A model that has previously been used to calculate the molecular orbitals in atomic collisions between neutral atoms and ions is extended to describe hollow atoms colliding with a solid. The energy levels and screening functions are obtained from density-functional calculations. The results show that the inner-shell holes in the hollow projectile, as well as the screening cloud within the solid, create important effects that are essential for the description of the interaction of multicharged ions with solids.

We investigate the convergence of diabatic scattering representations that make use of the commonly applied closure relation (which eliminates first and second derivative coupling terms from the Schrödinger equation for the scattering wave function) to the adiabatic scattering formulations from which they are derived (wherein the internal basis states depend upon the collision coordinate). Numerical examples using a simple model of electron transport in a tapered waveguide are presented. The convergence of the diabatic to the adiabatic results with respect to the number of basis states is extremely slow. We discuss the significance of these findings to atomic and molecular scattering calculations.

The interaction of a ${\mathrm{C}}_{60}$ cluster with a Lindhard gas of electrons at a density near that of the valence electrons of aluminum is calculated. The calculation includes the charge-state evolution of the ion fragments, the disintegration dynamics, and the interference effects of neighboring ions on the energy loss. Enhancement in the energy loss is calculated and it is predicted that this can be observed experimentally for sufficiently thin targets. In addition, the dependence of the energy-loss enhancement was studied as a function of cluster kinetic energy and target density.

We study the classical, semiclassical, and quantum dynamics of parabolic Rydberg states of hydrogen subject to half-cycle electromagnetic pulses as a function of the field strength and the duration of the pulses. We show that for the most ‘‘red-shifted’’ Stark state the quantum ionization probability oscillates around the classical value. These oscillations can be described semiclassically in terms of path interference. By contrast, the ionization probability of the extreme ‘‘blue-shifted’’ state is a smooth function of field strength. These predictions could be tested experimentally.

High-order frequency mixing experiments using the radiation of a high-power Ti:sapphire laser and its second harmonic are described and discussed. Linearly and circularly polarized light fields with comparable intensities have been used. For the theoretical description a three-dimensional quantum-mechanical calculation with a δ-function potential has been applied, showing quite good agreement with the experiments.

We report observations of the ellipticity dependence of harmonic generation in a thin layer of neon gas at an intensity of ${10}^{15}$ W/${\mathrm{cm}}^2$ and a wavelength of 7540 Å. We observe a markedly different ellipticity dependence and polarization for harmonic energies below and above the ionization potential of neon (21.56 eV). The ellipticity dependence of the higher harmonics can be understood in terms of free-bound transitions of ionizing electrons within the first cycle of the fundamental subsequent to tunnel ionization, while other mechanisms must be invoked to explain the characteristics of the lower harmonics.

It is shown that the weak anisotropy of a nonlinear medium with periodically varying parameters supports the propagation of vector gap solitons. They are governed by the same coupled nonlinear Schrödinger equations as solitons in birefringent optical fibers. If the frequency of the incoming radiation coincides with a stop gap edge the frequencies of the two mutually orthogonal polarizations of the electromagnetic field are tuned to and out of the gap.

The linear and nonlinear properties of propagation of an electromagnetic field through a medium may be derived by the effective elimination of the medium from the coupled Maxwell-Bloch equations. In this paper we suggest, on the other hand, the elimination of the field from the Maxwell-Bloch equations as a means to derive a nonlinear master equation for, e.g., an atomic sample in a laser field. This presents a straightforward and physically intuitive derivation of equations for ‘‘nonlinear atom optics,’’ obtained recently by other approaches.

Sub-Poissonian pulses of light are generated by means of traveling-wave optical parametric deamplification. Upon direct detection the quantum noise on the deamplified pulses is measured to be below the shot-noise limit by as much as 0.5±0.2 dB (11±4 %). The parametric-gain dependence of the measured Fano factor—direct-detection noise as a fraction of the shot-noise limit—agrees with the quantum theory of the amplifier when diffraction effects are taken into account.

We have discovered that the polarization of high harmonics generated by intense, short, elliptically polarized laser pulses is rotated with respect to the incident laser polarization. This strong-field effect is a test of models of intense laser-atom processes.

