共查询到20条相似文献,搜索用时 31 毫秒
1.
We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background. 相似文献
2.
We present three families of one-soliton solutions for (2+1)-dimensional Gross-Pitaevskii equation with both time-dependent scattering length and gain or loss in a harmonic trap. Then we investigate the dynamics of these solitons in Bose-Einstein condensates (BECs) by some selected control functions. Our results show that the intensities of these solitons first increase rapidly to the condensation peak, then decay very slowly to the background; thus the lifetime of a bright soliton, a train of bright solitons and a dark soliton in BECs can be all greatly extended. Our results offer a useful method for observing matter-wave solitons in BECs in future experiments. 相似文献
3.
Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential 下载免费PDF全文
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
4.
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
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WANG Tian-Yuan 《理论物理通讯》2009,51(2):255-258
We consider the one-dimensional nonlinear Schrǒdinger equations that describe the dynamics of a Bose-Einstein Condensates with time-dependent scattering length in a complex potential. Our results show that as long as the integrable relation is satisfied, exact solutions of the one-dimensional nonlinear Schrǒdinger equation can be found in a general closed form, and interactions between two solitons are modulated in a complex potential We find that the changes of the scattering length and trapping potential can be effectively used to control the interaction between two bright soliton. 相似文献
7.
We investigate the exact bright and dark solitary wave solutions of an effective 1D Bose-Einstein condensate (BEC) by assuming that the interaction energy is much less than the kinetic energy in the transverse direction. In particular, following the earlier works in the literature Pérez-García et al. (2004) [50], Serkin et al. (2007) [51], Gurses (2007) [52] and Kundu (2009) [53], we point out that the effective 1D equation resulting from the Gross-Pitaevskii (GP) equation can be transformed into the standard soliton (bright/dark) possessing, completely integrable 1D nonlinear Schrödinger (NLS) equation by effecting a change of variables of the coordinates and the wave function. We consider both confining and expulsive harmonic trap potentials separately and treat the atomic scattering length, gain/loss term and trap frequency as the experimental control parameters by modulating them as a function of time. In the case when the trap frequency is kept constant, we show the existence of different kinds of soliton solutions, such as the periodic oscillating solitons, collapse and revival of condensate, snake-like solitons, stable solitons, soliton growth and decay and formation of two-soliton bound state, as the atomic scattering length and gain/loss term are varied. However, when the trap frequency is also modulated, we show the phenomena of collapse and revival of two-soliton like bound state formation of the condensate for double modulated periodic potential and bright and dark solitons for step-wise modulated potentials. 相似文献
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Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates 下载免费PDF全文
We consider two coupled Gross-Pitaevskii equations describing a two-component Bose-Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential,and investigate the dynamics of vector solitons.By using a direct method,we construct a novel family of vector soliton solutions,which are the linear combination between dark and bright solitons in each component.Our results show that due to the superposition between dark and bright solitons,such vector solitons possess many novel and interesting properties.The dynamics of vector solitons can be controlled by the Feshbach resonance technique,and the vector solitons can keep the dynamic stability against the variation of the scattering length. 相似文献
10.
We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory. 相似文献
11.
Dario Poletti Elena A. Ostrovskaya Tristram J. Alexander Yuri S. Kivshar 《Physica D: Nonlinear Phenomena》2009,238(15):1338-1344
We study the dynamics of bright matter-wave solitons in a Bose-Einstein condensate with negative scattering length under the influence of a time-periodic ratchet potential. The potential is formed by a one-dimensional bichromatic optical lattice which flashes on and off so that the time average of its amplitude vanishes. Due to the broken space and time-reversal symmetries of the potential, the soliton is transported with a nonzero average velocity. By employing the non-dissipative mean-field model for the matter waves, we study the dependence of the transport velocity on the initial state of the soliton and show how the properties of the individual localized states affect the outcome of their collisions. A useful insight into the transport properties is provided by Hamiltonian theory for the mean field, which treats the extended matter-wave excitation as an effective classical particle. 相似文献
12.
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
13.
