量子相空间中对称受驱双势阱系统的量子隧穿动力过程

本文以纠缠轨线分子动力学方法研究对称受驱双势阱系统的量子隧穿动力学过程.驱动力的幅度和频率改变将对量子隧穿动力学过程产生巨大的影响,这为人们自主控制这一重要的过程提供理论基础.当体系的经典动力学呈现混沌状态时,它的量子动力学过程将发生显著的变化.在强驱动力作用下,双势阱系统的量子共振频率隧穿和非共振频率隧穿因为混沌行为的出现明显增强.通过对比相空间中具有相同初始态的纠缠轨线和经典轨线演化,我们给出量子隧穿过程清晰的物理图像.最后,我们讨论量子隧穿动力学过程中体系不确定度的演化和反映波包动力学过程的自关联函数演化.     

Dicke模型的量子经典对应关系

非旋波近似条件下Dicke模型表现为量子混沌动力学特征.在详细考察Dicke模型经典相空间结构特点的基础上,采用经典-量子"一对多"的思想,即经典相空间中的一点对应于量子体系两个初始相干态的演化,利用对两个初态量子纠缠动力学演化取统计平均的方法,得到了与经典相空间对应非常好的量子相空间结构.数值计算结果表明:经典混沌有利地促进系统两体纠缠的产生,平均纠缠可以作为量子混沌的标识,利用平均纠缠可以得到一种较好的量子动力学与经典相空间的对应关系. 关键词： Dicke模型 非旋波近似 量子混沌 经典量子对应     

相空间中对称的纠缠相干态及其非经典特性

研究相空间中对称的纠缠相干态, 通过引入正交基矢, 利用concurrence方法计算了纠缠度, 研究了它们的单、双模压缩以及反聚束效应. 数值计算表明, 相空间中对称的纠缠相干态与非经典效应之间存在着密切的联系. 关键词： 纠缠相干态 concurrence 非经典效应     

非对易相空间中谐振子体系热力学性质的探讨

2000年以来, 有关非对易空间的各种物理问题一直是研究的热点, 并在量子力学、场论、凝聚态物理、天体物理等各领域中已被广泛地探讨. 采用统计物理方法讨论非对易效应对谐振子体系热力学性质的影响. 先以对易相空间中确定二维和三维谐振子的配分函数求出谐振子体系的热力学函数; 非对易相空间中的坐标和动量通过坐标-坐标和动量-动量之间的线性变换而以对易相空间中的坐标和动量来表示; 最终以非对易相空间中求出配分函数来讨论非对易效应对谐振子体系热力学性质的影响. 结果显示, 在非对易相空间中谐振子体系的配分函数和熵表达式均包含因非对易引起的修正项. 从分析结果得出如下结论: 非对易效应对谐振子的配分函数和熵函数等微观状态函数有一定的影响, 但对谐振子体系的内能、热容量等宏观热力学函数没有影响. 研究结果只是对应于满足玻尔兹曼统计的经典体系, 对于满足费米-狄拉克和玻色-爱因斯坦统计的量子体系需进一步推广研究.     

玻色-爱因斯坦凝聚系统的量子Fisher信息与混沌

量子Fisher信息作为经典Fisher信息的自然推广,与量子信息中的纠缠判断具有密切联系.在表现为典型量子混沌特征的受击两分量玻色-爱因斯坦凝聚系统中,研究了与经典相空间对应的纠缠和量子Fisher信息动力学性质. 结果表明,初次撞击后的系统量子态是纠缠的,与初态所处相空间中的混乱程度无关.而量子Fisher信息的动力学演化对系统初态非常敏感,当初态处于混沌区域时,量子Fisher信息值比初态处于规则区域时大.利用这种较好的量子-经典对应关系,得到量子Fisher信息可以刻画量子混沌的结论. 关键词： 量子Fisher信息 玻色-爱因斯坦凝聚 量子混沌 量子-经典对应     

奇偶对相干态的维格纳函数和层析图函数

利用纠缠态η〉表象下的维格纳算符,重构了奇偶对相干态的维格纳函数.根据维格纳函数在相空间中随变量ρ和γ的变化规律,讨论了奇偶对相干态的非经典性质和量子干涉效应.研究发现,奇偶对相干态总呈现非经典性质,并且当q取奇数时,奇偶对相干态更容易出现非经典性质.奇偶对相干态的量子干涉效应的显著程度与q取值有关,但对于q的同一取值,奇对相干态的量子干涉效应更为显著.利用纠缠态η〉表象下的维格纳算符Δ1,2(ρ,γ)和纠缠态η,τ1,τ2〉的投影算符之间满足的拉东变换,获得了奇偶对相干态的量子层析图函数.     

