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International Journal of Modern Physics B

Stability of binary condensates with spatial modulations of quintic nonlinearities in optical lattices

Maïk Delon Mboumba, A. B. Moubissi, Thierry Blanchard Ekogo, D. Belobo Belobo, G. H. Ben-Bolie, Timoléon Crépin Kofané

Published Oct 14, 2014• 8 citations
Publisher

Abstract

The stability and collective excitations of binary Bose–Einstein condensates with cubic and quintic nonlinearities in variable anharmonic optical lattices are investigated. By using the variational approach, the influences of the quintic nonlinearities and the shape of the external potential on the stability are discussed in details. It is found that the quintic intraspecies and interspecies interatomic interactions profoundly affect the stability criterion and collective excitations of the system. The shape dependent potential form that characterizes the optical lattice deeply alters the stability regions. Direct numerical simulations of the mean-field coupled Gross–Pitaevskii equation describing the system agree well with the analytical predictions.

DOI
10.1142/s0217979215500083

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The stability and collective excitations of binary Bose–Einstein condensates with cubic and quintic nonlinearities in variable anharmonic optical lattices are investigated. By using the variational approach, the influences of the quintic nonlinearities and the shape of the external potential on the stability are discussed in details. It is found that the quintic intraspecies and interspecies interatomic interactions profoundly affect the stability criterion and collective excitations of the system. The shape dependent potential form that characterizes the optical lattice deeply alters the stability regions. Direct numerical simulations of the mean-field coupled Gross–Pitaevskii equation describing the system agree well with the analytical predictions.
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We study theoretically and numerically the dynamical behavior of two-component condensates with two- and three-body interactions in variable shape optical lattices and external feeding. By means of the variational approach, the evolution of the condensate amplitudes, widths and number of particles are investigated. The stability of stationary two-component solitons are derived through the Vakhitov–Kolokolov criterion which depends on the cubic and quintic nonlinearities. Direct numerical results of the two coupled Gross–Piteavskii equations (GPEs) which describe the dynamics of the two-component condensates are found to be in good agreement with the analytical predictions.
We investigate the profiles and stability of the localized nonlinear matter waves in a Bose–Einstein condensate with spatially inhomogeneous two- and three-body interactions in various external potentials both analytically and numerically. Several families of localized stationary solutions of the one-dimensional mean-field Gross–Pitaevskii equation with cubic–quintic nonlinearities are obtained by similarity transformation. It is shown that the whole Bose–Einstein condensate can have an infinite number of localized nonlinear matter waves determined by certain non-negative integers. The linear and dynamical stabilities of the localized stationary solutions are studied numerically, and some stable localized nonlinear matter waves are found. We demonstrate that the attractive inhomogeneous two- and three-body interactions support linearly and dynamically stable localized nonlinear matter waves, but attractive two-body interaction along with repulsive three-body interaction destroys the linear stability. Moreover, an anharmonic potential is proposed to stabilize the localized nonlinear matter waves in the Bose–Einstein condensate with spatially inhomogeneous interactions.
Solitons in one-dimensional (1D) Bose-Einstein condensates with attractive interaction in variable anharmonic periodic potentials are presented. These variable periodic potentials allow us to consider a variety of potential shapes between the two special limits of the Kronig-Penney model and the inverse Kronig-Penney model, with the sinusoidal optical lattice as an intermediate case. The Gross-Pitaevskii equation in (1D) is taken as a model [53]. We have derived the stability conditions for BECs in variable anharmonic periodic potentials using the Vakhitov-Kolokolov criterion. We have found that the stability condition for solitons depends significantly on the shape parameter. In particular, depending on the values of the shape parameter, one and three localized states for the 1D case, respectively, have been found. We have shown that some of these localized states are stable or unstable. The stability conditions obtained are an extension of the existing results to: (1) the more general class of external potential, and (2) the Vakhitov-Kolokolov criterion has been generalized in the case of an external potential of arbitrary shape. A fully numerical simulation of the 1D Gross-Pitaevskii equation finally tests the results of the variational approximation. A good agreement between both the methods is observed.
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.
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.