Spatiotemporal imaging of ultrafast molecular motion: collapse and revival of the D+2 nuclear wave packet

We report on a real-time imaging of the ultrafast D(+)2 rovibrational nuclear wave-packet motion performed using a combination of a pump-probe setup with 7 fs laser pulses and a "reaction-microscope" spectrometer. We observe fast dephasing (collapse) of the vibrational wave packet and its subsequent revival and prove rotational excitation in ultrashort laser pulses. Channel-selective Fourier analysis of the wave packet's long-term (approximately 3000 fs) evolution allows us to resolve its individual constituents, revealing unique information on the mechanisms of strong-field ionization and dissociation.     

Wave packets in the quantum theory of collisions

Two methodological difficulties of the quantum theory of collisions are considered. The first is the undesirable interference of the incident and scattered waves in the stationary approach to scattering. The second concerns the nonstationary approach to the theory of collisions of the type a + b → c + d. In order to calculate the cross section one uses the matrix element 〈cd|S|ab〉 of the S-matrix. The element is proportional to δ-function expressing the energy conservation. The corresponding probability |〈cd|S|ab〉|² contains δ², which is mathematically meaningless. The known regular way to overcome the difficulty seems to be unsatisfactory. In this paper, both the problems are resolved using wave packets of incident particles. The text was submitted by the author in English.     

Slowing down of the wave packets in quantum graphs

Necklace-type devices are studied, which are optical lines with periodically located segments replaced by two arches of different lengths. It is shown that one can choose parameters of the necklace in such a way that the dispersion relation for the whole line will be very flat in the neighbourhood of the prescribed frequency (although the corresponding band is not narrow). It is also shown that a finite piece of such a line creates a slowdown of wave packets without any significant loss of the energy due to the reflection.     

Slowing down of the wave packets in quantum graphs

Necklace-type devices are studied, which are optical lines with periodically located segments replaced by two arches of different lengths. It is shown that one can choose parameters of the necklace in such a way that the dispersion relation for the whole line will be very flat in the neighbourhood of the prescribed frequency (although the corresponding band is not narrow). It is also shown that a finite piece of such a line creates a slowdown of wave packets without any significant loss of the energy due to the reflection.     

外电场作用下平面转子Rydberg波包的演化和恢复

利用Rydberg波包分析量子力学体系的动力学行为是研究经典力学和量子力学的对应关系的一个非常重要的方法.本文主要研究了在外电场作用下平面转子的Rydberg波包的演化和恢复结构.结果表明:在弱电场作用下,波包仍可周期性的坍塌和恢复,但在强电场作用下,平面转子的Rydberg波包演化结构则与谐振子的相符.     

On the collapse of wave packets in a medium with normal group velocity dispersion

A solution to the problem of realizing the collapse of three-dimensional wave packets in nonlinear media with normal group velocity dispersion is proposed. Wave packets with pronounced hyperbolic topology are shown to collapse; i.e., the field increases infinitely near the system axis. In particular, wave collapse of the tubular axisymmetric packets occurs through the concentration of the compressed ring field distribution at the axis. The collapse is shown to stabilize due to the saturation of nonlinearity or nonlinear dissipation, which restrict the field increase and lead to the packet splitting in the transverse direction.     

Wave packet revivals and the energy eigenvalue spectrum of the quantum pendulum

The rigid pendulum, both as a classical and as a quantum problem, is an interesting system as it has the exactly soluble harmonic oscillator and the rigid rotor systems as limiting cases in the low- and high-energy limits, respectively. The energy variation of the classical periodicity (τ) is also dramatic, having the special limiting case of τ→∞ at the ‘top’ of the classical motion (i.e., the separatrix.) We study the time-dependence of the quantum pendulum problem, focusing on the behavior of both the (approximate) classical periodicity and especially the quantum revival and superrevival times, as encoded in the energy eigenvalue spectrum of the system. We provide approximate expressions for the energy eigenvalues in both the small and large quantum number limits, up to fourth order in perturbation theory, comparing these to existing handbook expansions for the characteristic values of the related Mathieu equation, obtained by other methods. We then use these approximations to probe the classical periodicity, as well as to extract information on the quantum revival and superrevival times. We find that while both the classical and quantum periodicities increase monotonically as one approaches the ‘top’ in energy, from either above or below, the revival times decrease from their low- and high-energy values until very near the separatrix where they increase to a large, but finite value.     

