具有经典混沌转变系统的能谱性质——耦合自旋模型的数值计算

用数值方法研究了一耦合自旋模型的最近邻能级间距涨落和能级随参数变化曲线的免交叉行为。计算结果表明,当变化参数,系统的经典运动出现从规则→混沌→规则的转变时,间距涨落分布P(s)的Brody参数很好地反映了混沌区域在相空间中占据的比例。在有大量混沌运动的参数范围里,计算观察到了大量的免交叉及它们的重叠,并且能级曲线图呈现相对无规的形貌。这些结果被看作经典混沌在量子能谱中的表现或痕迹。 关键词：     

单粒子在非轴对称八极形变势场中的混沌运动

针对单粒子处在长椭球谐振子势加上Y₃₂+Y_3－2形变势场中的情况, 从经典和量子两个角度分析了粒子在非轴对称八极形变势场中的混沌运动. 通过经典的轨道稳定性分析, 指出了系统等势能面性质对粒子运动特点的重要性. 又通过对体系存在的能级免交叉现象, 三维不对称谐振子相干态在势场中的演化特征的研究, 具体地说明了八级形变势的非轴对称性使单粒子更容易出现混沌运动.     

量子无规运动与核耗散

从动力学对称性观点出发考察了量子规则运动与无规运动 .用能级动力学研究了从量子规则运动向量子无规运动的过渡 ,给出了导致能级混沌的条件 ,揭示了造成能级混沌的机制 .用混沌态矢的特征解释了原子核的各态历经集体态的衰变特性 .研究了重离子碰撞中核耗散与动力学对称性破坏之间的关系. Quantum regular and irregular motions are investigated from the viewpoint of dynamical symmetry. The transition from quantum regular motion to chaotic motion is studied by level dynamics and computer experiments. The conditions for onset of quantum chaos are presented.The mechanism for causing chaotic level spectrum is unveiled. The decay behavior of the nuclear ergodic collective states is explained in terms of the peculiar property of chaotic states. The connection between nuclear...     

飞秒激光参数对非绝热耦合分子态布居的影响

利用含时波包法研究强飞秒泵浦-探测激光场中激光脉宽、波长和场强对非绝热耦合NaI分子各态布居的影响.波包在势能面上做周期性运动,周期约为1 000 fs.延时为200 fs时,波包第一次到达交叉区域分裂成两部分.波包在交叉区域的分裂情况影响各态布居.脉宽增长,NaI分子的激发概率增大,而解离概率减小.泵浦波长为共振波长318 nm时,激发概率最大.泵浦波长增长,NaI分子的解离概率减小.泵浦场强增大,激发概率增大,但解离概率不变.探测激光波长和场强不影响NaI分子各态布居分布.调节激光场参数可实现对波包运动的控制从而控制态布居的选择性分布.研究结果为实验上实现分子的光控制过程提供参考.     

量子混沌系统中的自旋压缩性质

量子信息是21世纪的一门新兴交叉学科,现已经成为世界关注的热门研究领域.近年来,量子计算机的研究正成为大家十分感兴趣的课题.在寻找量子计算的实现方案过程中,量子混沌引起了研究人员的极大关注,因为在量子计算机执行一些量子运算法则的过程中可能产生量子混沌,并可能破坏量子计算机的运算操作条件.近期有关量子纠缠与量子混沌之间的关系已经有所报道,而自旋压缩作为另外一种典型的纯量子效应,是否也与量子混沌之间存在一定关系呢?讨论了量子混沌研究中一个非常典型的QKT模型,研究了量子混沌系统中自旋压缩的性质.通过数值模拟计算,给出了两种不同定义的自旋压缩系数与混沌系数κ之间的变化关系,结果发现在经典相空间中,如果在规则区域占优势的情况下,当初始自旋相干态波包位于椭圆形中心时,随着时间的演化,系统压缩行为表现得非常强;而对于经典相空间中混沌区域占优势的情况下,初始自旋相干态波包同样位于椭圆形中心,则系统的压缩行为表现得非常弱,说明自旋压缩对相应的经典混沌非常敏感.通过比较还发现,采用Wineland等定义的自旋压缩系数比采用Kitagawa和Ueda等定义的自旋压缩系数对经典混沌更敏感一些,从而得出用自旋压缩可以刻画量子混沌的结论.     

