偶极-偶极相互作用下玻色-爱因斯坦凝聚体中涡旋的非线性动力学研究

基于平均场理论和分裂算符谱算法,研究了偶极-偶极相互作用下玻色爱因斯坦凝聚体中涡旋的非线性动力学.研究发现外势运动速度小于临界值时,偶极-偶极相互作用对系统涡旋的非线性动力学影响较小,而外势运动速度超过临界速度时,偶极-偶极相互作用对涡旋的非线性动力学影响很大,可使系统产生涡旋对、涡旋偶极子和简单涡旋,并使它们形成涡街.     

偶极玻色-爱因斯坦凝聚体干涉产生涡旋的数值研究

偶极原子间的相互作用具有长程各向异性且具有同时吸引和排斥的特点,因此偶极相互作用对偶极玻色-爱因斯坦凝聚体之间的干涉现象影响明显。本文用虚时演化方法和时间劈裂傅里叶谱方法具体研究了偶极原子极化方向对偶极凝聚体之间干涉现象的影响,当偶极原子极化矢量在凝聚体所处平面的投影方向关于两偶极凝聚体初始分割线对称时,凝聚体干涉图样也关于分割线对称,而干涉产生的涡旋手性刚好相反。当偶极原子间的相互作用各向异性时,偶极凝聚体干涉产生的涡旋分布呈现如下特征：当投影方向与初始分割线平行时,干涉不会产生涡旋,形成的干涉条纹为直线形且条纹宽度相同;当投影方向与初始分割线夹角接近π/4（或3π/4）时,在干涉图样的中心区域形成可见的沿直线分布的正（或反）涡旋结构;当投影方向与初始分割线夹角接近π/2时,中心区域会形成涡旋-反涡旋对。     

环形运动势搅拌下偶极玻色-爱因斯坦凝聚体中的von Kármán涡街

数值研究了偶极玻色-爱因斯坦凝聚体(Bose-Einstein condensate, BEC)在环形运动高斯势搅拌时的动力学行为.当高斯势运动速度和尺寸逐渐变化时,偶极BEC中将出现稳定层流、涡旋偶极子、Bénard–von Kármán(BvK)涡街以及混乱激发4种模式.结果表明高斯势在偶极BEC中圆周运动时产生涡街的条件非常苛刻,只有适当尺寸的高斯势以合适的速度运动时,尾流中周期性脱落的具有相同旋量的涡旋对稳定的分布在内外两个圆环上,形成BvK涡街.在实验参数下进行系统数值计算得到了不同偶极相互作用时的相图,讨论了偶极相互作用以及高斯势速度和尺寸对不同激发模式的影响.通过高斯势所受拖拽力的计算,分析了不同激发的物理学机制.     

偶极玻色-爱因斯坦凝聚体在类方势阱中的Bénard-von Kármán涡街

对偶极玻色-爱因斯坦凝聚体（Bose-Einstein condensate,BEC）在类方势阱中的Bénard-von Kármán涡街现象进行了数值研究.结果表明,当障碍势在BEC中的运动速度与尺寸在适当范围内时,系统中会出现稳定的两列涡旋对阵列,即Bénard-von Kármán涡街.研究了偶极相互作用强弱、障碍势尺寸以及运动速度对尾流中产生的涡旋结构的影响,得到了相图结构.对障碍势所受拖拽力进行计算,分析了涡旋对产生的力学机理.     

共心双环外势中两分量偶极玻色-爱因斯坦凝聚体的基态结构研究

利用虚时演化方法研究了共心双环外势中具有偶极-偶极相互作用的两分量玻色-爱因斯坦凝聚体的基态结构, 探索了接触相互作用和长程各向异性的偶极-偶极相互作用对系统基态的影响. 研究发现, 偶极-偶极相互作用作为系统的又一调控参数, 可用于得到系统的不同的基态相, 并用于控制不同基态相间的转化.     

