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Chinese Physics B

Accelerate Bose–Einstein condensate by interaction*

Jieli Qin

Published Oct 17, 2019• 3 citations
Publisher

Abstract

In recent years, accelerating waves have attracted great research interests both due to their unique properties and tempting applications. Here we investigate the effect of the inter-particle interaction on accelerating of Bose–Einstein condensate (BEC). We show that spatially homogeneous interactions will have no accelerating effect on BEC regardless of the interaction form (contact, dipole–dipole, or any others). But spatially inhomogeneous interactions may lead to an accelerating motion of the condensate. As an example, the accelerating dynamic of BEC under a spatially linear modulated contact interaction is studied in detail. It is found that such an interaction will accelerate the condensate with a time varying acceleration. Furthermore, an interaction engineering scheme to achieve constantly accelerating BEC is proposed and studied numerically. Numerical results suggest that this engineering scheme can also suppress profile changing of the condensate during its evolution, thus realize an accelerating profile-keeping matter wave packet. Our analysis also applies to optical waves with Kerr nonlinearity.

DOI
10.1088/1674-1056/ab4e8a

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In recent years, accelerating waves have attracted great research interests both due to their unique properties and tempting applications. Here we investigate the effect of the inter-particle interaction on accelerating of Bose–Einstein condensate (BEC). We show that spatially homogeneous interactions will have no accelerating effect on BEC regardless of the interaction form (contact, dipole–dipole, or any others). But spatially inhomogeneous interactions may lead to an accelerating motion of the condensate. As an example, the accelerating dynamic of BEC under a spatially linear modulated contact interaction is studied in detail. It is found that such an interaction will accelerate the condensate with a time varying acceleration. Furthermore, an interaction engineering scheme to achieve constantly accelerating BEC is proposed and studied numerically. Numerical results suggest that this engineering scheme can also suppress profile changing of the condensate during its evolution, thus realize an accelerating profile-keeping matter wave packet. Our analysis also applies to optical waves with Kerr nonlinearity.
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.
The dynamical behaviors of Bose-Einstein condensates (BECs) depend largely on the nonlinear interactions between BEC atoms. The advancement of experimental techniques enables the rapid and effective modulation of the nonlinear interactions through Feshbach resonance technique. At present, both the nonlinear time-varying interaction and nonlinear space-varying interaction have been realized, respectively, thus making it possible to simultaneously modulate the nonlinear interactions in time and space through the combination of techniques. It will provide more options to conduct various studies by manipulating the BECs. Therefore, BECs with time- and space-varying interactions must possess unique advantages in studying BEC dynamics. This paper focuses on the chaotic spatiotemporal dynamics of BECs with nonlinear time- and space-varying interactions in moving optical lattices. When the intensities of the moving optical lattice potential and the modulation of the nonlinear interaction are small, the system satisfies the perturbation conditions and the Melnikov-function method is used in the theoretical analyses to obtain the Melnikov spatiotemporal chaotic criterion of the system. When the system does not meet the perturbation conditions, numerical simulations show that for a BEC with an attractive atomic interaction, increasing the modulation intensity of the nonlinear interaction can deepen the degree of spatiotemporal chaos in the system. In certain parameter regions, the modulation frequency of the nonlinear interaction can have a significant influence on the spatiotemporal dynamical behavior of the system. Further numerical research results show that larger chemical potentials can suppress the spatiotemporal chaos not only in the attractive BEC but also in the repulsive BEC. Based on the above research results, spatiotemporal chaos in BEC system can be avoided or triggered off in experiments as needed.
We predict that classes of coherent matter waves can self-accelerate without the presence of an external potential. Such Bose-Einstein condensates can follow arbitrary power-law trajectories and can also take the form of diffraction-free Airy waves. We also show that suitably engineered radially symmetric matter waves can abruptly autofocus in space and time. We suggest different schemes for the preparation of the condensate using laser beams to imprint an amplitude or a phase pattern onto the matter wave. Direct and Fourier space generation of such waves is discussed using continuous and binary masks as well as magnetic mirrors and lenses. We study the effect of interactions and find that independently of the type and strength of the nonlinearity, the dynamics are associated with the generation of accelerating matter waves. In the case of strong attractive interactions, the acceleration is increased while the radiation reorganizes itself in the form of soliton(s).
With the maturation of experimental laser cooling and atom trapping techniques, various types of atomic optical devices developed by using cold atoms as media have been born in recent years, which play an important role in the field of atomic physics. In atomic optics, Bose-Einstein condensation (BEC) has been one of the hot topics in the study of scientists. It describes the phenomenon that bosons are concentrated in the lowest energy quantum state at extremely low temperatures. In general, atomic BEC can be expressed in the form of quantum wave packet. On the basis of previous studies, two kinds of motion behaviors of Bose-Einstein condensates passing through Gaussian laser field are investigated in this paper, namely the motion phenomena of atoms under the acceleration field and the S-wave scattering collision between atoms. The atomic motion equation is derived by establishing the theoretical model, and then the numerical simulation is carried out by MATLAB program. The results show that the acceleration field only affects the velocity of the wave packet. The attractive interatomic collision will cause the collapse of the wave packet. On the contrary, the repulsion will accelerate the diffusion of the wave packet. These results will provide more theoretical and feasible schemes for studying the coherent manipulation of atoms and laser in the future.
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.
We study the impact of collisionally inhomogeneous binary and three body interaction on Bose-Einstein condensates (BECs) of a dilute gas in a bichromatic optical lattice. We observe that the localized matter wave density which decreases after the introduction of repulsive spatially inhomogeneous binary interaction can be sustained by the addition of constant attractive binary strength in equal amounts. If the balance between repulsive spatially inhomogeneous binary interaction and constant attractive interaction is disturbed, the condensates collapse. Reversal of sign of interaction ensures the longevity of BECs. Any imbalance between attractive spatially inhomogeneous interaction and constant repulsive interaction either results in the collapse of BECs or in the occupation of the condensates at multiple sites on either sides. The introduction of a weak three body interaction in phase with the binary interaction increases the extent of instability of BECs. Reversing the sign of spatially inhomogeneous and constant interaction enhances the stability of BECs.