employing both semi-analytical and numerical methods. Using the time-dependent variational approach, we derive variational equations for the time evolution of the amplitude, phase of modulational perturbation, and effective potential of the system. By means of an effective potential, we retrieve the corresponding MI condition of the dynamical system under consideration. The interplay between three-body interaction and higher-order interaction is discussed in detail. The semi-analytical predictions are confirmed through numerical simulations.
We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a modified Gross-Pitaevskii equation with higher-order nonlinearity and external potentials generated by magnetic and optical fields. Using the time-dependent variational approach, we derive the ordinary differential equations for the time evolution of the amplitude and phase of modulational perturbation. Through an effective potential, we obtain the modulational instability condition of BECs and discuss the effect of the higher-order interaction in the dynamics of the condensates in presence of optical potential. We perform direct numerical simulations to support our analytical results, and good agreement is found.