Pump-probe photoionization study of the passage and bifurcation of a quantum wave packet across an avoided crossing

The application of femtosecond pump-probe photoelectron spectroscopy to directly observe vibrational wave packets passing through an avoided crossing is investigated using quantum wave packet dynamics calculations. Transfer of the vibrational wave packet between diabatic electronic surfaces, bifurcation of the wave packet, and wave packet construction via nonadiabatic mixing are shown to be observable as time-dependent splittings of peaks in the photoelectron spectra.     

Photoionization of NaK molecule with a double-well potential in femtosecond pump--probe pulse laser fields

The method of time-dependent quantum wave packet dynamics is used to calculate the femtosecond pump--probe photoelectron spectra and study the wave packet dynamic processes of the double-minimum potential state 6¹∑⁺ of NaK in intense laser fields. The evolutions of the wave packet and the photoelectron energy spectra with time and internuclear distance are described in detail. The wave packet dynamic information of the 6¹∑⁺ state can be extracted from the photoelectron energy spectra.     

Bound-bound state quantum wave packet dynamics in the intermediate coupling range: the A1Sigma+u (0+u) and b3IIu (0+u) system in Rb2

The real-time quantum dynamics of a wave packet confined to two coupled bound states at intermediate interaction strength is probed by experiment and calculations on the A1Sigma(+)(u) approximately b (3)II(u) system in Rb2 molecules. The general dynamics consists of rapid spreading out over the whole phase space. Particular conditions exist, however, under which the initial wave packet motion separates into two mesobatic trajectories with distinct frequencies. These diabatic or adiabatic hybrid trajectories are analogous to those responsible for longevity resonances in bound-unbound systems.     

Li2分子含时波包动力学的理论研究

利用含时量子波包方法计算得到了Li2分子的光电子能谱,并运用波包动力学理论对含有不同参量的光电子能谱现象给出了合理的解释。通过分析文中的直观图像,研究了波包的动力学过程。结果表明,泵浦-探测脉冲的延迟时间对光电子能谱的形状有重要的影响;在较短延迟时间下,能谱独特的四峰现象是由光诱导势的产生引起的。     

Li2分子含时波包动力学的理论研究

利用含时量子波包方法计算得到了Li2分子的光电子能谱,并运用波包动力学理论对含有不同参量的光电子能谱现象给出了合理的解释.通过分析文中的直观图像,研究了波包的动力学过程.结果表明,泵浦-探测脉冲的延迟时间对光电子能谱的形状有重要的影响;在较短延迟时间下,能谱独特的四峰现象是由光诱导势的产生引起的.     

Constrained relativistic mean-field approach with fixed configurations

A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean-field model. As an example, the potential energy surfaces of ²⁰⁸Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. It is shown that the diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to follow the evolution of single-particle orbits till the very deformed region, and to obtain several well-defined deformed excited states which can hardly be expected from the adiabatic PESs.     

IBr分子含时波包的理论探究

本文主要对IBr分子的飞秒含时光电子能谱进行了模拟计算.运用含时量子波包方法,对不同延迟时间的光电子能谱进行模拟计算与理论分析.应用波包和光诱导势理论,对光电子能谱共同的两峰系特征及多峰现象给予合理解释.光电子能谱的峰值随延迟时间的增加而递减现象,是由于波包在势能面上因分子解离发散,使整个波包在势能曲线上的振荡递减造成的.研究表明：波包的传播是一个能量减弱的过程;跃迁过程中不同电离通道之间的竞争,也对能谱存在一定的影响.     

IBr分子含时波包的理论探究

本文主要对IBr分子的飞秒含时光电子能谱进行了模拟计算.运用含时量子波包方法,对不同延迟时间的光电子能谱进行模拟计算与理论分析.应用波包和光诱导势理论,对光电子能谱共同的两峰系特征及多峰现象给予合理解释.光电子能谱的峰值随延迟时间的增加而递减现象,是由于波包在势能面上因分子解离发散,使整个波包在势能曲线上的振荡递减造成的.研究表明：波包的传播是一个能量减弱的过程;跃迁过程中不同电离通道之间的竞争,也对能谱存在一定的影响.     