激子自旋弛豫对简并量子点发射光子对纠缠度的影响

利用粒子数运动方程和量子回归理论，计算了单个半导体量子点双激子体系脉冲激发下粒子在各能级间辐射跃迁的二阶交叉相关函数以及系统发射光子对的偏振密度矩阵.分析了激子态能级简并量子点体系发射光子对偏振纠缠特性，讨论了纠缠度随激子态间自旋弛豫的变化关系.研究表明，激子自旋弛豫会破坏该系统发射光子对的纠缠度. 关键词： 纠缠光子对 半导体量子点 二阶相关函数     

一维谐振子量子运动中的经典特性

利用量子力学的态叠加原理和算符劈裂法,对处于一维谐振子势中的初始态为高斯波包的中心位置的量子运动进行了研究.结果表明:其中心位置的量子运动呈现出经典谐振子的运动特性;波包的初始位置和初始时刻所加动量对波包中心位置量子动力学的影响与经典谐振子类似条件对运动的影响有相同的性质.本结果对理解复杂量子运动中的高斯波方法有一定的启示作用.     

动力学对称性研究的拓扑途径——互作用玻色子模型中的应用示例

运用拓扑观点对IBM系统动力学对称性破坏的过程进行了研究,着重揭示了与能级免交叉联系的奇异行为及其根源.它实际上是动力学映射的不稳定不动点所导致的结果.越过不稳定不动点后,为了给出连续映射,就必须涉及能级的置换操作,因而呈现出能级免交叉的现象,并合映射不再能表示为动力学群生成元的函数,于是动力学对称性局域地实质性地受到了破坏.     

飞秒激光脉宽对非绝热耦合分子波包运动的影响研究

利用含时波包法研究了强飞秒泵浦-探测激光场中激光脉宽对非绝热耦合NaI分子波包运动的影响.发现波包的振荡周期随脉宽增长而增大,而振荡幅度随脉宽增长而减小.非绝热效应引起的波包在交叉区域的分裂情况影响各态布居.脉宽增长,NaI分子的激发概率增大,而解离概率减小.研究表明调节激光场脉宽可实现对波包运动的控制从而控制态布居的选择性分布.研究结果可以为实验上实现分子的光控制以及量子调控过程提供一定的参考.     

经典混沌系统在相应于初始相干态的量子子空间中的随机性

Poincare截面是反映经典系统是否达到混沌的有力手段,无规矩阵理论被看成是显示量子系统规则运动与不规则运动特征的有效方法．那么,当一个经典相点在混沌体系的某一能量面E₀上的不变环面被全部破坏后,与这一相点所对应的中心能量E₀等于E₀的相干态波包在它所占据的量子系统的子空间中有何表现呢？以原子核Lipkin模型为例,用重整化约化方法,对SU（3）群的广义相干态所占据的量子子空间进行了约化后对其中有关量的随机性作了考察,结果表明,在这样的等效子空间内能级间距的涨落,等效哈密顿量的矩阵元以及从可积体系的子空间到这一等效子空间的一一映射的矩阵元的分布均与无规矩阵理论的预言相符合,从而为进一步研究经典部分可积体系的量子表现奠定了基础. 关键词：     

The Spatiotemporal Evolution of Wave Packets under Chaotic Condition

Using the minimum uncertainty state of quantum integrable system H0 as initial state,the spatiotemporal evolution of the wave packet under the action of perturbed Hamiltonian is studied causally as in classical mechanics,Due to the existence of the avoided energy level crossing in the spectrum there exist nonlinear resonances between some paris of neighboring components of the wave packet,the deterministic dynamical evolution becomes very complicated and appears to be chaotic.It is proposed to use expectation values for the whole set of basic dynamical variables and the corresponding spreading widths to describe the topological features concisely such that the quantum chaotic motion can be studied in contrast with the quantum regular motion and well characterized with the asymptotic behaviors .It has been demonstrated with numerical results that such a wave packet has indeed quantum behaviors of ergodicity as in corresponding classical case.     

