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Acta Physica Sinica

Surface gap solitons and their stabilities in quasi-1D Bose-Einstein condensate with three-body interactions

Qingqing Wang, Yushan Zhou, Jing Wang, Xiaobei Fan, Kaihua Shao, Yuexing Zhao, Song Yan, Yu-Ren Shi

Published Jan 1, 2023• 0 citations
Publisher

Abstract

The dynamical stability properties of surface gap solitons in quasi-one-dimensional Bose-Einstein condensate loaded in the interface between uniform media and a semi-infifinite Jacobian elliptic sine potential with three-body interactions are investigated numerically. Under the mean-fifield approximation, the dynamical behaviors can be well-described by the nonlinear cubic-quintic Gross-Pitaevskii equation. Firstly, many kinds of surface gap solitons, including the surface bright solitons, surface kink solitons and surface bubble solitons, are obtained numerically by the Newton-conjugate gradient method. The surface bright solitons can be excited in the gap only for the case that the chemical potential is negative and their power is beyond a threshold value. All of them are not bifurcated from the Bloch band. A class of surface solitons with new structures, named the surface dark solitons, can be formed when the three-body interactions are taken into account. The surface dark solitons can exist not only in gap but also in band. The numerical results indicate that the amplitude of the surface gap solitons decreases as the three-body interaction strength increases. Both linear stability analysis and nonlinear dynamical evolution methods are applied to investigate the stability properties of surface gap solitons. For surface bright solitons in the semi-infinite gap, there is a critical value when the chemical potential is given. The surface bright solitons become linearly stable as the three-body interaction exceeds the critical value, or they are linearly unstable. Therefore, the three-body interaction strength plays an important role on the stability of surface gap solitons. One can change the dynamical behaviors of surface gap solitons by adjusting the three-body interaction strength in experiments. Numerical results also show that both stable and unstable surface kink solitons exist. However, all the surface bubble solitons are unstable.