Phase-space-interference approaches employ interference on the phase plane to explain a quantum state’s photon-number distribution. This paper generalizes the approach so that knowledge of the photon-number distribution explains the state’s quantum phase-plane distribution. The required generalization is as follows. The Bohr-Sommerfeld ‘‘band’’ or trajectory of the mixture of number states ∼(‖N〉〈N‖+‖M〉〈M‖) consists of two annuli centered on the origin. In contrast, the trajectory of the pure number state superposition ∼(‖N〉+‖M〉) (with M>N) contains additional interference structures, namely, (M-N) symmetrically positioned radial spokes connecting the annuli. These spokes intersect the circular band attributed to a photon-number state at (M-N) locations, with the resulting destructive interference eliminating states ‖N+1〉 to ‖M-1〉. These structures build state phase-plane quantum probability distributions, as we illustrate for the squeezed vacuum. This state is missing every odd-numbered photon number state, and thus its trajectory consists of a repeated pattern of two heavily emphasized bars eliminating every odd-numbered state. These bars sum to generate the traditional ‘‘cigar’’ shape of the squeezed state.

The quantum-mechanical operators that represent the radiation pressure on a perfect mirror are determined. It is shown that these operators reproduce the known forms of the mean and the variance of the Casimir force from the vacuum field on a perfect mirror when a suitable time average is taken. The mean and the variance of the radiation pressure are increased in the presence of an incident light beam. These quantities are determined here for optical pulses of coherent, chaotic, and number-state light, again with suitable time averaging to take into account the measurement process. It is found that the increase in mean pressure is the same for the different kinds of light, but that the variances found for chaotic and number-state light are, respectively, greater and smaller than the variance for coherent light.

A theorem is proven for quantum information theory that is analogous to the noiseless coding theorem of classical information theory. In the quantum result, the von Neumann entropy S of the density operator describing an ensemble of pure quantum signal states is equal to the number of spin-1/2 systems (‘‘quantum bits’’ or ‘‘qubits’’) necessary to represent the signal faithfully. The theorem holds whether or not the signal states are orthogonal. Related results are also presented about the fidelity of quantum coding and about representing entangled quantum states.

In Bohm’s causal or trajectory interpretation of quantum mechanics, it is straightforward to determine, from a sufficiently large number of calculated particle trajectories, probability distributions for time delays caused by a potential barrier, or for transmission times through a barrier. We show that these distributions can be calculated directly and more efficiently from probability currents, without the calculation of Bohm trajectories as an intermediate step. The ideas are illustrated for Gaussian wave packets incident on a square potential barrier and used to explain why average causal delay times differ from the average delay times calculated in other approaches.

Schrödinger’s integral equation for the first-passage-time probability is applied to a quantum particle moving in a time-dependent stochastic potential that mimics Brownian motion. In the limit of large particle mass, it is shown that quantum and classical first-passage-time distributions agree. Possible applications include time delays in quantum tunneling and electron transport in nanostructures and biological molecules.

The bound-state and continuum solutions of the Schrödinger equation in a Coulomb potential are presented once again, but in a form that makes similarities in their structure much more apparent than before. The similarity is particularly striking if Laplace transforms are used. Not only are both bound state and continuum solutions of the same form, but they also have a simple structure for arbitrary energy eigenvalues. The usefulness of the formalism is illustrated by considering a number of examples involving infinite sums over bound states and integrals over continuum states of matrix elements that were relevant in past work.

A connection between random kicked systems and the Milburn theory for quantum decoherence is presented. The dynamics of the kicked system suggests a possible generalization of the Milburn model for decoherence including external fields. Irreversibility is explored using a suitable Lyapunov function and the stationary solution is examined.

Matrix elements of two-body operators between many-particle permutational symmetry-adapted functions in hyperspherical coordinates are constructed. The matrix elements are evaluated using the appropriate hyperspherical coefficients of fractional parentage, the Raynal-Revai coefficients, and the hyperspherical recoupling coefficients. We use the power expansion of the two-body operators and obtain an analytic expression for the matrix element of each term. These expressions are studied numerically. The results allow precise evaluations of two-body matrix elements for few-body calculations in nuclear, atomic, and molecular physics.

The classical and the quantum Malus laws for light and spin are discussed. It is shown that for spin 1/2, the quantum Malus law is equivalent in form to the classical Malus law provided the statistical average involves a quasidistribution function that can become negative. A generalization of Malus’s law for arbitrary spin s is obtained in the form of a Feynman path-integral representation for the Malus amplitude. The classical limit of the Malus amplitude for s→∞ is discussed.

Two-photon spectroscopy of the hydrogen 1S-2S transition in a cold atomic beam has reached a resolution Δν/ν of 1 part in ${10}^{11}$ in hydrogen and 7 parts in ${10}^{12}$ in deuterium. The hydrogen and deuterium 1S-2S transition frequencies have been determined with a precision of 1 part in ${10}^{11}$. This leads to an accurate value for the Rydberg constant, while the 1S Lamb shift and the isotope shift are determined with order of magnitude improvements over previous measurements. We describe in detail the 1S-2S spectrometer, calculate the line shape of the resonance, and compare it to the experimental data.