Navigating localized wave packets in phase space

The ability to localize and to steer Rydberg wave packets in phase space using tailored sequences of half-cycle pulses is demonstrated. Classical phase-space portraits are used to explain the method and to illustrate the level of control that can be achieved. This is confirmed experimentally by positioning a phase-space-localized wave packet at the center of a stable island or navigating it around its periphery. This work provides a valuable starting point for further engineering of electronic wave functions.     

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.     

Dynamics of localized wave packets of rotational states of a molecule in a strong laser field

Numerical simulations are performed to examine the rotational dynamics of a molecule in a strong laser field when the molecular axis is initially oriented in a certain direction. The results obtained by solving the quantum-mechanical problem are compared with those computed in the framework of classical mechanics. It is found that certain characteristics of rotational motion cannot be described by classical theory, particularly for light molecules. It is demonstrated that the axis of a heteronuclear molecule can be reversed by tunneling.     

Resonance-assisted decay of nondispersive wave packets

We present a quantitative semiclassical theory for the decay of nondispersive electronic wave packets in driven, ionizing Rydberg systems. Statistically robust quantities are extracted combining resonance-assisted tunneling with subsequent transport across chaotic phase space and a final ionization step.     

State reconstruction of one-dimensional wave packets

76 , 1985 (1996)] for quantum-state reconstruction of one-dimensional non-relativistic wave packets from position observations. We illuminate the theoretical background of the technique and show how to extend the procedure to the continuous part of the spectrum. Received: 7 July 1997     

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.     

Transverse compression of two-photon wave packets

A method for generating two-photon wave packets (biphotons) with a small width of the spatial intensity correlation function (correlation radius) has been considered. We propose to prepare a two-photon wave packet inhomogeneously broadened in the angle by means of spontaneous parametric down-conversion in an inhomogeneous crystal. Such biphotons are not diffraction limited; i.e., their correlation radius is much larger than the inverse width of the spatial spectrum. However, the correlation radius of such a biphoton decreases as the biphoton propagates in free space, and transverse compression occurs at a certain distance from the crystal; i.e., the biphoton becomes diffraction limited.     

Aperiodic behaviour of baroclinic wave packets

The amplitude evolution equation for weakly non-linear wave packets in a continuously stratified and sheared baroclinic flow, in which both dissipation and dispersion effects are strong, is shown to be the generalised time-dependent Ginzburg-Landau equation. This equation possesses both periodic and aperiodic solutions, depending critically on parameter values.     

Semiclassical propagation of Gaussian wave packets

We analyze the semiclassical evolution of Gaussian wave packets in chaotic systems. We show that after some short time a Gaussian wave packet becomes a primitive WKB state. From then on, the state can be propagated using the standard time-dependent WKB scheme. Complex trajectories are not necessary to account for the long-time propagation. The Wigner function of the evolving state develops the structure of a classical filament plus quantum oscillations, with phase and amplitude being determined by geometric properties of a classical manifold.     

Nonspreading wave packets in quantum mechanics

In this paper a nonspreading, unnormalizable wave packet satisfying the Schrödinger equation is constructed. A modification of the Schrödinger equation is considered which allows the normalization of the wave packet. The case is generalized for relativistic mechanics.     

General quasi-nonspreading linear three-dimensional wave packets

We introduce a general approach for generation of sets of three-dimensional quasi-nonspreading wave packets propagating in linear media, also referred to as linear light bullets. The spectrum of rigorously nonspreading wave packets in media with anomalous group velocity dispersion is localized on the surface of a sphere, thus drastically restricting the possible wave packet shapes. However, broadening slightly the spectrum affords the generation of a large variety of quasi-nonspreading distributions featuring complex topologies and shapes in space and time that are of interest in different areas, such as biophysics or nanosurgery. Here we discuss the method and show several illustrative examples of its potential.     

From wave packets to stationary waves

Time-dependent Hartree-Fock solutions describing the scattering of heavy ions are used to generate stationary waves. The latter can then be inserted into the usual formula which defines the T-matrix.     

Creating and transporting Trojan wave packets

Nondispersive localized Trojan wave packets with n(i) ~ 305 moving in near-circular Bohr-like orbits are created and transported to localized near-circular Trojan states of higher n, n(f) ~ 600, by driving with a linearly polarized sinusoidal electric field whose period is slowly increased. The protocol is remarkably efficient with over 80% of the initial atoms being transferred to the higher n states, a result confirmed by classical trajectory Monte Carlo simulations.     

Forms of localization of Rydberg wave packets

A graphic method for describing the localization of quantum wave packets in several dimensions is proposed. The method employs classical action-angle coordinates. Different kind of wave packets arising in the two-and three-dimensional Coulomb problems are described from a unified point of view. Specifically, a more precise interpretation of the structure of “angular” Rydberg wave packets is given. Certain additional features of the proposed approach are discussed.