Harmonic mixing in the classical charge density wave model above threshold

The third order response properties of the classical model for charge transport by charge density waves above the conductivity threshold are investigated analytically. The model is isomorphic to that of a resistively shunted Josephson circuit (RSJ model) and thus exhibits an oscillating solution above a threshold electric driving field with a characteristic internal frequencyω _ph . By a systematic perturbation expansion in powers of the perturbing field strengths thedc response of the time varying state to twoac fields of frequencies ω and 2ω is evaluated. This determines the harmonic mixing signal (HMS) as a third order response. The general formula is explicitly evaluated far above threshold giving a result similar to the Kanter-Vernon formula for the rectified signal in second order. In addition to the resonance atω _ph =ω a second resonance is found atω _ph =2ω. A characteristic feature for the HMS above threshold is the absence of an out of phase component, i.e. the internal phase shift is zero.     

Laser-induced excitation of electronic rydberg wave packets

We give a qualitative review of theoretical ideas and experimental work on laser-induced excitation of atomic Rydberg wave packets. Studying the motion of Rydberg wave packets with the help of short or intense laser pulses provides a bridge between quantum mechanics and the classical concept of the trajectory of an electron and corresponds to the real-time observation of atomic dynamics.     

Recovery time in quantum dynamics of wave packets

A wave packet formed by a linear superposition of bound states with an arbitrary energy spectrum returns arbitrarily close to the initial state after a quite long time. A method in which quantum recovery times are calculated exactly is developed. In particular, an exact analytic expression is derived for the recovery time in the limiting case of a two-level system. In the general case, the reciprocal recovery time is proportional to the Gauss distribution that depends on two parameters (mean value and variance of the return probability). The dependence of the recovery time on the mean excitation level of the system is established. The recovery time is the longest for the maximal excitation level.     

Nondispersive wave packets as solitonic solutions of level dynamics

We discuss the analogy between nondispersive wave packets in periodically driven hydrogen atoms and solitons as solitary wave solutions of nonlinear dynamical systems. Whereas the wave packet eigenstates should not be considered as solitons propagating in real space, they are shown to display the essential features of solitonic solutions as they propagate through the irregular lattice of quasienergy levels evolving with a fictitious time like the strength or the frequency of the driving force.     

Nonlinear space-time dynamics of ultrashort wave packets in water

We have monitored the space-time transformation of a 150-fs pulse undergoing self-focusing and filamentation in water, by means of the nonlinear gating technique. We have observed that pulse splitting and subsequent recombination apply to axial temporal intensity only, whereas the space-integrated pulse profile preserves its original shape.     

Zitterbewegung of electronic wave packets in III-V zinc-blende semiconductor quantum wells

We study the zitterbewegung of electronic wave packets in III-V zinc-blende semiconductor quantum wells due to spin-orbit coupling. Our results suggest a direct experimental proof of this fundamental effect, confirming a long-standing theoretical prediction. For electron motion in a harmonic quantum wire, we numerically and analytically find a resonance condition maximizing the zitterbewegung.     

Invariants of the dynamics of molecular vibrational wave packets in phase modulation

An exact analytic solution was obtained for the correlation function of the motion of a phase-modulated Gauss wave packet in an anharmonic potential. The solution is expressed through the theta-function with the parameters depending on both the potential and phase modulation of the initial wave packet. Changes in both linear and quadratic chirps result in an invariant correlation function time shift in a weakly anharmonic potential with the conservation of all the total and fractional revivals. At a strong potential anharmonicity, translational invariance with respect to a quadratic chirp is preserved in certain instances, whereas the dynamics of packets experiences qualitative changes depending on linear phase modulation. This approach can be used to qualitatively analyze intramolecular dynamics if the potential energy surface is not known exactly, which is especially useful for quantum control of large molecules, in particular, photochromes.     

Holography of wave packets

We describe the principles of holographic storage and reconstruction of ultrashort light pulses using spectrally nonselective media. This can be achieved by the application of a 3-D recording medium and by the holography of waves produced by spatial spectral decomposition of light pulses. We also describe various transformations of optical temporal signals based on holographic spectral filtering and nonlinear interaction of spectral decomposition waves.     

On the theory of wave packets

In this paper we discuss some aspects of the theory of wave packets. We consider a popular noncovariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic particles. We revise this approach by considering a covariant model of Gaussian wave packets, and examine our results by inspecting a wave packet of arbitrary form. A general formula for the time dependence of the dispersion of a wave packet of arbitrary form is found. Finally, we give a transparent interpretation of the disappearance of the wave function over time due to the dispersion—a feature often considered undesirable, but which is unavoidable for wave packets. We find, starting from simple examples, proceeding with their generalizations and finally by considering the continuity equation, that the integral over time of both the flux and probability densities are asymptotically proportional to the factor 1/|x|² in the rest frame of the wave packet, just as in the case of an ensemble of classical particles.     

Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics

Ultrafast atomic processes, such as excitation and ionization occurring on the femtosecond or shorter time scale, were explored by employing attosecond high-harmonic pulses. With the absorption of a suitable high-harmonic photon a He atom was ionized, or resonantly excited with further ionization by absorbing a number of infrared photons. The electron wave packets liberated by the two processes generated an interference containing the information on ultrafast atomic dynamics. The attosecond electron wave packet, including the phase, from the ground state was reconstructed first and, subsequently, that from the 1s3p state was retrieved by applying the holographic technique to the photoelectron spectra comprising the interference between the two ionization paths. The reconstructed electron wave packet revealed details of the ultrafast photoionization dynamics, such as the instantaneous two-photon ionization rate.     

Theory of dynamics of electron wave packets in time-resolved two-photon photoemission via image states

Time-resolved two-photon photoemission (TR2PPE) from the Cu(100) surface is investigated by the Keldysh Green function method in order to analyze ultrafast dynamics of an electron wave packet in the image states of the surface. By numerical analysis, the quantum beats in the TR2PPE spectrum due to interference among the image states are reproduced, and the motion of the electron wave packet in front of the surface is demonstrated. It is discussed on the basis of the obtained results as to how the motion of the electron wave packet is evaluated from the TR2PPE spectrum.