Shape Of Wave Packet Research Articles

Nuclear wave-packet dynamics in the localized excitons of halogen-bridged platinum complexes

The luminescence of self-trapped excitons in halogen-bridged platinum complexes [Pt(en) 2] [Pt(en) 2X 2](ClO 4) 4 (en=ethylenediamine, X=Br, Cl) has been studied by means of femtosecond up-conversion techniques. The time evolution of the nuclear wave-packet shape is visualized for a Pt–Br system and interpreted in terms of a harmonic-oscillator model.

Nonperturbative approach for a time-dependent quantum mechanical system

We present a variational method which uses a quartic exponential function as a trial wave-function to describe time-dependent quantum mechanical systems. We introduce a new physical variable $y$ which is appropriate to describe the shape of wave-packet, and calculate the effective action as a function of both the dispersion $\sqrt{< \hat{q}^2>}$ and $y$. The effective potential successfully describes the transition of the system from the false vacuum to the true vacuum. The present method well describes the long time evolution of the wave-function of the system after the symmetry breaking, which is shown in comparison with the direct numerical computations of wave-function.

General formulation of locally designed coherent control theory for quantum system

A general local control theory for manipulating quantum system dynamics is developed. Basic concept of the present theory is lying in the realization of monotonous increasing condition of the performance index, which is locally (in time domain) defined to major how the present quantum state satisfies the current objective. The local control field is designed to satisfy the above condition taking into account the equation of motion of the system. It is found, through the formulation, that the monotonous increasing condition can be achieved as long as the performance index is given as a function of expectation values of time-dependent observable operators, whose equation of motion is governed by the field-free system Hamiltonian or Liouvillian. It is also shown that the present theory is a generalization of the local optimization approach which has been successfully applied to many of molecular dynamics control problems. As for the special cases, performance indices for “transition path control,” “population distribution control,” and “wave packet shaping” are proposed. The theory is applied to vibrational control problems of the one-dimensional model system of hydrogen fluoride. The results show that the present method works effectively for the population dynamics control as well as the wave packet shaping.

Quantum optimal control of wave packet dynamics under the influence of dissipation

Optimal control within the density matrix formalism is applied to the production of desired non-equilibrium distributions in condensed phases. The time evolution of a molecular system modeled by a displaced harmonic oscillator is assumed to be described by the Markoffian master equation with phenomenological relaxation parameters. The physical objectives of concern are the creation of a specified vibronic state, population inversion and wave packet shaping. The effects of an initial thermal distribution and dissipation on these targets are examined. In order to transfer a large amount of population (i.e., the strong-field regime) to a target wave packet in an electronic excited state, it is shown that creating a shaped packet in the ground state is often required to achieve high yield. This control pathway cannot be taken into account within the weak-field approximation, and is especially important when the target state includes vibrational states that are weakly accessible from the initial state or that have preferential indirect excitation paths from the initial state. Although relaxation effects usually reduce the control efficiency, under certain conditions, the bath-induced dynamics can help to create an objective state.

Using feedback for coherent control of quantum systems

A longstanding goal in chemical physics has been the control of atoms and molecules using coherent light fields. This paper provides a brief overview of the field and discusses experiments that use a programmable pulse shaper to control the quantum state of electronic wavepackets in Rydberg atoms and electronic and nuclear dynamics in molecular liquids. The shape of Rydberg wavepackets was controlled by using tailored ultrafast pulses to excite a beam of caesium atoms. The quantum state of these atoms was measured using holographic techniques borrowed from optics. The experiments with molecular liquids involved the construction of an automated learning machine. A genetic algorithm directed the choice of shaped pulses which interacted with the molecular system inside a learning control loop. Analysis of successful pulse shapes that were found by using the genetic algorithm yield insight into the systems being controlled.

Variational dynamics of Bose-Einsteincondensates in deep optical lattices

We study the dynamics of a Bose-Einstein condensatewavepacket trapped in an optical lattice. In the tight-bindinglimit, the system maps onto a discrete nonlinear Schrödingerequation. Using a collective coordinate approximation, weinvestigate different dynamical regimes: diffusive (in whichthe boson wavepacket spreads out), self-trapped (with aself-induced pinning), breathing (where the centre of mass ofthe wavepacket moves with an oscillating width), and solitonic(in which the wavepacket shape is exactly preserved duringthe dynamics).

Propagation of wave packets in randomly stratified media.

The propagation of a narrow-band signal radiated by a point source in a randomly layered absorbing medium is studied asymptotically in the weak-scattering limit. It is shown that in a disordered stratified medium that is homogeneous on average, a pulse is channelled along the layers in a narrow strip in the vicinity of the source. The space-time distribution of the pulse energy is calculated. Far from the source, the shape of wave packets is universal and independent of the frequency spectrum of the radiated signal. Strong localization effects manifest themselves also as a low-decaying tail of the pulse and a strong time delay in the direction of stratification. The frequency-momentum correlation function in a one-dimensional random medium is calculated.