Controlling the amplitude of soliton in agrowing Bose--Einstein condensate by means of Feshbach resonance 下载免费PDF全文
By using Darboux transformation, this paper studies analytically the nonlinear dynamics of a one-dimensional growing Bose-Einstein condensate (BEC). It is shown that the growing model has an important effect on the amplitude of the soliton in the condensates. In the absence of the growing model, there exhibits the stable alternate bright solitons in the condensates. In the presence of the growing model, the obtained results show that the amplitude of the bright soliton decreases (increases) for the BEC growing coefficient Ω 〈 0 (Ω 〉 0). Furthermore, we propose experimental protocols to manipulate the amplitude of the bright soliton by varying the scattering length via the Feshbach resonance in the future experiment. 相似文献
14.
We study the formation of bright solitons in a Bose-Einstein condensate of 7Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment [Nature (London) 417, 150 (2002)]]. The numerical simulations are performed by using the Gross-Pitaevskii equation with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results. We find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior. 相似文献
15.
Emmanuel Kengne Abdourahman Shehou Ahmed Lakhssassi 《The European Physical Journal B - Condensed Matter and Complex Systems》2016,89(3):78
We investigate the dynamics of matter-wave solitons in the one-dimensional (1-D)Gross-Pitaevskii (GP) equation describing Bose-Einstein condensates (BECs) withtime-dependent scattering length in varying trapping potentials with feeding/loss term. Byperforming a modified lens-type transformation, we reduce the GP equation into a classicalnonlinear Schrödinger (NLS) equation with distributed coefficients and find its integrablecondition. Under the integrable condition, we apply the generalized Jacobian ellipticfunction method (GJEFM) and present exact analytical solutions which describe thepropagation of a bright and dark solitons in BECs. Their stability is examined usinganalytic method. The obtained exact solutions show that the amplitude of bright and darksolitons depends on the scattering length, while their motion and the total number of BECatoms depend on the external trapping potential. Our results also shown that the loss ofatoms can dominate the aggregation of atoms by the attractive interaction, and thus thepeak density can decrease in time despite that the strength of the attractive interactionis increased. 相似文献
16.
We investigate the coupled Gross-Pitaevskii equation describing the dynamics of two hyperfine states of Bose-Einstein condensates and deduce the integrability condition for the propagation of bright vector solitons. We show how the transient trap and scattering length can be suitably tailored to bring about fascinating collisional dynamics of vector solitons. 相似文献
17.
The evolution characteristics of a matter-wave bright soliton are investigated by means of the variational approach in the presence of spatially varying nonlinearity. It is found that the atom density envelope of the soliton is changed as a result of the spatial variation of the s-wave scattering length. The stable soliton can exist in appropriate initial conditions. The movement of the soliton depends on the sign and value of the coefficient of spatially modulated nonlinearity. These theoretical predictions are confirmed by the full numerical simulations of the one-dimensional Gross-Pitaevskii equation. 相似文献
18.
We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low. 相似文献
19.
W. P.?Zhong M.?Beli? R. H.?Xie G.?Chen Y. Q.?Lu 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2009,55(1):147-153
Bright and dark matter wave solitons are
constructed analytically in a three-dimensional (3D) highly anisotropic
Bose-Einstein condensate (BEC) with a time-dependent parabolic potential,
and numerical simulations are performed to confirm the existence and
dynamics of such analytical solutions. Different classes of bright and dark
solitons are discovered among the solutions of the generalized anisotropic
(3+1)D Gross-Pitaevskii equation. Our results demonstrate that the bright
and dark solitary waves can be manipulated and controlled by changing the
scattering length, which can be used to compress the second-order bright and
dark solitons of BECs into desired peak density. 相似文献
20.
《Waves in Random and Complex Media》2013,23(1):151-160
We consider a generalized fifth-order KdV equation with time-dependent coefficients exhibiting higher-degree nonlinear terms. This nonlinear evolution equation describes the interaction between a water wave and a floating ice cover and gravity-capillary waves. By means of the subsidiary ordinary differential equation method, some new exact soliton solutions are derived. Among these solutions, we can find the well known bright and dark solitons with sech and tanh function shapes, and other soliton-like solutions. These solutions may be useful to explain the nonlinear dynamics of waves in an inhomogeneous KdV system supporting high-order dispersive and nonlinear effects. 相似文献