Study on wave packet dynamics of E~1Σ_g~+ state of Li_2 with femtosecond-resolved photoelectron spectra

Wave packet dynamics of the Li₂ molecule are investigated by using the time-dependent quantum wave packet method, and the time-resolved photoelectron spectra of the Li₂ molecule are calculated. The time-resolved wave packet theory is used to reasonably interpret the phenomena of the photoelectron spectra for different parameters. Our calculation shows that the loss of the wave packets in the shelf state area of E{ }^1\Sigma_g^ + plays a prominent role in the process of photoionization with the increase of the delay time. Moreover, the oscillation of the wave packet on the E{ }^1\Sigma_g^ + curve symbolizes a decreasing process of energy.     

Spectroscopic effects of conical intersections of molecular potential energy surfaces

A simple vibronic coupling model involving two electronic states and two vibrational modes is considered. The model is based on harmonic diabatic potentials and linear coupling of the diabatic electronic states. It is shown that the adiabatic electronic potential energy surfaces exhibit, in general, a conical intersection. The well known E × E and E × B Jahn-Teller problems are contained as special cases. Using numerical methods the optical absorption spectrum is calculated exactly. Extremely complex vibronic spectra are obtained when the conical intersection occurs within the Franck-Condon (FC) zone. The exact vibronic spectra are compared with spectra calculated in the adiabatic and FC approximation. The genuine spectroscopic effects of conical intersections are revealed by a comparison with the results of standard one-dimensional vibronic coupling calculations. The presence of a conical intersection limits the applicability of the adiabatic and FC approximations much more strongly than in the one-dimensional case. The upper adiabatic electronic state is strongly affected by non-adiabatic coupling even when the point of intersection lies outside the FC zone. The relevance of these results for the calculation of molecular electronic spectra is briefly discussed.     

Theoretical studies of inelastic atomic collisions in a two-state model problem

A two-state scattering problem in which two non-crossing Morse curves are coupled by an exponential potential is discussed theoretically in both the diabatic and adiabatic approximations. Inelastic cross sections are estimated by various approximate analytical formulas, which are expressed in terms of the distorted wave matrix elements. The Landau (steepest descent) method is applied to estimate the distorted wave matrix element. The previously proposed separable potential approximation in the adiabatic method is found to be best among others by comparing with the exact numerical results. Transition probability as a function of l (angular momentum of relative motion) is well reproduced by this approximation. A glory effect in the velocity dependence of the cross section is found in the low energy region, and the adiabatic approximation reproduces this undulation phenomenon well.     

Predissociation resonances in CO and IBr. Smooth exterior scaling combined with the discrete variable representation

Smooth exterior scaling (SES) and the discrete variable representation (DVR) are combined to accurately compute predissociation resonances of a bound state non-adiabatically coupled to a dissociative state. For the CO( predissociation interaction good agreement is found with approaches based on optical potentials and complex scaling. The comparison is done both in the diabatic and the adiabatic representation. The effect of the coupling strength in the IBr predissociation interaction and the transition from the diabatic to the adiabatic picture was studied by computing resonances for coupling strengths from up to . The transition from weak (diabatic) to strong (adiabatic) coupling was clearly seen. The intermediate case leads to a complicated resonance distribution. Comparison was made with recent studies using pump-probe spectroscopy [M. Shapiro, M.J.J. Vrakking, A. Stolow, J. Chem. Phys. 110, 2465 (1999)]. It was found that the overall features of the experiment could be explained from the resonance distribution, but for a detailed comparison more accurate potential energy surfaces and couplings are needed. Received 12 July 1999 and Received in final form 6 December 1999     

Direct XUV probing of attosecond electron recollision

We demonstrate that the recolliding electron wave packet, fundamental to many strong field phenomena, can be directly imaged with sub-A spatial and attosecond temporal resolution using attosecond extreme ultraviolet (XUV) pulses. When the recolliding electron revisits the parent ion, it can absorb an XUV photon yielding high energy electron and thereby providing a measurement of the electron energy at the moment of recollision. The full temporal evolution of the recollision wave packet can be reconstructed by measuring the photoelectron spectra for different time delays between the driving laser and the attosecond XUV probe. The strength of the photoelectron signal can be used to characterize the spatial distribution of the electron density in the longitudinal direction. Elliptical polarization can be used to characterize the electron probability in transversal direction.     