偶极旋量玻色-爱因斯坦凝聚体在外场中的自旋混合动力学

探讨了外场中偶极旋量玻色-爱因斯坦凝聚体的静态和动力学行为.研究结果表明,可以调节外场、自旋交换相互作用和偶极-偶极相互作用来调控三组分之间的隧穿,控制布居数动力学演化范围和相对相位动力学行为. 关键词： 玻色-爱因斯坦凝聚 偶极-偶极相互作用 自旋混合动力学     

动力学压缩真空与原子间偶极-偶极力

利用Milonni源理论方法研究了动力学压缩真空中两原子间偶极-偶极(d-d)相互作用力的性质与真空压缩的关系.结果发现:由于真空压缩的存在,两原子间d-d吸引力将受到削弱.当压缩系数为零时,得到通常文献中所熟知的结果.     

磁偶极相互作用下玻色-爱因斯坦凝聚体中出现的奇特涡旋晶格结构

文章简要地介绍了玻色-爱因斯坦凝聚体中出现的涡旋和铬原子玻色-爱因斯坦凝聚体的实验研究进展，还介绍了文章作者的一项最新的理论工作。研究指出，由于铬原子磁偶极相互作用的影响，凝聚体中将出现奇特的各向异性的涡旋晶格结构。     

光晶格中双组分偶极玻色-爱因斯坦凝聚体的调制不稳定性

利用线性稳定性分析的方法,对光晶格中双组分偶极玻色-爱因斯坦凝聚体(Bose-Einstein condensates,简称BECs)的调制不稳定性进行了研究.得到了光晶格中双组分偶极BECs原子系统调制不稳定性区域的分布与在位相互作用和由偶极-偶极相互作用所导致的格点间BECs相互作用之间的关系.结果显示,格点间BECs的相互作用对光晶格中双组分偶极BECs的调制不稳定性有较大的影响,这可为实际应用中如何操控双组分偶极BECs提供有用的信息. 关键词： 光晶格 双组分玻色-爱因斯坦凝聚体 调制不稳定性 偶极-偶极相互作用     

稠密共振介质中近偶极-偶极相互作用的局域场效应

 为研究存在由近偶极-偶极相互作用诱导的局域场效应时超短强激光脉冲与稠密共振介质相互作用的特性,采用光与物质相互作用的半经典理论,建立了稠密二能级体系中考虑原子间近偶极-偶极相互作用的修正光学Bloch方程,并用四阶Runge-Kutta法数值求解了该方程。研究结果表明:局域场效应对稠密二能级体系中Bloch矢量的瞬态相干过程和稳态性质都具有强烈的调制作用。并由此提出了调控稳态粒子数布居的两种方案。     

Quantized vortex stability and interaction in the nonlinear wave equation

The stability and interaction of quantized vortices in the nonlinear wave equation (NLWE) are investigated both numerically and analytically. A review of the reduced dynamic law governing the motion of vortex centers in the NLWE is provided. The second order nonlinear ordinary differential equations for the reduced dynamic law are solved analytically for some special initial data. Using 2D polar coordinates, the transversely highly oscillating far field conditions can be efficiently resolved in the phase space, thus giving rise to an efficient and accurate numerical method for the NLWE with non-zero far field conditions. By applying this numerical method to the NLWE, we study the stability of quantized vortices and find numerically that the quantized vortices with winding number m=±1 are dynamically stable, and resp. |m|>1 are dynamically unstable, in the dynamics of NLWE. We then compare numerically quantized vortex interaction patterns of the NLWE with those from the reduced dynamic law qualitatively and quantitatively. Some conclusive findings are obtained, and discussions on numerical and theoretical results are made to provide further understanding of vortex stability and interactions in the NLWE. Finally, the vortex motion under an inhomogeneous potential in the NLWE is also studied.     

弱相互作用玻色-爱因斯坦凝聚体中涡旋动力学与量子混沌轨道简

利用变分法和数值模拟方法,我们分别从解析上和数值上研究了弱相互作用玻色-爱因斯坦凝聚体中不同涡旋蔟的动力学性质.借助玻姆量子力学中的方法,我们定义了相应量子流体中的量子轨道,并且研究了由于不同涡旋结构的存在而导致量子轨道出现混沌的性质.当存在一单涡旋,我们发现混沌轨道出现与否和涡旋轨道的形状紧密相关.此外,玻色凝聚体原子中的两体相互作用对各向异性谐振子势下涡旋对出现时量子轨道混沌的发生也具有重要的作用.因为这一非线性相互作用会破坏相应速度场的时间周期性.最后,在涡旋极子情形下,我们还讨论了由于涡旋相互激发或淹没的作用而导致规则岛膨胀的性质.这些规则区域镶嵌在一定的混沌海中.     

