共查询到20条相似文献,搜索用时 296 毫秒
1.
E. Fersino B. A. Malomed G. Mussardo A. Trombettoni 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(3):417-426
We study the effect of an optical lattice (OL) on the ground-state properties of one-dimensional ultracold bosons with three-body
attractive interactions and two-body repulsive interactions, which are described by a cubic-quintic Gross-Pitaevskii equation
with a periodic potential. Without the optical lattice and with a vanishing two-body interaction term, normalizable soliton
solutions of the Townes type are possible only at a critical value of the interaction strength, at which an infinite degeneracy of the ground state
occurs; a repulsive two-body interaction makes such localized solutions unstable. We show that the OL opens a stability window
around the critical point when the strength of the periodic potential is above a critical threshold. We also consider the
effect of an external parabolic trap, studying how the stability properties depend on the matching between minima of the periodic
potential and the minimum of the parabolic trap. 相似文献
2.
Dark soliton in one-dimensional Bose–Einstein condensate under a periodic perturbation of trap 下载免费PDF全文
The perturbation of a confining trap leads to the collective oscillation of a Bose--Einstein condensate, thereby the propagation of a dark soliton in the condensate is affected. In this study, periodic perturbation is employed to match the soliton oscillation. We find that the soliton dynamics depends sensitively on the coupling between the moving direction of the trap and that of the soliton. The soliton energy/depth evolves periodically, and a relevant shift in the soliton trajectory occurs as compared with the unperturbed case. Overall, the soliton oscillation frequency changes little even if the perturbation amplitude and frequency vary. 相似文献
3.
The dynamics of dark soliton in a growing Bose-Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential. 相似文献
4.
Control of soliton characteristics of the condensate by an arbitrary x-dependent external potential 下载免费PDF全文
This paper presents a family of soliton solutions of the one-dimensional nonlinear Schrdinger equation which describes the dynamics of the dark solitons in Bose-Einstein condensates with an arbitrary x-dependent external potential.The obtained results show that the external potential has an important effect on the dark soliton dynamical characteristics of the condensates.The amplitude,width,and velocity of the output soliton are relative to the source position of the external potential.The smaller the amplitude of the soliton is,the narrower its width is,and the slower the soliton propagates.The collision of two dark solitons is nearly elastic. 相似文献
5.
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
6.
Effects of localized impurity on a dark soliton in a Bose--Einstein condensate with an external magnetic trap 下载免费PDF全文
The dynamics of a dark soliton has been investigated in a Bose--Einstein
condensate with an external magnetic trap, and the effects of localized
impurity on the dynamics are discussed by the variational approach
based on the renormalized integrals of motion. The reciprocal
movement of the dark soliton is discussed by performing a standard
linear analysis, and it is found that the effects of the localized
impurity depend strictly on the positive or negative value of the
impurity strength corresponding to the repulsive or attractive
impurity. The numerical results confirm the theoretical analysis,
and show that the effects also depend on the effective nonlinear
coefficient and the harmonic frequency. 相似文献
7.
Shu-Wen Guan 《中国物理 B》2022,31(8):80506-080506
We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter- and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton (without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects. 相似文献
8.
It is shown that grey soliton dynamics in a one-dimensional trap can be treated within the framework of the local density approximation as Landau dynamics of a quasiparticle. A soliton of arbitrary amplitude moves in the trapping potential without deformation of its density profile as a particle of mass 2m. The dynamics in the local density approximation is shown to be consistent with the perturbation theory for dark solitons. Dynamics of a vortex ring in a trap is discussed qualitatively. 相似文献
9.
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
10.
We present several families of exact solutions to a system of
coupled nonlinear Schr\"{o}dinger equations. The model describes a
binary mixture of two Bose--Einstein condensates in a magnetic trap
potential. Using a mapping deformation method, we find exact
periodic wave and soliton solutions, including bright and dark
soliton pairs. 相似文献
11.
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
12.
By using the multiple-scale method, this paper analytically
studies the effect of a barrier potential on the dynamical
characteristics of the soliton in Bose--Einstein condensates. It
is shown that a stable soliton is exhibited at the top of the
barrier potential and the region of the absence of the barrier
potential. Meanwhile, it is found that the height of the barrier
potential has an important effect on the dark soliton dynamical
characteristics in the condensates. With the increase of height of
the barrier potential, the amplitude of the dark soliton becomes
smaller, its width is narrower, and the soliton propagates more slowly. 相似文献
13.
LI Hua-Mei 《理论物理通讯》2007,47(1):63-68
Evolution of periodic waves and solitary waves in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the mapping deformation method, we successfully obtain periodic wave solutions and solitary wave solutions, including the bright and dark soliton solutions.The results in this paper include some in the literatures [Phys. Rev. Lett. 94 (2005) 050402 and Chin. Phys. Left. 22 (2005) 1855]. 相似文献
14.
Longitudinal confinement of dark solitons in quasi-one-dimensional Bose-Einstein condensates leads to sound emission and reabsorption. We perform quantitative studies of the dynamics of a soliton oscillating in a tight dimple trap, embedded in a weaker harmonic trap. The dimple depth provides a sensitive handle to control the soliton-sound interaction. In the limit of no reabsorption, the power radiated is found to be proportional to the soliton acceleration squared. An experiment is proposed to detect sound emission as a change in amplitude and frequency of soliton oscillations. 相似文献
15.
Two dark solitons are considered in a two-component Bose-Einstein condensate with an external magnetic trap, and effects of the trap potential on their dynamics are investigated by the numerical simulation. The results show that the dark solitons attract, collide and repel periodically in two components as time changes, the time period depends strictly on the initial condition and the potential, and there are obvious self-trapping effects on the two dark solitons. 相似文献
16.
A proof of the existence of stationary dark soliton solutions of a cubic-quintic nonlinear Schrödinger equation with a periodic potential is given. It is based on the interpretation of the dark soliton as a heteroclinic of the Poincaré map. 相似文献
17.
We study the existence of dark solitons of the defocusing cubic nonlinear Schrödinger (NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincaré map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity. 相似文献
18.
19.
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
20.
We study, theoretically and experimentally, the nonlinear dynamics of a wave packet launched inside a trap potential. Increasing the power of the wave packet transforms its dynamics from linear tunneling through a potential barrier, to soliton tunneling, and eventually, above a well-defined threshold, to the ejection of a soliton from the potential trap. 相似文献