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.     

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.     

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.     

Realization of localized Bohr-like wave packets

We demonstrate a protocol to create localized wave packets in very-high-n Rydberg states which travel in nearly circular orbits around the nucleus. Although these wave packets slowly dephase and eventually lose their localization, their motion can be monitored over several orbital periods. These wave packets represent the closest analog yet achieved to the original Bohr model of the hydrogen atom, i.e., an electron in a circular classical orbit around the nucleus. The possible extension of the approach to create "planetary atoms" in highly correlated stable multiply excited states is discussed.     

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.     

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.     

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.     

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.     

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.     

Velocity locking of incoherent nonlinear wave packets

We show both theoretically and experimentally in an optical fiber system that a set of incoherent nonlinear waves irreversibly evolves to a specific equilibrium state, in which the individual wave packets propagate with identical group velocities. This intriguing process of velocity locking can be explained in detail by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the selection of the velocity-locked state is shown to result from the natural tendency of the isolated wave system to approach the state that maximizes the nonequilibrium entropy.     

Nondiffracting accelerating wave packets of Maxwell's equations

We present the nondiffracting spatially accelerating solutions of the Maxwell equations. Such beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams to the full domain of the wave equation. For both TE and TM polarizations, the beams exhibit shape-preserving bending which can have subwavelength features, and the Poynting vector of the main lobe displays a turn of more than 90°. We show that these accelerating beams are self-healing, analyze their properties, and find the new class of accelerating breathers: self-bending beams of periodically oscillating shapes. Finally, we emphasize that in their scalar form, these beams are the exact solutions for nondispersive accelerating wave packets of the most common wave equation describing time-harmonic waves. As such, this work has profound implications to many linear wave systems in nature, ranging from acoustic and elastic waves to surface waves in fluids and membranes.     

Anomalous spreading of power-Law quantum wave packets

We introduce power-law tail quantum wave packets. We show that they can be seen as eigenfunctions of a Hamiltonian with a physical potential. We prove that the free evolution of these packets presents an asymptotic decay of the maximum of the wave packets which is anomalous for an interval of the characterizing power-law exponent. We also prove that the number of finite moments of the wave packets is a conserved quantity during the evolution of the wave packet in the free space.     

Non-linear distortion of ion acoustic wave packets

Non-linear ion acoustic waves are excited by a positive voltage step applied on a grid in a quiescent plasma. The distortion of the excited wave packet during propagation agrees with Ichikawa and Taniuti's theory.