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1.
张涛  杨战营  赵立臣  岳瑞宏 《中国物理 B》2010,19(7):70502-070502
The exact solitonic solutions of the one-dimensional nonlinear Schr?dinger equation, which describes the dynamics of bright soliton in Bose—Einstein condensates with the time-dependent interaction in an expulsive parabolic and complex potential, are obtained by Darboux transformation. The results show that one can compress a bright soliton into an assumed peak of matter wave density by adusting the experimental parameter of the ratio of axial oscillation to radial oscillation or feeding parameter. Especially,when parameters satisfy the relation λ=2γ, the soliton is stable with time evolution without changing its shape and amplitude.  相似文献   

2.
The dynamics of the ring dark soliton in an inhomogeneous Bose-Einstein condensates (BEC) with thin disk-shaped potential trapping is investigated analytically and numerically. Analytical result shows that the ring dark soliton is governed by a variable coefficients Korteweg-de Vries (KdV) equation. The effect of the ring curvature (nonplanar geometry) and the inhomogeneous of the background on soliton amplitude and the emitted radiation profiles are obtained analytically. The theoretical results are confirmed by the direct numerical results.  相似文献   

3.
By developing multiple-scale method combined with Wentzel--Kramer--Brillouin expansion, this paper analytically studies the modulating effect of weakly periodic potential on the dynamical properties of the Bose--Einstein condensates (BEC) trapped in harmonic magnetic traps. A black--grey soliton transition is observed in the BEC trapped in harmonic magnetic potential, due to the weakly periodic potential modulating effect. Meanwhile, it finds that with the slight increase of the weakly periodic potential strength, the velocity of the soliton decreases, while its width firstly decreases then increases, a minimum exists there. These results show that the amplitude, velocity, and width of matter solitons can be effectively managed by means of a weakly periodic potential.  相似文献   

4.
We make use of a coordinate-free approach to implement Vakhitov-Kolokolov criterion for stability analysis in order to study the effects of three-body atomic recombination and lattice potential on the matter-wave bright solitons formed in Bose-Einstein condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number by a factor of √1 − bg 3 with g 3 the coupling constant of the lattice potential and b = 0.7301.   相似文献   

5.
《Physics letters. A》2020,384(7):126163
We investigate a quasi one dimensional spin-1 Bose-Einstein Condensates (BEC) in the absence of an external confinement governed by a system of three coupled Gross-Pitaevskii (GP) equation. Based on the Lax-pair, we construct one soliton solution employing gauge transformation method. In addition, the multiple bright and dark soliton solutions are obtained by properly choosing amplitude dependent parameter in the Lax-pair. The results of the paper emphasizes the richness in the structure of soliton solutions admitted by the spin components, a phenomenon which has never been brought out to the fore. We have also extended the gauge transformation method to generate two soliton solutions.  相似文献   

6.
We present a controlling potential method for solving the three-dimensional Gross-Pitaevskii equation (GPE), which governs the nonlinear dynamics of the Bose-Einstein condensates (BECs) in an inhomogeneous potential trap. Our method allows one to construct ground and excited matter wave states whose longitudinal profiles can have bright solitons. This method provides the confining potential that filters and controls localized BECs. Moreover, it is predicted that, while the BEC longitudinal soliton profile is controlled and kept unchanged, the transverse profile may exhibit oscillatory breathers (the unmatched case) or move as a rigid body in the form of either coherent states (performing the Lissajous figures) or a Schrödinger cat state (matched case).  相似文献   

7.
We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton's parameters (amplitude, width, and period) can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.  相似文献   