Study ofthe single-band Bloch oscillation effect with the pseudo-spectralmethod

Using the pseudo-spectral method for wave-packet evolution, we formulate and implement a new theoretical approach for studying the Bloch oscillation effect in a general number of dimensions. For this purpose, a novel recursive formula is obtained in the representation of Wannier functions for the infinitesimal time evolution of an electronic wave packet within the single-band approximation. This formula is valid for general position-dependent applied electric fields and arbitrary initial wave-packet shapes and crystal structures, and can also be generalized for time-dependent fields. For a tight-binding simple `cubium' band, the infinitesimal time evolution can always be expressed in terms of Bessel functions of integer order; and for the `empty-lattice model' band it can be expressed in terms of Fresnel functions for arbitrary electric fields also. As a further analytical application of our formalism, we derive an exact (finite-time) wave-packet evolution for the homogeneous and static electric field in the simple `cubium' band. For this case, an estimate of the numerical error of the pseudo-spectral method is obtained for the mean position of the wave packet. As an illustrative example of the numerical implementation of our theoretical formalism, we present a simple one-dimensional numerical simulation for a Gaussian wave packet moving in a parabolic potential well. Finally, a general proof of the unitarity of the predicted time evolution is also presented, and different properties of our formalism pointed out.

Quantum control of nuclear wave packets by locally designed optimal pulses

A new approach to locally design a control pulse is proposed. This locally optimized control pulse is explicitly derived, starting with optimal control formalism, and satisfies the necessary condition for a solution to the optimal control problem. Our method requires a known function, g(t), a priori, which gives one of the possible paths within the functional space of the objective functional. A special choice of g(t)≡0 reduces the expression of the control pulse to that derived by Kosloff et al. For numerical application, we restrict ourselves to this special case; however, by combining an appropriate choice of the target operator together with the backward time-propagation technique, we apply the local control method to population inversion and to wave packet shaping. As an illustrative example, we adopt a two-electronic-surface model with displaced harmonic potentials and that with displaced Morse potentials. It is shown that our scheme successfully controls the wave packet dynamics and that it can be a convenient alternative to the optimal control method for wave packet shaping.

Wave packet tunneling

AbstractThe tunneling of Gaussian wave packets has been investigated by numerically solving the one‐dimensional Schrödinger equation. The shape of wave packets interacting with a square barrier has been monitored for various values of the barrier width, height and initial width of the wave packet. Compared to the case of free propagation, the maximum of a tunneled wavepacket exhibits a shift, which can be interpreted as an enhanced velocity during tunneling.

Wave packet tunneling

The tunneling of Gaussian wave packets has been investigated by numerically solving the one-dimensional Schrödinger equation. The shape of wave packets interacting with a square barrier has been monitored for various values of the barrier width, height and initial width of the wave packet. Compared to the case of free propagation, the maximum of a tunneled wavepacket exhibits a shift, which can be interpreted as an enhanced velocity during tunneling.

Beyond MGR: Wave packet squeezing

The MGR scenario for Electron-Stimulated Desorption proved to be a very fruitful model allowing for theoretical interpretation for a broader class of desorption experiments than originally intended. New experimental tools and techniques require, however, considering alternative scenarios to interpret the results. Depending on one's preferences, almost all of them can either be considered as genuinely new ones or merely an MGR in disguise. I am concentrating here on one such scenario, the Wave Packet Squeezing model, which was invoked recently to account for the experimental features of ESD of physisorbed atoms from metal surfaces which the Antoniewicz version of the MGR model cannot deal with. Time evolution of the wave packet shape rather than that of its position is seen as the most important feature of the desorption process. It is shown that wave packet squeezing in three dimensions may affect drastically the angular as well as the kinetic energy distributions of particles desorbing in the direction of the surface normal. Several examples of the wave packet spreading/squeezing scenarios, invoked recently by other researchers in the context of rotational distributions of desorbing molecules, are also briefly discussed.

Field structure of collapsing wave packets in 3D strong Langmuir turbulence.

A simple model is constructed for the electric fields in the collapsing wave packets found in 3D simulations of driven and damped isotropic strong Langmuir turbulence. This model, based on a spherical-harmonic decomposition of the electrostatic potential, accounts for the distribution of wave-packet shapes observed in the simulations, particularly the predominance of oblate wave packets. In contrast with predictions for undamped and undriven subsonic collapse of scalar fields, oblate vector-field wave packets do not flatten during collapse but, instead, remain approximately self-similar and rigid.

Resonantly scattered wave packets

The effect of a resonant scattering on the shape of a (spherical) wave packet is investigated for the illustrative case of an incident packet Lorentzian in momentum. In the elastic case, packets both broader and narrower than the resonance are considered, and the relation of their time-delays to the Wigner-Eisenbud estimate elucidated. The effects on the elastically-scattered packet of (a) a double-pole resonance and (b) inelasticity are obtained as well.