Structural Foundation and Geometry of the Material Singularity (and Its Quantum Entanglement)

In this paper we develop and study, as the second part of one more general development, the energy transmutation equation for the material singularity, previously obtained through the symmetrisation of a wave packet, that is, we develop the correlation between the terms of this equation, which accounts for the formation of matter from a previous vibrational state, and the different possible energy species. These energetic species are ascribed, in a simplified form, to the equation E¯ω=E¯k+E¯f, which allows us, through its associated phase factor, to gain an insight into the wave character of the kinetic energy and thus to attain the basis of the matter-wave, and all sorts of related phenomenologies, including that concerning quantum entanglement. The formation of the matter was previously identified as an energetic process, analogous to the kinetic one, in which finally the inertial mass is consolidated as a mass in a different phase, now, in addition, the mass of the material singularity is identified as a volumetric density of waves of toroidal geometry created in the process of singularisation or energy transfer between species, which makes it possible to establish the real relation or correspondence between the corpuscular and photonic energy equation (E=mc2=hν), i.e. to explain through m the intimate sense of the first equivalence, which explains what νis in the second one.

Observation of Quantum Beat in Rb by Parametric Four-Wave Mixing

Two coupled paralnetric four-wave-mixing processes in Rb atoms are studied using perturbation theory, which reveals clear evidence of tile appearance of quantum beat at 608cm^-1, corresponding to the energy difference of the 7s - 5d states of Rb atoms, in the parametric four-wave-mixing signals. A pump-probe technique is utilized to observe the quantum beat. Tinle-varying characteristics of the quantum beat are investigated using time-dependellt Fourier transform. The results show that the time-varying characteistics of the quantum beat not oldy offers a sensitive detecting method for observing the decay of atomic wave packets, but also provides a potential tool for monitoriHg the dissociation of molecules.

Autocorrelation Function of Hydrogen Atoms in Magnetic Fields

The autocorrelation function is an important quantity that can reflect the dynamical properties of the Rydberg wave packet and can be measured in experiments. Applying time-dependent perturbation theory and rotating wave approximation, we derive the autocorrelation function of the double-pulse laser describing the evolution of a Rydberg wave packet of hydrogen atoms in magnetic fields. The resulting expression is written as a sum of the modified Caussian terms. Each Caussian term comes from a parent semiclassical closed orbit. It provides a direct explanation and experimentally controllable measurement scheme, which allows us therefore to recognize the closed orbit and to determine its returning time in high precision.

Autler-Townes Splitting in Photoelectron Spectrum of Three-Level Li2 Molecule in Ultrashort Pulse Laser Fields

The Autler-Townes （AT） splitting in femtosecond photoelectron spectrum of three-level Li2 molecules is theoretically investigated using time-dependent quantum wave packet method. With proper femtosecond laser pulses, three peaks of the AT splitting can be observed in the photoelectron spectrum. The AT splitting stems from rapid Rabi oscillation caused by intense ultrashort laser pluses. The effects of laser parameters on the molecular ionization dynamics are also discussed.

Discrete Spectra and Continuous Spectrum of the BarotropicQuasi-Geostrophic Model-A Calculation ofMeteorological Data

Atmospheric disturbances at 300 hPa are decomposed into normal modes, referred as discrete—spectrum disturbances which can propagate freely in the observed zonal mean flow, and non—modal transient disturbances, referred as continuous—spectrum disturbances which are continuously sheared and eventually absorbed by the zonal flow. It is shown that normal modes represent only a small fraction of the observed atmospheric disturbances, while continuous—spectrum disturbances represent the majority of observed disturbances, even when the basic flow is unstable. Daily variabilities of the observed continuous—spectrum disturbances are presented. They are shown to follow the results of wave—packet theory. Calculations suggest that there are abundant sources to excite continuous—spectrum disturbances in the atmosphere.

