Quantum Signatures of Chaos in Adiabatic Interaction Between a Trapped Ion and a Laser Standing Wave

We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.     

激光脉冲作用下囚禁离子在Lamb-Dicke区域精确的量子运动

研究驻波型激光脉冲作用下,囚禁于Paul阱中的单离子在Lamb-Dicke区域的久期运动.通过试探解方法,得到系统的量子力学精确解.基于精确解描述的概率波包串,发现：1）波包串中心以及波包串的高度和宽度受激光脉冲强度的控制,通过调节激光强度可以控制波包串的形变和传播;2）在激光脉冲作用瞬间,离子的能量期待值发生跳变,而在激光关闭时段,有窄的能带形成;3）存在一个激光脉冲强度的临界值,在临界点附近,系统的稳定性发生变化.     

激光脉冲作用下囚禁离子在Lamb-Dicke区域精确的量子运动

研究驻波型激光脉冲作用下,囚禁于Paul阱中的单离子在Lamb-Dicke区域的久期运动.通过试探解方法,得到系统的量子力学精确解.基于精确解描述的概率波包串,发现：1）波包串中心以及波包串的高度和宽度受激光脉冲强度的控制,通过调节激光强度可以控制波包串的形变和传播;2）在激光脉冲作用瞬间,离子的能量期待值发生跳变,而在激光关闭时段,有窄的能带形成;3）存在一个激光脉冲强度的临界值,在临界点附近,系统的稳定性发生变化. 关键词： 囚禁离子 激光脉冲 Lamb-Dicke近似 精确解     

Dimension-dependent stimulated radiative interaction of a single electron quantum wavepacket

In the foundation of quantum mechanics, the spatial dimensions of electron wavepacket are understood only in terms of an expectation value – the probability distribution of the particle location. One can still inquire how the quantum electron wavepacket size affects a physical process. Here we address the fundamental physics problem of particle–wave duality and the measurability of a free electron quantum wavepacket. Our analysis of stimulated radiative interaction of an electron wavepacket, accompanied by numerical computations, reveals two limits. In the quantum regime of long wavepacket size relative to radiation wavelength, one obtains only quantum-recoil multiphoton sidebands in the electron energy spectrum. In the opposite regime, the wavepacket interaction approaches the limit of classical point-particle acceleration. The wavepacket features can be revealed in experiments carried out in the intermediate regime of wavepacket size commensurate with the radiation wavelength.     

含时量子蒙特卡罗方法研究两电子原子在强激光作用下电子的动力学行为

通过改进含时量子蒙特卡罗方法研究了一维模型双电子原 子在强激光作用下的电子动力学过程. 与准确的数值积分求解含时薛定谔方程相比, 计算得到的波包对应的量子系综中粒子的动力学变化和含时波包演化结果定性一致, 且大幅度地提高了计算效率. 根据计算得到的经典粒子系综的动力学演化行为, 分析了原子在强激光作用下的激发、电离、重散射等非线性过程.     

Laser controlled quantum motion of two Paul trapped ions

We investigate the quantum motion of two ions stored in a Paul trap and interacting with a time-periodic laser field. In the pseudopotential approximation and large detuning condition, we find that the relative motion is independent of the laser field, but the exact centre-of-mass motion is closely related to the laser field. By adjusting the laser intensity and frequency, we can well control the quantum motion of the centre-of-mass. We illustrate some physical properties described by the centre-of-mass states, such as the squeezed coherent property, the widths and heights of the wavepackets of probability density, the classical-quantum correspondence, the resonance ladders of expectation energy and the transition probabilities between time-dependent quantum levels.     