8.
We present a family of nonautonomous bright and dark soliton solutions of Bose-Einstein condensates with the time-dependent scattering length in an expulsive parabolic potential. These solutions show that the amplitude, width, and velocity of soliton can be manipulated by adjusting the atomic scattering length via Feshbach resonance. For the cases of both attractive and repulsive interactions, the total particle number is a conservation quantity, but the peak (dip) density can be controlled by the Feshbach resonance parameter. Especially, we investigate the modulation instability process in uniform Bose-Einstein condensates with attractive interaction and nonvanishing background, and clarify that the procedure of pattern formation is in fact the superposition of the perturbed dark and bright solitary waves. At last, we give the analytical expressions of nonautonomous dark one- and two-soliton solutions for repulsive interaction, and investigate their properties analytically.  相似文献   

9.
We obtain the bright matter wave solitons in Bose–Einstein condensates from a trivial input solution by solving the time dependent Gross–Pitaevskii (GP) equation with quadratic potential and exponentially varying scattering length. We observe that the matter wave density of bright soliton increases with time by virtue of the exponentially increasing scattering length. We also understand that the matter wave densities of bright soliton trains remain finite despite the exchange of atoms during interaction and they travel along different trajectories (diverge) after interaction. We also observe that their amplitudes continue to fluctuate with time. For exponentially decaying scattering lengths, instability sets in the condensates. However, the scattering length can be suitably manipulated without causing the explosion or the collapse of the condensates.  相似文献   

10.
The Gross–Pitaevskii equation (GPE) describing the evolution of the Bose–Einstein condensate (BEC) order parameter for weakly interacting bosons supports dark solitons for repulsive interactions and bright solitons for attractive interactions. After a brief introduction to BEC and a general review of GPE solitons, we present our results on solitons that arise in the BEC of hard-core bosons, which is a system with strongly repulsive interactions. For a given background density, this system is found to support both a dark soliton and an antidark soliton (i.e., a bright soliton on a pedestal) for the density profile. When the background has more (less) holes than particles, the dark (antidark) soliton solution dies down as its velocity approaches the sound velocity of the system, while the antidark (dark) soliton persists all the way up to the sound velocity. This persistence is in contrast to the behaviour of the GPE dark soliton, which dies down at the Bogoliubov sound velocity. The energy–momentum dispersion relation for the solitons is shown to be similar to the exact quantum low-lying excitation spectrum found by Lieb for bosons with a delta-function interaction.  相似文献   

11.
We discuss bright soliton compression in Bose–Einstein condensates described by a cubic-quintic derivative Gross–Pitaevskii model which takes into account the delayed nonlinear response of condensates confined in a complex potential. The external potential consists of an attractive parabolic background, a linear potential that may represent the gravitational field, and a complex part (introduced phenomenologically) which characterizes the rate of injection of atoms into the condensate. In our approach, the bright soliton evolution is described analytically by applying the variational approximation. The influences of the soliton width and the rate of injection of atoms are considered because of practical applications. To ensure the validity of the variational approximation, all analytical results are compared with the numerical data obtained with the split-step Fourier algorithm. The roles of the linear potential on the evolution and stabilization of compressed solitons are unveiled.  相似文献   

12.
何章明  张志强 《物理学报》2016,65(11):110502-110502
考虑周期性驱动线性势, 利用Darboux变换法解析地研究了玻色-爱因斯坦凝聚体(BEC)中的双孤子相互作用, 得到了S-波散射长度的临界值. 结果表明: 当S-波散射长度高于临界值时, BEC中的两个亮孤子相互吸引并融合; 而当S-波散射长度低于临界值时, 两个亮孤子保持局域稳定. 此外, 在外部势阱的驱动下, 两个稳定的亮孤子产生周期性振荡行为.  相似文献   

13.
考虑了描述玻色 爱因斯坦凝聚的Gross-Pitaevskii(GP)方程, 得到了在球对称非谐势阱中玻色-爱因斯坦凝聚GP方程的精确亮孤子解。In this paper, we analyze Gross Pitaevskii equation which describes the dynamics of a bright soliton in trapped atomic Bose Einstein condensates, and obtain the exact bright soliton solution of Gross Pitaevskii equation in spherically symmetric non harmonic trap.  相似文献   