Two-pulse nondegenerate excitation of electron-hole wave packets in quantum wells: tunable terahertz emission

It was shown recently that driving an optically excited quantum well with a terahertz (THz) frequency electric field can lead to higher-harmonic generation in the THz regime: the THz analog of the dynamic Franz-Keldysh effect. We propose a new double-pulse excitation method that not only increases the efficiency of the harmonic generation but is also able to control somewhat the dominant upshifted harmonic of the THz radiation by means of selective excitation of spatially chosen electron-hole relative motion wave packets.     

Wave packet reduction in quantum mechanics: A model of a measuring apparatus

We investigate the problem of wave packet reduction in quantum mechanics by solving the Schrödinger equation for a system composed of a model measuring apparatusM interacting with a microscopic objects. The instrument is intended to be somewhat more realistic than others previously proposed, but at the same time still simple enough to lead to an explicit solution for the time-dependent density matrix. It turns out that,practically, everything happens as if the wave packet reduction had occurred. This is a consequence of the fact that the apparatus is made up of a very large number of microsystems interacting withs. More precisely, our model shows that the macroscopic size of a measuring apparatus can lead by itself to a density matrix for the systemM + s which is physically equivalent to the density matrix of a statistical mixture corresponding to the reduced wave packet.     

Relativistic wave packets in the quantum field approach to the theory of neutrino oscillations

A covariant theory of wave packets and its application to the quantum field method of calculation of the probabilities of neutrino oscillations in vacuum that is based on the technique of macroscopic Feynman diagrams, which describe the processes of emission and absorption of virtual massive neutrinos ν _i (i = 1, 2, 3) at macroscopicly separated space-time points, is considered. The effect of flavor oscillations is reduced to an interference of amplitudes with different vi in an intermediate state. A macroscopic amplitude is calculated that describes a class of processes which go with nonconservation of leptonic numbers, and statistical averaging of the squared modulus of this amplitude is performed. The averaged probability of a process with ultrarelativistic neutrino exchange is representable in the form of an integral of the product of three factors: the flux of massless neutrinos from the source, the differential cross-section for the interaction of a neutrino with the detector, and a dimensionless factor that describes the flavor transition. The conditions under which the last factor can be interpreted as the probability of the flavor transition in the conventional quantummechanical sense are analyzed.     

Propagation of arbitrary initial wave packets in a quantum parametric oscillator: Instability zones for higher order moments

We consider the dynamics of a particle in a parametric oscillator with a view to exploring any quantum feature of the initial wave packet that shows divergent (in time) behaviour for parameter values where the classical motion dynamics of the mean position is bounded. We use Ehrenfest's theorem to explore the dynamics of nth order moment which reduces exactly to a linear non autonomous differential equation of order $n+1$. It is found that while the width and skewness of the packet is unbounded exactly in the zones where the classical motion is unbounded, the kurtosis of an initially non-gaussian wave packet can become infinitely large in certain additional zones. This implies that the shape of the wave packet can change drastically with time in these zones.     

Pure states,mixtures, and reduction of the wave packet

The usual distinction in quantum mechanics between pure states and mixtures is shown not to be independent of the interpretation adopted. Thus, in a causal theory, certain states should be regarded as sharing the nature of both pure states and mixtures and, as a result, important questions in the theory of measurement must be considered in a different light.Associated with CNRS     

Deformations and dilations of chaotic billiards: dissipation rate, and quasiorthogonality of the boundary wave functions

We consider chaotic billiards in d dimensions, and study the matrix elements M(nm) corresponding to general deformations of the boundary. We analyze the dependence of |M(nm)|(2) on omega = (E(n)-E(m))/Planck's over 2pi using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency omega. We show that, for dilations and translations of the boundary, |M(nm)|(2) vanishes like omega(4) as omega-->0, for rotations such as omega(2), whereas for generic deformations it goes to a constant. Such special cases lead to quasiorthogonality of the eigenstates on the boundary.     

Dynamics of a wave packet in a system with a quantum dot in the Coulomb blockade regime

The nonstationary problem of electron tunneling through a quantum dot in the Coulomb block-ade regime is studied. The temporal Schrödinger equation is solved and the dynamics of the wave packet in a system consisting of a quantum dot connected to two one-dimensional contacts is investigated. The transmission coefficient is calculated. Dependences of the transmission on the tunneling electron energy are constructed.     

k光子Jaynes—Cummings模型中原子的相干性对崩溃和再生现象的影响

研究了k光子Jaynes-Cummings模型中原子的相干性对崩溃和再生现象的影响,结果表明,原子的反转依赖原子和场的初始相位.     

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.