高Q腔中原子内态布居对原子平移运动的影响

基于原子作双光子共振跃迁的原子－场缀饰态，讨论了驻波腔场中两能级原子的量子化平移运动与原子内态布居间的相互影响，结果表明原子平移运动敏感地依赖于原子的内态布居，特别当原子处于两内态等权重同相位叠加态时，平移运动呈现出很稳定的特征。     

Quantization of a free particle interacting linearly with a harmonic oscillator

We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic.     

Stueckelberg Oscillations in a Two‐State Two‐Path Model of a Conical Intersection

The two‐state two‐path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi‐classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.     

Observing the phase space trajectory of an entangled matter wave packet

We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin-dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon distributions throughout the action of the displacement force. Our investigation shows corrections to simplified models of the system evolution. The precise knowledge of these dynamics may improve quantum gates for ion crystals and lead to entangled matter wave states with large displacements.     

Temporal ghost imaging of a time object,dispersion cancelation,and nonlocal time lens with bi-photon state

We present a theory of temporal diffraction, temporal imaging of a bi-photon state, and temporal ghost imaging of a time object. By applying factional Fourier transform to the bi-photon wave packet propagating in space, we could obtain a theory that shows the physical origin of dispersion cancelation, temporal imaging, nonlocal effects of time lenses, and temporal ghost imaging. We introduce the temporal diffraction distance for bi-photon wave packet and show that the bi-photon wave packet behaves like a single wave packet whose temporal diffraction distance is determined by the coherent sum of the temporal diffraction distances for the signal and the idler beams. This property yields the well known dispersion cancelation, the recovery of original bi-photon wave packet in temporal imaging, and the nonlocal combination of two time lenses placed in different arms. We also propose a method for ghost imaging of an arbitrary time object.     

Properties of Coherent State for Hydrogen Atom

We construct the coherent state for the two-dimensional hydrogen atom, for which the averaged motion ofposition describes a Kepler ellipse. The coherent state can be expanded with respect to the eigenstates of 2D hydrogenatom, from which we evaluate the binding energy of the wave packet for this state.     

Proliferation of atomic wave packets at the nodes of a standing light wave

A quantum analysis is presented of the motion and internal state of a two-level atom in a strong standing-wave light field. Coherent evolution of the atomic wave-packet, atomic dipole moment, and population inversion strongly depends on the ratio between the detuning from atom-field resonance and a characteristic atomic frequency. In the basis of dressed states, atomic motion is represented as wave-packet motion in two effective optical potentials. At exact resonance, coherent population trapping is observed when an atom with zero momentum is centered at a standing-wave node. When the detuning is comparable to the characteristic atomic frequency, the atom crossing a node may or may not undergo a transition between the potentials with probabilities that are similar in order of magnitude. In this detuning range, atomic wave packets proliferate at the nodes of the standing wave. This phenomenon is interpreted as a quantum manifestation of chaotic transport of classical atoms observed in earlier studies. For a certain detuning range, there exists an interval of initial momentum values such that the atom simultaneously oscillates in an optical potential well and moves as a ballistic particle. This behavior of a wave packet is a quantum analog of a classical random walk of an atom, when it enters and leaves optical potential wells in a seemingly irregular manner and freely moves both ways in a periodic standing light wave. In a far-detuned field, the transition probability between the potentials is low, and adiabatic wave-packet evolution corresponding to regular classical motion of an atom is observed.     

Level Dynamics and Universality of Spectral Fluctuations

The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics for the fictitious gas of particles associated with the parametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known clues to that goal are an appropriate equilibrium ensemble and a certain ergodicity of level dynamics. We here complete the reasoning by establishing a power law for the dependence of the mean parametric separation of avoided level crossings. Due to that law universal spectral fluctuations emerge as average behavior of a family of quantum dynamics drawn from a control parameter interval which becomes vanishingly small in the classical limit; the family thus corresponds to a single classical system. We also argue that classically integrable dynamics cannot produce universal spectral fluctuations since their level dynamics resembles a nearly ideal Pechukas–Yukawa gas.