14.
In this work I generalize and apply an analytical approximation to analyze 1D states of non-equilibrium spinor polariton Bose–Einstein condensates (BEC). Solutions for the condensate wave functions carrying black solitons and half-dark solitons are presented. The derivation is based on the non-conservative Lagrangian formalism for complex Ginzburg–Landau type equations (cGLE), which provides ordinary differential equations for the parameters of the dark soliton solutions in their dynamic environment. Explicit expressions for the stationary dark soliton solution are stated. Subsequently the method is extended to spin sensitive polariton condensates, which yields ordinary differential equations for the parameters of half-dark solitons. Finally a stationary case with explicit expressions for half-dark solitons is presented.  相似文献   

15.
We study modulational instability of matter-waves in Bose-Einstein condensates (BEC) under strong temporal nonlinearity-management. Both BEC in an optical lattice and homogeneous BEC are considered in the framework of the Gross-Pitaevskii equation, averaged over rapid time modulations. For a BEC in an optical lattice, it is shown that the loop formed on a dispersion curve undergoes transformation due to the nonlinearity-management. A critical strength for the nonlinearity-management strength is obtained that changes the character of instability of an attractive condensate. MI is shown to occur below (above) the threshold for the positive (negative) effective mass. The enhancement of number of atoms in the nonlinearity-managed gap soliton is revealed.  相似文献   

16.
The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-one-dimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.  相似文献   

17.
宋伟为  李秋艳  李再东  傅广生 《中国物理 B》2010,19(7):70503-070503
This paper develops the Hirota method carefully for applying into the growing model of quasi-one-dimensional Bose—Einstein condensations with attractive and repulsive interaction, respectively. After a tedious calculation it obtains the exact bright and dark soliton solutions analytically. It shows that the growing model has the important effect on the soliton amplitude and the time-dependent potential only contributes to the phase and phase velocity. A detailed analysis for the asymptotic behaviour of two-soliton solutions shows that the collision of two soliton is elastic.  相似文献   

18.
宗丰德  杨阳  张解放 《物理学报》2009,58(6):3670-3678
提出了一种处理玻色-爱因斯坦凝聚啁啾孤子动力学的拓展变分方法,深入研究了玻色-爱因斯坦凝聚孤子在周期势与抛物势联合作用下的动力学演化,利用拓展变分法给出了解析处理,并和基于分步傅里叶变换的直接数值法进行比较,发现这种拓展变分方法能够充分揭示上述外势场中的玻色-爱因斯坦凝聚啁啾孤子的动力学行为和特征.同时给出了能支持多稳定晶格囚禁玻色-爱因斯坦凝聚啁啾孤子的周期势与抛物势强度比值的临界值和一种通过控制外势场可有选择地移动玻色-爱因斯坦凝聚啁啾孤子的操控方法,这为玻色-爱因斯坦凝聚的实验和应用研究提供了理论参 关键词: 玻色-爱因斯坦凝聚 Gross-Pitaevskii方程 啁啾孤子 操控  相似文献   

19.
雍文梅  陈海军 《物理学报》2014,63(15):150302-150302
利用变分法研究了线性和非线性交叉光晶格中偶极玻色-爱因斯坦凝聚(BEC)体系中物质波孤立子的稳定性.选用柱对称高斯型试探波函数,得出参数的Euler-Lagrange方程和体系的有效作用势能,根据有效势能是否具有局域最小值判断体系是否具有稳定孤立子解.结果表明,由于存在接触相互作用的空间调制,在排斥和吸引偶极相互作用下,均能形成稳定的孤立子解.给出了参数空间中存在稳定解的区域和物质波波包宽度随时间的变化曲线.  相似文献   

20.
We analyze the dynamics of a bright soliton in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential. Under a safe range of parameters in which the Gross-Pitaevskii (GP) equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomicscattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.  相似文献   

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