An integral expression that is formally valid only for short-range potentials is applied to the problem of calculating the amplitude for electron-impact ionization. It is found that this expression provides a practical and accurate path to the calculation of singly differential cross sections for electron-impact ionization. Calculations are presented for the Temkin-Poet and collinear models for ionization of hydrogen by electron impact. An extension of the finite-element approach using the discrete-variable representation, appropriate for potentials with discontinuous derivatives like the Temkin-Poet interaction, is also presented.

Exterior complex scaling enables one to solve the time-independent Schrödinger equation for three charged particles without explicitly imposing the asymptotic boundary condition for three-body breakup. We have used this formalism to study electron-impact ionization of atomic hydrogen by directly solving for the radial components of the scattered wave on a complex, exterior scaled numerical grid. Computational procedures, presented briefly elsewhere [T. N. Rescigno, M. Baertschy, W. A. Isaacs, and C. W. McCurdy, Science 286, 2474 (1999)], are discussed here in greater detail and additional results are presented. Our method is limited only by the finite size of the grid and the number of partial-wave components retained in the expansion of the wave function and, unlike other methods that have been used to study ionization, involves no uncontrolled approximations. Our calculated triply differential cross sections at 17.6, 20, 25, and 30 eV are found to be in excellent agreement with recent measurements.

In this work, we study the dependence of the lifetime $\left(\tau \right)$ of an autoionizing state with the velocity ${(v}_P)$ of an ionic projectile of charge Z. We use a C2 model to represent the final state of the autoionized electron in the continuum of two centers. Explicit calculations for the helium autoionizing states ${2s}^2{(}^{1}S),$ ${2p}^2{(}^{1}D),$ and ${2s2p(}^{1}P)$ are analyzed. We evaluate the decay law for the metastable initial state and find that $\tau$ increases as the projectile becomes faster and converges to the photoionization lifetime for high impact energies. A scaling law for $\tau$ is obtained in terms of the Sommerfeld parameter ${(Z/v}_P).\mathrm{}$ Finally, we evaluate the transition probability for the autoionized electron and show that the mean half-width of the focusing peak decreases as $v_P$ increases.

Gold-cluster beams of ${\mathrm{Au}}_n^{+},$ $n=1\mathrm{}–4,$ have been used to measure the secondary-ion emission from organic (biomolecules) and inorganic (CsI) targets over the very large energy range of 4 keV to 10 MeV per atom. The nonlinear enhancement of secondary-ion emission yields with regard to the constituent number in the cluster projectiles is shown to vary with the incident velocity and the type of secondary ions. For complex secondary ions, the yields as a function of the projectile energy per atom present an unexpected maximum around 50–80 keV per atom. The yields increase again above 1 MeV per atom.

An analytical formula for the angular distribution of photoelectrons emitted from a highly excited hydrogenic state in the weak-field limit $(I<~{10}^9{\mathrm{W}/\mathrm{c}\mathrm{m}}^2)$ is presented. With the use of this formula, results obtained for models involving different numbers of states are compared. The conclusion is that models with restricted-state basis overestimate the population redistribution among Rydberg states and its photoionization consequences.

We investigate the center-of-mass motion of cold atoms in a standing amplitude modulated laser field. We use a simple model to explain the momentum distribution of the atoms after any distinct number of modulation cycles. The atoms starting near a classical phase-space resonance move slower than we would expect classically. We explain this by showing that for a wave packet on the classical resonances we can replace the complicated dynamics in the quantum Liouville equation in phase space by its classical dynamics with a modified potential.

In this paper the quantum hydrodynamic equation describing the collective, low-energy excitations of a dilute atomic Bose-Einstein gas in a given trapping potential is investigated with the JWKB semiclassical method. In the case of spherically symmetric harmonic confining potential a good agreement is shown between the semiclassical and the exact energy eigenvalues as well as wave functions. It is also demonstrated that for larger quantum numbers the calculation of the semiclassical wave function is numerically more stable than the exact polynomial with large alternating coefficients.