量子态的可分性与纠缠度量

正1.引言量子纠缠是量子物理区别于经典物理的特征之一,量子纠缠态在量子信息处理中起到关键的作用,是许多量子信息处理过程中必不可少的资源~([1])。例如在量子隐形传态中,利用一对分别处于甲地与乙地的纠缠粒子,可以把一个未知量子态从甲地传到乙地。对量子纠缠理论及其应用的研究,已经把数学、物理、计算、信息等许多领域紧密地结合了起来。量子态的纠缠度的大小,与量子信息处理的成功     

光学体系宏观-微观纠缠及其在量子密钥分配中的应用

宏观-微观纠缠最早起源于“薛定谔的猫”思想实验, 是指在宏观体系与微观体系之间建立量子纠缠. 实现宏观-微观纠缠可以利用多种物理体系来完成, 本文重点介绍了在光学体系中制备和检验宏观-微观纠缠的发展过程. 从最初的受激辐射单光子量子克隆到光学参量放大, 再到相空间的位移操作, 实验上制备宏观-微观纠缠的方法取得了长足的进步. 利用非线性光学参量放大过程制备的宏观-微观纠缠的光子数可以达到10⁴量级, 人眼已经可以观察到, 因此使用人眼作为探测器来检验宏观-微观纠缠的实验开始出现. 但随后人们意识到, 粗精度的光子数探测器, 例如人眼, 无法严格判定宏观-微观纠缠的存在. 为了解决这个难题, 提出了一种巧妙的方法, 即在制备宏-微观纠缠后, 利用局域操作过程将宏观态再变为微观态, 通过判定微观纠缠存在的方法来判定宏微观纠缠的存在. 之后相空间的位移操作方法将宏观态的粒子数提高到10⁸, 并且实现了纠缠的严格检验. 利用光机械实现宏观-微观纠缠的方案也被提出. 由于量子密钥分配中纠缠是必要条件, 而宏观-微观纠缠态光子数较多这一优势可能会对量子密钥分配的传输距离有所提高. 本文介绍了利用相位纠缠的相干态来进行量子秘钥分配的方案, 探讨了利用宏观-微观纠缠实现量子密钥分配的可能性.     

腔光力学研究进展

腔光力学研究光子与宏观机械振子的相互作用，目前已成为研究量子世界与经典世界之间的过渡以及研究非经典和非线性效应的重要领域。本文首先介绍该领域中的基本物理概念，包括辐射压力、光机械哈密顿量、海森堡–朗之万方程、方程的线性化等。然后综述近年来一些新奇光力学效应的发现和研究进展，包括光力诱导透明、非互易光传播、高阶边带产生、光机械纠缠等。最后提出了一些研究展望。     

正方体量子台球的半经典分析(英文)

近几年,量子台球问题引起人们的广泛兴趣.以前有很多对二维量子台球做过研究,相对于二维台球来说,三维台球更接近实际体系.本文以三维正方体量子台球为例,利用半经典闭合轨道理论计算了正方体量子台球中的经典开轨道,并研究量子谱函数与经典轨道长度之间的对应关系,发现他们之间对应的很好.这将有助于我们分析开放型量子台球中输运性质问题.利用这种方法物理图像清晰,计算量小并且可以帮助理解一些混沌体系的性质.这是半经典理论为联系量子力学与经典力学起桥梁作用的又一证明.     

Semiclassical Ehrenfest paths

Trajectories are a central concept in our understanding of classical phenomena and also in rationalizing quantum mechanical effects. In this work we provide a way to determine semiclassical paths, approximations to quantum averages in phase space, directly from classical trajectories. We avoid the need of intermediate steps, like particular solutions to the Schroedinger equation or numerical integration in phase space by considering the system to be initially in a coherent state and by assuming that its early dynamics is governed by the Heller semiclassical approximation. Our result is valid for short propagation times only, but gives non-trivial information on the quantum-classical transition.     

Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process

The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger’s equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The “effect of entanglement” is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.     

Modeling and visualization of quantum bifurcations in phase space

We investigate quantum-mechanical counterpart of a classical instability in a phase space by the numerical method of quantum trajectories with moving basis. As an application the model of coupled two oscillators driven by a monochromatic force in the presence of dissipation (intracavity second harmonic generation) is analyzed. The system of interest is characterized by two bifurcations leading to ranges of instability: the Hopf bifurcation which connects a steady state dynamics of the oscillatory modes to a self-pulsing temporal dynamics and the bifurcation of the period-doubling. The both two regimes are analyzed on the framework of the semiclassical phase trajectories and the Wigner functions of the oscillatory modes in phase space.     

Semiclassical quantization of complex Henon–Heiles systems

Semiclassical eigenenergies and power spectra of PT-symmetric Henon–Heiles systems are obtained by using classical trajectories in complex phase space. It was found that some of the semiclassical methods developed for real multidimensional systems are equally valid when systems are complex as well. Semiclassical results are compared with exact quantum mechanical results.     

On the dynamics of a quantum system which is classically chaotic

We investigate the dynamics of one anisotropic spin in an external time-dependent magnetic field. The classical dynamics of the system is nonintegrable (and very similar to the standard map). We present results on this model for a quantum spin (i.e. for finite values of the spin lengthS). In particular we discuss the semiclassical regime,S1, using the concept of Wigner functions to define a suitable probability distribution. In regular regions of phase space the time evolution of the probability distribution shows an algebraic decay of correlations as in quantum mechanics. In chaotic regions of phase space it is characterised by a positive Lyapunov exponent which depends onS. In these regions semiclassical trajectories coincide with classical ones fort <₀ where ₀InS.     

Semiclassical propagator of the Wigner function

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.     

Harmonic oscillator in Snyder space: The classical case and the quantum case

The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual harmonic oscillator is obtained through an effective mass and an effective frequency introduced in the model. This modified parameters give us a modified energy spectrum also.