Critical dynamics associated with dynamic disordering near the depinning transition in different vortex phases

We study a depinning transition based on transient dynamics of vortices driven by a suddenly applied dc current, focusing on whether a difference in the equilibrium vortex phase that can lead to a different vortex flow will change the critical behavior. After preparing an ordered initial vortex configuration, we measure the time evolution of voltage associated with dynamic disordering in three magnetic fields, corresponding to the ordered phase (OP), disordered phase (DP), and coexistence phase. The critical behavior of the depinning transition is commonly observed in these phases, pointing to the universality of the transition. However, the critical behavior is most marked in the coexistence phase, while the suppression of the critical region and that of dynamic disordering are observed in OP and DP, respectively, whose origin is attributed to the different flow states among these phases.     

Long-time relaxation processes in the nonlinear Schrödinger equation

The nonlinear Schrödinger equation, known in low-temperature physics as the Gross-Pitaevskii equation, has a large family of excitations of different kinds. They include sound excitations, vortices, and solitons. The dynamics of vortices strictly depends on the separation between them. For large separations, some kind of adiabatic approximation can be used. We consider the case where an adiabatic approximation can be used (large separation between vortices) and the opposite case of a decay of the initial state, which is close to the double vortex solution. In the last problem, no adiabatic parameter exists (the interaction is strong). Nevertheless, a small numerical parameter arises in the problem of the decay rate, connected with an existence of a large centrifugal potential, which leads to a small value of the increment. The properties of the nonlinear wave equation are briefly considered in the Appendix A.     

Exotic vortex structures of the dipolar Bose–Einstein condensates trapped in harmonic-like and toroidal potential

Based on the tunable intensity and waist of Gaussian laser, harmonic-like and toroidal potentials can be achieved and the ground-state properties of the dipolar Bose–Einstein condensate (BEC) trapped in such potentials are investigated. It is found that, in the harmonic-like potential, the singly and doubly quantized vortices can exist in the scale condensate and translate respectively into vortex pairs and triangular vortex lattice with increasing dipole–dipole interaction (DDI). Especially, the sandwich-like structure can be observed in the ground-state density profiles by tuning the direction and strength of DDI for some rotating frequency. In the toroidal potential, the competition between the inter-component interaction and DDI can induce the transition between immiscible and miscible states, and results in the structures of a doubly quantized vortex surrounded by a vortex ring. It is worth emphasizing that, with the increasing of DDI, the doubly quantized vortex in the harmonic-like potential becomes two singly quantized vortices, while in the toroidal potential it is no happen due to the presence of Gaussian barrier.     

Pinning of vortices by the domain structure in a two-layered type II superconductor-ferromagnet system

The effectiveness of magnetic pinning of vortices in a layered system formed by a uniaxial ferromagnet and type II superconductor is considered. It is shown that, irrespective of the saturation magnetization of the ferromagnet, the energy of pinning at the domain structure does not exceed, in order of magnitude, the energy of artificial pinning at a column-type defect. The limitation of pinning energy is caused by the interaction of external vortices with a spontaneous vortex lattice formed in the superconducting film when the magnetization of the ferromagnetic film exceeds the critical value.     

Pinning effects on the vortex critical velocity in type-II superconducting thin films

We study the influence of artificial pinning centers on the vortex critical velocity in Al thin films deposited on top of a periodic array of Permalloy (FeNi) square rings. We demonstrate that the field dependence of the flux flow velocity strongly depends on the particular magnetic state of the rings. In particular, we find that, even when the rings are in a flux closure state, i.e. with little stray field, the vortex critical velocity shows a non-monotonic magnetic field dependence. This behaviour is in sharp contrast with the results obtained in a reference plain film, with no rings underneath. A comparison with the intrinsic strong pinning Nb films previously studied, suggests an interpretation in terms of a channel-like motion of vortices, here induced by the artificial pinning structure.