Suppression of decoherence in a wave packet via nonlinear resonance

We propose a simple approach for suppressing decoherence of a wave packet excited in an anharmonic oscillator. We show that when a resonant external field forces the oscillator to follow the driving force, motion around the resonant trajectory inside a stable resonant island can be made almost completely immune to the environment. As an example, we study suppression of decoherence due to coupling to thermally populated rotations in vibrational wave packets in a Na2 molecule.     

Control the revisit time of the electron wave packet

Ionization of molecules by strong laser fields launches an electron wave packet. This electron wave packet, which can be driven back by the field to recollide with the parent ion, has been widely explored to probe the ultrafast nuclear dynamics. We numerically demonstrate the precise control of the temporal characteristic of the recolliding electron wave packet (REWP) by orthogonally polarized two-color fields. Through changing the relative phase of the two fields, the revisit time of REWP can be manipulated with a resolution of less than 200 attos, thus significantly improving the resolution of the well known molecular clock. This provides an efficient method for real-time observation of the ultrafast molecular dynamics with attosecond resolution.     

Time development of a wave packet and the time delay

A one-dimensional scattering problem off a δ-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schrödinger equation. The exact and explicit expression of the scattered wave packet supplies us with interesting information about the “time delay” by potential scattering in the asymptotic region. It is demonstrated that a wave packet scattered by a spin-flipping potential can give us quite a different value for the delay times from that obtained without spin-degrees of freedom.     

Preferred states of decoherence under intermediate system-environment coupling

The notion that decoherence rapidly reduces a superposition state to an incoherent mixture implicitly adopts a special representation, namely, the representation of preferred (pointer) states (PS). For weak or strong system-envrionment interaction, the behavior of PS is well known. Via a simple dynamical model that simulates a two-level system interacting with few other degrees of freedom as its environment, it is shown that even for intermediate system-environment coupling, approximate PS may still emerge from the coherent quantum dynamics of the whole system in the absence of any thermal averaging. The found PS can also continuously deform to expected limits for weak or strong system-environment coupling. Computational results are also qualitatively explained. The findings should be useful towards further understanding of decoherence and quantum thermalization processes.     

Tunnelling time of a gaussian wave packet through two potential barriers

The resonant and non-resonant dynamies of a Gaussian quantum wave packet travelling through a double barrier system is studied as a function of the initial characteristics of the spectrum and of the parameters of the potential. The behaviour of the tunnelling time shows that there are situations where the Hartman effect occurs, while, when the resonances are dominant, and in particular for b>π/Δk (b being the inter-barrier distance and Δk the spectrum width), the tunnelling time becomes very large and the Hartman effect does not take place.     

Delay time of electron wave packet through a two-dimensional semiconductor heterostructure

In this work, we systematically investigate the group delay time of an electron wave packet through a two-dimensional semiconductor heterostructure. It is shown that the lateral displacement, resulting from the angular spread of the electron wave packet, plays an important role in total delay time. In the propagating case, the group delay time can be negative due to the effect of lateral displacement, and is greatly enhanced by transmission resonances. In the evanescent case, the delay time saturates to a constant in the opaque limit, which is simply the Hartman effect observed for a two-dimensional situation.     

Microimplosions: cavitation collapse and shock wave emission on a nanosecond time scale

A streak camera with high spatial and temporal resolution was used for imaging the dynamics of the violent collapse in single-bubble sonoluminescence. The high pressure in the last phase of the bubble collapse leads to the emission of a shock wave, which is launched with a shock velocity of almost 4000 m/s. The shock amplitude decays much faster than approximately 1/r. From the strongly nonlinear propagation the pressure in the vicinity of the bubble can be calculated to be in the range of 40-60 kbar.     

Collapse of the wave packet without mixture

An explicit model of the quantum measurement process with determinstic dissipative dynamics is presented. The usual results of quantum mechanics are recovered, in complete compatibility with the realistic interpretation. The model exhibits the famous reduction of the wave packet and the occurrence of probability is explained as being due to a random correlation variable whose value is fixed at the very beginning of each of the individual processes. The way that the experimentalist observes the result has no effect on the final state of the system and, consequently, paradoxes like Schrödinger's cat or Wigner's friend are avoided.Partially supported by the Swiss National Science Foundation.     

Hamiltonian approach for wave packet dynamics: Beyond Gaussian wave functions

It is known that Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space. We construct several generalizations of this approach that include non-Gaussian wave packets. These generalizations lead to the further extension of the phase space while retaining the Hamilton structure of the equations of motion.     

Stochasticity,decoherence and an arrow of time from the discretization of time?

Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an arrow of time that follows from the fact that the replacement of the time derivative by the backward difference operator alone can preserve the non-negativity of the phase space density. It is seen that, even for free particles, all the degrees of freedom are correlated in principle. The forward evolution of functions of phase space variables by a finite number of time steps, in this discrete-time mechanics, depends on the entire continuous-time history in the interval [0, ∞]. In this sense, discrete time evolution is nonlocal in time from a continuous-time point of view. A corresponding quantum mechanical treatment is possible via the density matrix approach. The interference between nondegenerate quantum mechanical states decays exponentially. This decoherence is present, in principle, for all systems; however, it is of practical importance only in macroscopic systems, or in processes involving large energy changes.     

Isotope-selective femtosecond wave packet dynamics: The rare molecule

For the first time, the femtosecond real-time vibrational dynamics of the rare ^41,41K₂ isotope, excited to the electronic state, could be selectively studied by means of time-resolved three photon ionization. A vibrational period of fs is determined. Superimposed, a beat structure with a period of 20 ps is observed. A detailed Fourier analysis reveals a strong band of three lines centered around 65.5 cm^-1. A significant perturbation of the wave packet caused by spin-orbit coupling of the A and the crossing state is found. This perturbation is the reason for the fast dephasing of the initially generated wave packet within about 10 ps. The spectrogram of the real-time data shows total revivals of the wave packet at 20 ps and 40 ps. Fractional revivals are found for times around 10 ps and 30 ps. Due to high intensity effects a remarkable slightly broadened line at 90 cm^-1 appears and can be assigned to the wave packet propagation generated in the dimer's ground state by impulsive stimulated Raman scattering. Revivals of this ground state wave packet are found at 17ps and 34ps. A comparison with other isotopes of K₂ is given. Received: 9 February 1998 / Revised: 15 May 1998 / Accepted: 2 June 1998     

On the reality of supraluminal group velocity and negative delay time for a wave packet in a dispersion medium

It is shown that, in the case of the supraluminal group velocity of a wave packet in a dispersion medium, a wave packet with a smooth (analytical) envelope does propagate with a supraluminal velocity. In the case of a negative group velocity, the signal maximum does arrive at the detector earlier than at the transmitter. These facts are consistent with both the finiteness of the velocity of light in free space for information transfer (in the case of supraluminal propagation velocity) and the principle of causality (in the case of negative delay time). Basically, the effect of negative delay time may be employed for predicting an observable effect.     

Controlled splitting of an atomic wave packet

We propose a simple scheme capable of adiabatically splitting an atomic wave packet using two independent translating traps. Implemented with optical dipole traps, our scheme allows a high degree of flexibility for atom interferometry arrangements and highlights its potential as an efficient and high fidelity atom optical beam splitter.     

Non-linear wave packet dynamics of coherent states

We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.     

On the mass of a wave packet in plasma

The relativistic mass density which is transported by a quasi-monochromatic transverse wave packet is derived. The wave packet is assumed to propagate in isotropic cold collisionless plasma. The co-ordinate frame moving with the group velocity appears as the rest frame for both the mass density and the total mass of the wave packet. The equivalence of the energy-mass relation and the dispersion equation is demonstrated.     

Compatible statistical interpretation of a wave packet

A compatible statistical interpretation of a wave packet is proposed. De Broglian probabilities which unite wave and particle features of quantons are evaluated for free wave packets and Jor a superposition of wave packets. The obtained expressions provide a very plausible and physically appealing explanation of coherence in apparently incoherent beams and of the characteristic modulation of the momentum distribution, found recently in neutron interferometry combined with spectral filtering. Certain conclusions about dualism and objectivity in quantum domain are also derived.     

Gaussian wave packet states of relic gravitons

In this contribution, we investigate quantum effects of relic gravitons in a Friedmann–Robertson–Walker (FRW) cosmological background. We reduce the problem to that of a generalized time-dependent harmonic oscillator and find the corresponding exact Schrödinger states with the help of linear invariants and of the dynamical invariant method. Afterwards, we construct Gaussian wave packet states and calculate the quantum dispersions as well as the quantum correlations for each mode of the quantized field.     

Proposed experimental test of wave packet reduction and the uncertainty principle

A practical experiment using coincidence techniques is suggested to test the validity of the following concepts:(1) wave packet reduction and(2) the measurement-uncertainty principle for position and momentum. The suggested experiment uses the time-of-flight method to determine an electron's momentum and a coincident photon, emitted from a system excited by the electron, to determine its initial position. It is shown that this method does constitute a simultaneous measurement of position and momentum for a single system. Also, it is pointed out that the traditional statement of the measurementuncertainty principle must be slightly modified even within the Copenhagen interpretation of quantum mechanics.Work supported by the Leverhulme Trust Foundation and the National Aeronautics and Space Administration under Grant No. NSG-1378.