DOI
10.7498/aps.72.20222195

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The dynamical stability properties of surface gap solitons in quasi-one-dimensional Bose-Einstein condensate loaded in the interface between uniform media and a semi-infifinite Jacobian elliptic sine potential with three-body interactions are investigated numerically. Under the mean-fifield approximation, the dynamical behaviors can be well-described by the nonlinear cubic-quintic Gross-Pitaevskii equation. Firstly, many kinds of surface gap solitons, including the surface bright solitons, surface kink solitons and surface bubble solitons, are obtained numerically by the Newton-conjugate gradient method. The surface bright solitons can be excited in the gap only for the case that the chemical potential is negative and their power is beyond a threshold value. All of them are not bifurcated from the Bloch band. A class of surface solitons with new structures, named the surface dark solitons, can be formed when the three-body interactions are taken into account. The surface dark solitons can exist not only in gap but also in band. The numerical results indicate that the amplitude of the surface gap solitons decreases as the three-body interaction strength increases. Both linear stability analysis and nonlinear dynamical evolution methods are applied to investigate the stability properties of surface gap solitons. For surface bright solitons in the semi-infinite gap, there is a critical value when the chemical potential is given. The surface bright solitons become linearly stable as the three-body interaction exceeds the critical value, or they are linearly unstable. Therefore, the three-body interaction strength plays an important role on the stability of surface gap solitons. One can change the dynamical behaviors of surface gap solitons by adjusting the three-body interaction strength in experiments. Numerical results also show that both stable and unstable surface kink solitons exist. However, all the surface bubble solitons are unstable.
The stability properties of dark solitons in quasi-one-dimensional Bose-Einstein condensate (BEC) loaded in a Jacobian elliptic sine potential with three-body interactions are investigated theoretically. The solitons are obtained by the Newton-Conjugate Gradient method. A stationary cubic-quintic nonlinear Schrödinger equation is derived to describe the profiles of solitons via the multi-scale technique. It is found that the three-body interaction has distinct effect on the stability properties of solitons. Especially, such a nonlinear system supports the so-called dark solitons (kink or bubble), which can be excited not only in the gap, but also in the band. The bubbles are always linearly and dynamically unstable, and they cannot be excited if the three-body interaction is absent. Both stable and unstable kinks, depending on the physical parameters, can be excited in the BEC system.
Abstract The existence and stability of gap solitons in a quasi-one-dimensional Bose–Einstein condensate with three-body interactions loaded in a PT-symmetric potential are investigated numerically. Under the mean-field approximation, the dynamical behaviors of the system are described by a cubic-quintic Gross–Pitaevskii equation. Firstly, we obtained the band-gap structures via linearizing the GPE. The PT-symmetric of the system will be broken if the magnitude of the imaginary part of the external potential exceeds a critical value. Secondly, various of gap solitons were found by the Newton-Conjugate-Gradient method. Finally, the stability properties of gap solitons were investigated through the linear stability analysis and the direct long-time nonlinear dynamical evolution. The results indicated that the stability of on-site and off-site solitons was remarkably influenced by three-body interactions. There exists unstable on-site gap solitons when the PT-symmetric potential is taken into account. Additionally, the magnitude of the imaginary part of the potential also affects the profile and stability of the gap solitons. When it increases, the symmetry of the solitons will be broken.
By developing a multiple-scale method, we study analytically the dynamics of the soliton inside the semi-infinite band gap (SIBG) of quasi-one-dimensional Bose–Einstein condensates trapped in an optical lattice. In the linear case, a stable condition of soliton formation is obtained. For a weak nonlinearity, whether there occurs a spatially propagating or localized gap soliton is determined by the lattice depth. Meanwhile, we predict the existence of the dark (bright) gap solitons for the repulsive (attractive) interactions in the SIBG, different from that of the gap solitons in other energy gaps. And the collision of two dark (or bright) solitons is nearly elastic under a safe range of atomic numbers. An experimental protocol is further designed for observing these phenomena.
We investigate the properties of modulational instability in the Salerno equation in quasi-one dimension in Bose-Einstein condensate (BEC). We analyzed the regions of modulational instability of nonlinear plane waves and determine the conditions of its existence in BEC. The existence and stability of strongly localized modes in discrete media is investigated with the framework of the Salerno model by using a linear analysis method. The regions of stability and instability are determined. Also the existence of localized modes for different values of parameters is shown numerically by homoclinic orbits intersection method. The response of Bose–Einstein condensates is studied with strong dipole–dipole atomic interactions to periodically varying perturbation. The dynamics is governed by the Gross–Pitaevskii equation with an additional nonlinear term, corresponding to nonlocal dipolar interactions. A mathematical model, based on the variational approximation, has been developed and applied to study parametric excitation of the condensates due to coefficient of nonlocal nonlinearity varying periodically. The model predicts the waveform of solitons in dipolar condensates and describes their small amplitude dynamics quite accurately. Theoretical predictions are verified by numerical simulations of the nonlocal Gross–Pitaevskii equation and a good agreement between them is found. The results can lead to better understanding of the properties of ultra-cold quantum gases, such as 52Cr, 164Dy and 168Er, where the long-range dipolar atomic interactions dominate the usual contact interactions. Dynamics of a matter wave soliton bouncing on the reflecting surface (atomic mirror) under the effect of gravity has been studied by analytical and numerical means. The iv analytical description is based on the variational approach. Resonant oscillations of the soliton's center of mass and width, induced by appropriate modulation of the atomic scattering length and the slope of the linear potential are analyzed. In numerical experiments, we observe the Fermi type acceleration of the soliton when the vertical position of the reflecting surface is periodically varied in time. Analytical predictions are compared with the results of numerical simulations of the Gross-Pitaevskii equation and a qualitative agreement between them is found.
We consider the dynamics of dark matter wave solitons moving through non-uniform cigar-shaped Bose–Einstein condensates described by the mean field Gross–Pitaevskii equation with generalized nonlinearities, in the case when the condition for the modulation stability of the Bose–Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is derived for nonlinearities which are arbitrary functions of the density, while specific results are discussed for the physically relevant case of a cubic–quintic nonlinearity modelling two- and three-body interactions, respectively. Opposite to the usual (cubic) Gross–Pitaevskii equation for which the dark soliton effective mass is known to be constant (equal to 2), in the presence of a cubic–quintic nonlinearity we find that the effective mass depends on the product of the initial density background and the ratio between the coefficient of quintic and cubic nonlinearities, this leading to the interesting possibility of measuring three-body interactions directly from the dark soliton dynamics. A comparison between analytical results and direct numerical simulations of the cubic–quintic Gross–Pitaevskii equation shows good agreement between them which confirms the validity of our approach.
The existence and stability of solitons in Bose-Einstein condensates with attractive interatomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic form. We find a one-parameter family of stable 3D solitons in a certain interval of values of their norm, provided that the strength of the potential exceeds a threshold value. The minimum number of 7Li^{7}\mathrm{Li}7Li atoms in the stable solitons is 60, and the energy of the soliton at the stability threshold is $\ensuremath{\approx}6$ recoil energies in the lattice. The respective energy versus norm diagram features two cuspidal points, resulting in a typical swallowtail pattern, which is a generic feature of 3D solitons supported by quasi-two-dimensional or fully dimensional lattice potentials.