一维双组分玻色-爱因斯坦凝聚体系的量子隧穿特性

利用双模近似方法研究了一维双组分玻色-爱因斯坦凝聚体(Bose-Einstein condensates,BECs)的量子隧穿特性.从描述三维双组分BECs系统的Gross-Pitaevskii方程(GPE)出发,得到了描述一维体系的GP方程.把体系波函数写成原子数和相位指数的乘积,得到描述体系隧穿特性的费曼方程.数值求解费曼方程,研究了原子之间相互作用(双组分BECs体系原子之间的相互作用包括组分内部原子之间的相互作用和不同组分原子之间的相互作用)对隧穿特性的影响.结果显示,当原子之间的相互作用较弱时,体系发生量子隧穿现象,表现为原子数在平衡位置附近作周期振荡;随着原子之间相互作用增强,体系经历一个临界状态,进入自俘获状态,即由于原子之间相互作用的存在,在对称双势阱中演化的BECs可以呈现出原子数高度的不对称分布,好像绝大数原子被其中一个势阱俘获.从隧穿到自俘获原子之间的相互作用存在一个临界值,从而体系的能量也对应一个临界值,根据体系的哈密顿函数,就能求出相互作用临界值的表达式.     

Bose--Einstein Condensates with Two- and Three-Body Interactions in an Anharmonic Trap at Finite Temperature

The transition temperature, the depletion of the condensate atoms and the collective excitations of a Bose-Einstein condensation （BEC） with two- and three-body interactions in an anharmonic trap at finite temperature are studied in detail. By using the Popov version of the Hartree-Fock-Bogoliubov （HFB） approximation, an extended self-consistent model describing BEC with both two- and three-body interactions in a distorted harmonic potential at finite temperature is obtained and solved numerically. The results show that the transition temperature, the condensed atom number and the collective excitations are modified dramatically by the atomic three-body interactions and the distortion of the harmonic trap.     

Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential

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.     

Nonlinear Landau--Zener Tunnelling with Two and Three-Body Interactions

We investigate the nonlinear Landau-Zener tunnelling of Bose-Einstein condensate （BEC） in an accelerating optical lattice with two- and three-body interactions between the particles. The influence of the three-body interaction on the eigenstates and the transition probability are discussed both anaJytically and numerically. The analytical eigenstates and the tunnelling probability are obtained, which are verified by numerical methods. It is shown that the eigenstates and the tunnelling probability are modified dramatically by three-body interaction.     

相对论热等离子体中电子声波的非线性频移

研究了相对论电磁波在热等离子体中传播时的色散特性以及由于非线性电子声波激发引起的电子声波的非线性频移。基于相对论激光在热等离子体中传播的电磁流体物理模型,采用流体的非线性频移理论,利用微扰法得到了描述相对论激光与热等离子体相互作用时谐波产生的非线性频移方程。结果表明,等离子体密度、电子温度和一阶谐波振幅是决定相对论热等离子体中非线性频移的主要因素。在弱激发下,非线性频移随着电子温度和一阶谐波振幅的增大而增大,等离子体密度抑制非线性频移。电子声波非线性频移对等离子体密度和电子温度的依赖表现出了强烈的非线性特征。研究结果为深入理解高能量激光与热等离子体相互作用中谐波的产生及引起的非线性频移提供了理论依据。     

Laser-driven relativistic electron dynamics in a cylindrical plasma channel

The energy and trajectory of the electron, which is irradiated by a high-power laser pulse in a cylindrical plasma channel with a uniform positive charge and a uniform negative current, have been analyzed in terms of a single-electron model of direct laser acceleration. We find that the energy and trajectory of the electron strongly depend on the positive charge density, the negative current density, and the intensity of the laser pulse. The electron can be accelerated significantly only when the positive charge density, the negative current density, and the intensity of the laser pulse are in suitable ranges due to the dephasing rate between the wave and electron motion. Particularly, when their values satisfy a critical condition,the electron can stay in phase with the laser and gain the largest energy from the laser. With the enhancement of the electron energy, strong modulations of the relativistic factor cause a considerable enhancement of the electron transverse oscillations across the channel, which makes the electron trajectory become essentially three-dimensional, even if it is flat at the early stage of the acceleration.     

Parametric instabilities in quantum plasmas with electron exchange-correlation effects

Parametric instabilities induced by the nonlinear interaction between high frequency quantum Langmuir waves and low frequency quantum ion-acoustic waves in quantum plasmas with the electron exchange-correlation effects are presented.By using the quantum hydrodynamic equations with the electron exchange-correlation correction,we obtain an effective quantum Zaharov model,which is then used to derive the modified dispersion relations and the growth rates of the decay and four-wave instabilities.The influences of the electron exchange-correlation effects and the quantum effects on the existence of quantum Langmuir waves and the parametric instabilities are discussed in detail.It is shown that the electron exchange-correlation effects and quantum effects are strongly coupled.The quantum Langmuir wave can propagate in quantum plasmas only when the electron exchange-correlation effects and the quantum effects satisfy a certain condition.The electron exchange-correlation effects tend to enhance the parametric instabilities,while quantum effects suppress the instabilities.     

Impurity-induced localization of Bose-Einstein condensates in one-dimensional optical lattices

The impurity-induced localization of two-component Bose-Einstein condensates loaded into deep one-dimensional optical lattices is studied both analytically and numerically.It is shown that,the analytical criteria for self-trapping and moving soliton/breather of the primary-component condensate are modified significantly by an admixture of an impurity component (the second component).The realization of the self-trapped state and the moving soliton/breather states of the primary-component becomes more easy with the minor admixture of the impurity-component,even if the two components are partly overlapped.     

Tunnelling Dynamics of Bose--Einstein Condensates in a Five-Well Trap

We develop a five-well model for describing the tunnelling dynamics of Bose-Einstein condensates （BECs） trapped in 2D optical lattices. The tunnelling dynamics of BECs in this five-well model are investigated both analytically and numerically. We focus on the self-trapped states and the difference of the tunnelling dynamics among two- well, three-well and five-well systems. The criterions for the self-trapped states and the phase diagrams of the five trapped BECs in zero-phase mode and π-phase mode are obtained. We find that the criterions and the phase diagrams are largely modified by the dimension of the system and the phase difference 5etween wells. The five-well model is a good model and can give us an insight into the tunnelling dynamics of BECs trapped in 2D optical lattices.