Detection of Electronic Coherence via Two-Dimensional Electronic Spectroscopy in Condensed Phase

Two dimensional Fourier transforrn electronic spectroscopy （2DES） in the visible region enables direct observation of complex dynamics of molecules including quantum coherence in the condensed phase. This review aims to provide a bridge between the principles and intuitive physical description of 2DES for tutorial purpose. Special emphasis is laid upon how 2DES circumvents the restrictions from both uncertainty principle and the wave-packet collapse during the coherent detection, leading to the successful detection of the coherence in terms of energy difference between the eigenstates showing as the quantum beats; then upon the possible mixing among the pure electronic transition, single-rnode and multi-mode coupled vibronic transition leading to the observed beating phenomena. Finally, recent ad- vances in experimentally distinguishing between the electronic coherence and the vibrational coherence are briefly discussed.

Effect of Pulse Temporal Profile on Autler-Townes Splitting in Photoelectron Spectrum

The effect of pulse temporal profiles on the Autler-Townes （AT） splitting in photoelectron spectra is theoretically studied by employing the time-dependent wave packet method for a rotational Na2 molecule. The AT splitting which results from the sufficient Rabi oscillations is affected by the pulse profile and molecular alignment. The AT splitting may be observed only by utilizing proper pulse profiles with a certain intensity.

Time-dependent theoretical approach to the influence of laser fields on the resonance enhanced multi-photon ionization of SH radical

This paper reports that the （2＋1） resonance enhanced multi-photon ionization spectra of SH radical in external fields are simulated using the split-operator scheme of time-dependent wave-packet method. Two ionic states, i.e. a1△ and b1∑＋, are involved in the simulation. It gives the simulated photoelectron spectra, the population in each electronic state, as well as the projection of the wave-packet in each electronic state on different vibrational states. These results show that the so-called four-state model can represent the experimental results well.

Laser-induced Alignment and Coulomb Explosion of CO2

Dynamic processes of CO2 are experimentally studied in intense femtosecond laser fields with laser intensity varying from 1×10^13 W/cm^2 to 6×10^14 W/cm^2. When the laser intensity is below the ionization threshold, a coherent rotational wave-packet is formed for CO2 at room temperature through nonadiabatic rotational excitation. The evolution of the wave-packet leads to transient alignment. The field-free alignment revives periodically after the laser pulse is over. The revival structure can be modified by a second laser pulse for the rotational wave-packet through precisely adjusting the time delays between the two laser pulses. When the laser intensity excesses the ionization threshold, ionization and Coulomb explosion occur. The atomic ions C^m＋ （re=1-3） and On＋ （n=1-3） observed in the experiment exhibit highly anisotropic angular distributions relative to the laser polarization. Using two linearly polarized laser pulses with crossed polarization, we conclude that the anisotropic angular distribution results from dynamic alignment, in which the rising edge of the laser pulse aligns the neutral CO2 along the laser polarization direction prior to ionization.

Zitterbewegung of Dirac quasiparticles emerged in a Su-Schrieffer-Heeger lattice

We analytically and numerically investigate the dynamical properties of the tilted dispersion relativistic quasiparticles emerged in a cold atomic optical lattice system.By introducing the next nearest neighboring(NNN)hopping term into Su-Schrieffer-Heeger(SSH)model,the Dirac quasiparticles with tilted dispersion relation are realized.The results show that the tilted dispersion causes a drift in relativistic quasiparticles rather than affecting interference behavior between inner states.To be specific,the relativistic phenomena of the quasiparticles induced by the inner state interference(such as Zitterbewegung,Klein paradox,etc.)is completely unaffected by the tilted dispersion.In order to distinguish the drift induced by tilted dispersion and common initial velocity,we calculate the momentum distribution of the relativistic quasiparticles.We obtain the difference between the drift induced by initial velocity and tilted dispersion.The former affects the ZB,while the latter does not.By using this character,we propose a quench dynamics scheme to obtain a stable mono-spin state.The proposed cold atomic lattice system would provide a promising platform in exploring the intrinsic exotic physics of relativistic quasiparticles and the related systems.