Control of diabatic versus adiabatic field dissociation in a heavy Rydberg system

A novel phenomenon is observed in the dynamics of laser-prepared coherent wave packets, bound by the Coulombic 1/r potential of an ion-pair system. After exciting weakly bound (approximately 3 meV) H(+)(-) wave packets in a Stark field, and permitting them to evolve in time, control of field dissociation via adiabatic and diabatic routes is demonstrated by applying delayed pulsed-electric fields, involving a zero-field crossing. Control manifests itself through the production of ions from each pathway at a different instant in time. This phenomenon is applied to map the oscillatory behavior of an angular momentum wave packet in a heavy Rydberg system. The characteristic frequencies of the observed Stark oscillations verify predicted mass-scaling laws for heavy Rydberg systems.     

NaLi分子飞秒含时光电子能谱的理论研究

运用三态模型和含时波包方法,研究了NaLi分子处于强飞秒抽运-探测激光场中的波包动力学过程和时间分辨光电子能谱,并且揭示了飞秒激光脉冲参数与NaLi分子光电子能谱之间的关系.研究发现:对于不同的激光波长,波包的振动周期是不同的,而且随着抽运-探测脉冲延迟时间的不同,NaLi分子光电子能谱的谱峰高度和位置发生变化;当λ1=352 nm并且?t=400 fs时,外阱中相应的光电离信号(0.5 eV处)明显强于内阱中相应的光电离信号(1.35 eV处).计算结果表明,NaLi分子激发态41Σ+上波包动力学的一些信息能够通过其光电子能谱反映出来.这些结果可以为实验上实现分子的光控制以及量子操控过程提供一些有价值的参考信息,并为进一步的理论研究提供重要依据.     

Quasi diabatic CASSCF state functions

A new method to determine quasi diabatic (QD) CASSCF states is presented. The adiabatic states are subjected to a unitary transformation resulting from diagonalization of a state-selection operator. The latter is constructed from the overlap of the adiabatic states with a suitable set of reference states. The multi-state (MS) CASPT2 method is used to account for the dynamical correlation effects in an approach where the QD-CASSCF wave functions are used as reference states. The procedure is applied to avoided crossings in excited states of BeH, LiO and ozone. The advantages of the proposed formulation are discussed.     

NaI分子的非绝热效应

利用含时波包法研究了NaI分子在飞秒脉冲激光作用下的动力学演化情况.由于受非绝热效应的影响,波包运动到势能面的交叉区域时发生分裂.研究表明:非绝热效应引起的波包分裂是分子解离的根源,而且随着演化时间的增加非绝热效应变得越来越明显.同时,分别采用量子力学和经典力学理论探讨了NaI分子在非绝热过程中的演化规律以及解离概率随脉冲波长的变化关系. 关键词： 非绝热效应 NaI分子 飞秒脉冲 含时波包     

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.     

Optical potential discrete variable representation method in the adiabatic representation

The optical potential discrete variable representation method (OP-DVR) has been applied recently to calculate resonances in the framework of the diabatic representation [J. Chem. Phys. 101, 7580 (1994)]. This method is based on the conjoint use of the discrete variable representation (DVR) method and the properties of a complex absorbing potential (CAP). The OP-DVR method is the DVR version of the CAP stabilization method initially proposed by Jolicard and Austin [Chem. Phys. Lett. 121, 106 (1985)]. In the present study, we show that this efficient and accurate method can also be applied within the adiabatic representation since it allows one to overcome in a simple way, numerical difficulties associated with the first derivative operator which appears in the expression of non adiabatic couplings. Within the OP-DVR method, the choice of the representation (diabatic or adiabatic) is governed by physical arguments and by the fact that the potentials and the couplings are known in one or the other of these two representations. In the case where the potentials and the couplings are obtained in the adiabatic representation, we show in this paper that the transformation into the diabatic framework is not necessary. We demonstrate that the discrete variable representation can be a simple and an efficient way to deal with the adiabatic representation. Received: 30 April 1998 / Revised: 29 September 1998 /Accepted: 21 October 1998     

原子双阱势中电子波包的非绝热操控

交叉电场和磁场中的氢原子具有双阱势能结构。本文基于量子力学模拟,采用半周期脉冲（HCP）序列开展电子波包的非绝热操控。详细研究了HCP的电场幅度、数量和时间间隔对电子波包的空间和能量分布的影响,实现了将初始电子波包非绝热转移到远离库伦中心的外势阱中的低能态,这些低能态较为稳定且显示出很大的电偶极矩。相比光激发和绝热操控,本文的方法更为快速、高效,可以应用于更为复杂的外场或分子体系。