Control of wavepacket dynamics in mixed alkali metal clusters by optimally shaped fs pulses

We have performed adaptive feedback optimization of phase-shaped femtosecond laser pulses to control the wavepacket dynamics of small mixed alkali-metal clusters. An optimization algorithm based on Evolutionary Strategies was used to maximize the ion intensities. The optimized pulses for NaK and Na₂K converged to pulse trains consisting of numerous peaks. The timing of the elements of the pulse trains corresponds to integer and half integer numbers of the vibrational periods of the molecules, reflecting the wavepacket dynamics in their excited states. Received 4 December 2001     

Bohmian Mechanics,the Quantum-Classical Correspondence and the Classical Limit: The Case of the Square Billiard

Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum amplitude being controlled by the spread of the corresponding classical statistical distribution. We investigate wavepacket dynamics and compute the corresponding de Broglie-Bohm trajectories in the quantum square billiard. We also determine the trajectories and statistical distribution dynamics for the equivalent classical billiard. Individual Bohmian trajectories follow the streamlines of the probability flow and are generically non-classical. This can also hold even for short times, when the wavepacket is still localized along a classical trajectory. This generic feature of Bohmian trajectories is expected to hold in the classical limit. We further argue that in this context decoherence cannot constitute a viable solution in order to recover classicality.     

波包动力学-飞秒激光操纵波包过程

本文介绍了波包动力学的基本理论和数值模拟方法,尤其是在飞秒激光与分子相互作用领域中的应用,探讨了飞秒激光引起的波包过程（包括波包的制备、波包的干涉）,以及利用调频脉冲、脉冲串和优化脉冲形状控制波包动力学的方案。     

波包动力学-飞秒激光操纵波包过程

本文介绍了波包动力学的基本理论和数值模拟方法,尤其是在飞秒激光与分子相互作用领域中的应用,探讨了飞秒激光引起的波包过程（包括波包的制备、波包的干涉）,以及利用调频脉冲、脉冲串和优化脉冲形状控制波包动力学的方案。     

Photoemission of a single-electron wave packet in a strong laser field

The radiation emitted by a single-electron wave packet in an intense laser field is considered. A relation between the exact quantum formulation and its classical counterpart is established via the electron's Wigner function. In particular, we show that the wave packet, even when it spreads to the scale of the wavelength of the driving laser field, cannot be treated as an extended classical charge distribution, but rather behaves as a pointlike emitter carrying information on its initial quantum state. We outline an experimental setup dedicated to put this conclusion to the test.     

Fluctuations of expectation values in chaotic systems and broken time-reversal symmetry

Fluctuations of expectation values of observables are calculated in complex quantum systems, such as disordered metallic grains or quantum systems with classical chaotic motion. We derive an exact expression for these fluctuations valid for systems with and without time-reversal symmetry, as well as in the transition region between these two cases. We compare our results with those of a semiclassical theory and with simulations of random matrices.     

囚禁单离子的量子阻尼运动

用包含偶极和四极虚势能项的非厄米哈密顿算符来描述Paul阱中囚禁阻尼单离子在静电场下的量子运动.通过导出和分析系统的精确解,得到在PT对称和不对称情形下的不同实能谱与稳定量子态,以及PT不对称情形的虚能谱和衰减量子态,同时给出相应于不同态的参数区域和存活概率.结果发现该非厄米系统外场参数能惟一确定量子稳定态并导致波函数形态变化,据此提出非相干操控相应量子跃迁的方法.让量子态衰减导致的离子位置期待值的衰减与经典阻尼谐振子的衰减一致,得到虚势能参数与经典阻尼参数的对应关系.所得结果将进一步丰富具有广泛应用背景的囚禁离子动力学.     

激光脉冲作用下囚禁离子的规则与混沌运动

研究驻波型激光脉冲作用下，失谐量足够大时，囚禁于Paul阱中的单离子系统的久期运动.通过分析和数值计算相结合的方法，导出系统的精确解及其描述的时间演化性质，得到系统的规则和混沌运动轨道以及阱频很小时系统进入整体混沌的临界条件,并提出了控制系统共振失稳的方法. 关键词： 激光脉冲 囚禁离子 规则与混沌运动 精确解 稳定性     

Classical versus quantum symmetries for Toda theories with a nontrivial boundary perturbation

In this paper we present a detailed study of the quantum conservation laws for Toda field theories defined on the half plane in the presence of a boundary perturbation. We show that total derivative terms added to the currents, while irrelevant at the classical level, become important at the quantum level and in general modify significantly the quantum boundary conservation. We consider the first nontrivial higher-spin currents for the simply laced a_n⁽¹⁾ Toda theories: we find that the spin-three current leads to a quantum conserved charge only if the boundary potential is appropriately redefined through a finite renormalization. Contrary to the expectation we demonstrate instead that at spin four the classical symmetry does not survive quantization and we suspect that this feature will persist at higher-spin levels. Finally, we examine the first nontrivial conservations at spin four for the d₃⁽²⁾ and c₂⁽¹⁾ nonsimply laced Toda theories. In these cases the addition of total derivative terms to the bulk currents is necessary but sufficient to ensure the existence of corresponding quantum exact conserved charges.     