State-to-state dynamics of reactions H+DH'(v=0,j=0)→HH'(v',j')+D/HD(v',j')+H'with time-dependent quantum wave packet method

State-to-state time-dependent quantum dynamics calculations have been carried out to study H+DH'→HH'+D/HD+H'reactions on BKMP2 surface.The total integral cross sections of both reactions are in good agreement with earlier theoretical and experimental results,moreover the rotational state-resolved reaction cross sections of H+DH'→HH‘+D at collision energy Ec=0.5 eV are closer to the experimental values than the ones calculated by Chao et al[J.Chem.Phys.1178341(2002)],which proves the higher precision of the quantum calculation in this work.In addition,the state-to-state dynamics of H+DH'→HD'+H reaction channel have been discussed in detail,and the differences of the micro-mechanism of the two reaction channels have been revealed and analyzed clearly.

Differential Cross Sections for the H＋D2O→HD＋OD Reaction： a Full Dimensional State-to-State Quantum Dynamics Study

The time-dependent wave-packet method was employed to calculate the first full-dimensional state-to-state differential cross sections （DCS） for the title reaction with D2O in the ground and the first symmetric （100） and asymmetric stretching （001） excited states. The calculated DCSs for these three initial states are strongly backward peaked at low collision energies. With the increase of collision energy, these DCSs become increasingly broader with the peak position shifting gradually to a smaller angle, consistent with the fact that the title reaction is a direct reaction via an abstraction mechanism. It is found that the （100） and （001） states not only have roughly the same integral cross sections, but also have essentially identical DCS, which are very close to that for the ground state at the same total energy of reaction. The reaction produces a small fraction of OD in the v=1 state, with the population close to the relative reactivity between the ground and vibrationally excited states, therefore confirming the experimental result of Zare et al. and the local mode picture [J. Phys. Chem. 97, 2204 （1993）]. Unexpectedly, the stretching excitation reduces the rotation excitation of product HD at the same total energy.

measurement weak repeatability covariant condition wave-packet collapse

The conflict between the dynamics postulate（unitary evolution） and the measurement postulate（wavepacket collapse） of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys.Rev. A 76（2007） 052110], and has further been extended to a more general scenario [Phys. Rev. A 87（2013） 052111].In this paper, we reconsider Zurek＇s new derivation by using weak repeatability postulate or covariant condition instead of repeatability postulate.

Quantum carpets:efficiently probing fractional revivals in position-dependent mass systems

Position-dependent-mass systems are of great importance in many physical situations,such as the transport of charge carriers in semiconductors with non-uniform composition and in the theory of many-body interactions in condensed matter.Here we investigate,numerically and analytically,the phenomenon of fractional revivals in such systems,which is a generic characteristic manifested by the wave-packet evolution in bounded Hamiltonian systems.Identifying the fractional revivals using specific probes is an important task in the theory of quantum measurement and sensing.We numerically simulate the temporal evolution of probability density and information entropy density,which manifest self-similarly recurring interference patterns,namely,quantum carpets.Our numerical results show that the quantum carpets not only serve as an effective probe for recognizing the fractional revivals of various order but they efficiently describe the effect of spatially-varying mass on the structure of fractional revivals,which is manifested as a symmetry breaking in their designs.

Time-dependent treatment of intramolecular energy transfer for HeICl complex

The time-dependent golden wave packet method has been used for calculating the decay widths of vibrational predissociation for HeICl complex in the B state with total angular momentum J=0. This is a good example of intramolecular energy transfer, We examine the dependence of the final rotational distribution (partial decay width) of ICI fragment an the stretching excitation. It is found that computed final rotational distributions are weakly dependent on the vibrational level being excited. Unlike the smoothly varying rotational distribution for lower initial vibrational levels, for higher initial vibrational levels the rotational distribution indicates the very pronounced oscillatory structure. The analysis of the rotational distribution as a function of propagation time reveals the predominant role of the final states interaction in determining the final rotational distribution.