共面两囚禁离子体系精确的量子运动

研究Paul阱中共面两离子体系精确的量子运动. 在考虑库仑关联的条件下，得到了系统Schr?dinger方程的精确解和以此为基础的微扰解，包括精确的离散本征态和本征能量，以及近似的分段连续谱和能带结构. 以低能级的几个态为例，用数值方法计算了两离子间的平均距离，并绘出了两离子的概率分布图. 关键词： Paul阱 共面两离子 平均距离 能带结构     

Dust and radiation quantum perfect fluid cosmology: selection of time variable

We studied the expectation value of the scale factor in radiation and dust quantum perfect fluid cosmology. We used Schutzs variational formalism to describe the perfect fluid and selected the conjugate coordinate of the perfect fluid to be the dynamical variable. After quantization and solving the Wheeler-DeWitt equation we obtained an exact solution. By superposition of exact solutions, we obtained one wave packet and used it to compute the expectation value of the scale factor. We found that if one selects a different dynamical variable being the time variable in each of these two systems, the expectation value of the scale factor of these two systems can fit in with the prediction of General Relativity. Therefore we thought that the selection of a reference time can be different for different quantum perfect fluid systems.     

Two-state system coupled to a boson mode: Quantum dynamics and classical approximations

The relation between classical and quantum mechanical integrability is investigated for a boson mode coupled to a two-level system. Different semi-classical approximations of this system are considered which are obtained by (i) factorization of expectation values of the two-state variable and the boson, (ii) making a WKB-type approximation, (iii) replacing the boson by a classical field of constant amplitude and fixed frequency and (iv) putting the boson into a self-consistent coherent state. The results vary considerably and include cases of non-integrable and integrable classical dynamics. Quantum mechanically the system is found to satisfy a criterion of quantum mechanical integrability, which we formulate, but the separated Hamiltonian of the boson alone does not have a well-defined classical limit. Numerical results for the energy spectrum and expectation values are obtained, which show a high degree of regularity but also display overlapping avoided crossings usually associated with non-integrable Hamiltonians. The exact dynamics of the occupation probabilities of the two levels is also analysed numerically. The dependence of quantum mechanical recurrence effects (in quantum optics known as revivals) on coupling strength, frequency detuning and initial conditions is studied. The revivals are found to disappear in the case of strong coupling. The Fourier spectra of the dynamical expectation values are also calculated     

Quantum chaos of an ion trapped in a linear ion trap

We describe the transition to quantum chaos of an ion trapped in a linear ion trap and interacting with two laser fields. Under the conditions of adiabatic illumination of the upper level of the ion, and when the frequencies of the two laser beams are slightly different, the system is reduced to a quantum linear oscillator interacting with a monochromatic wave. The property of localization over the quantum resonance cells is proposed to exploit in order to facilitate the process of measurement of the probability distribution of an ion on the vibrational levels. In the regime of strong chaos the time-averaged values of the energy and dispersion of energy are computed and compared with the corresponding classical quantities for different values of the perturbation amplitude. In the exact resonance case, the classical analog of the system possesses an infinite inhomogeneous stochastic web. We analyze the quantum dynamics inside the inhomogeneous web. It is shown that the quantum system mimics on average the dynamics of the corresponding classical system. Formation of the quantum resonance cells is illustrated in the case of a finite detuning from the exact resonance, and under increasing of the wave amplitude. The parameters of the model and the initial conditions are close to the real physical situation which can be realized in the system of cold trapped ion perturbed by two lasers fields with close frequencies. (c) 2000 American Institute of Physics.