An analytical expression for the refractive index of atomic and molecular matter waves in ultracold gases is obtained. Asymptotic formulas for the refractive index are derived for high and low projectile velocities, and intermediate velocities are investigated with the eikonal approximation. The real and imaginary parts of the matter wave refractive index are expressed via the complex scattering length of elastic and superelastic collisions. It is shown that superelastic collisions dramatically influence the low-energy behavior of the refractive index. A discussion is given of proposed measurements of the real and imaginary parts of the scattering length using the interferometry of slow de Broglie waves.

We study the spectrum of rotating Bose-Einstein condensates in the limit of weak repulsive interactions and present analytical and numerical results for energies and wave functions. While the low-lying states are of collective nature, the high-lying states are dominated by single-particle excitations and can be accurately approximated by simple polynomial expressions. In the limit that the number of particles is large compared to the number of excited quanta, the single-particle states become excellent approximations to the eigenstates, and a rather simple ordering scheme is obtained.

The electromagnetic problem of modeling vertical-cavity surface-emitting lasers with their full three-dimensional characteristics is analyzed, including oxide confinement, mesa mirrors, metal contacts, and noncircular geometries. The model is based on the mode expansion of the electromagnetic field in the continuous basis of cylindrical TE and TM modes of the cavity medium and on coupled mode theory. The full vectorial treatment of the problem allows a correct analysis of the polarization characteristics of these lasers, which is a topic of great interest both for the device physics and for many applications. A comparison between the fully vectorial treatment and the LP scalar approximation is carried out and polarization resolved results for rectangular and elliptical structures are presented.

We present joint experimental and theoretical investigations of the emission characteristics of oxide-confined vertical-cavity surface-emitting lasers (VCSEL’s). The transverse mode formation in medium-sized VCSEL’s is determined by the interaction between spatial cavity characteristics and spectral properties of the optical gain: depending on a detuning between the cavity fundamental resonance and the spectral gain maximum, we find the VCSEL’s emitting either on the fundamental transverse mode or on modes of particularly high radial order. For a quantitative interpretation of these characteristics, we adopt a model that considers the detailed electromagnetic structure of the VCSEL and yields wavelength, spatial field distribution, and threshold gains of all supported cavity modes. Combining these solutions with the quantum-well optical response provides the laser threshold operation conditions. The theoretical results are in excellent quantitative agreement with the experimental observations. Thus, our work identifies the relevant mechanisms and offers the perspective to control and to utilize high-order mode emission from oxide-confined VCSEL’s.

We derive from first principles the dynamical equations for the interaction between a heat bath and a multilevel atom with some near degenerate states. Such dynamical equations exhibit atomic coherence terms which arise from the interference of transition amplitudes. We address the question whether such equations lead to a steady state that is consistent with the thermodynamic equilibrium. We show that coherence affects the dynamics of the system, but the equilibrium conditions are still characterized by Boltzmann factors. We also show how an asymmetric treatment of spontaneous and stimulated processes could lead to a steady state which is at variance with the principles of thermodynamic equilibrium. We show that such a steady state can be realized by pumping with broadband laser fields. Finally, we show that coherences in the dynamical equations can be probed via the spectrum of fluorescence.

The modification of lifetime experienced by a fluorescent molecule placed in an arbitrary environment is investigated theoretically within the framework of linear response theory. We present a complete description of the interaction of the particle with arbitrary structures on a plane substrate or inside a cavity. The theory is based on a self-consistent scattering procedure in which retardation effects and contributions from both homogeneous and evanescent modes of the electromagnetic field are included. The decay rate variations are computed and the concept of single-molecule near-field probe is discussed.

Recently there has been experimental and theoretical interest in cross-dispersion effects in rubidium vapor, which allows one beam of light to be guided by another. We present theoretical results which account for the complications created by the D line hyperfine structure of rubidium as well as the presence of the two major isotopes of rubidium. This allows the complex frequency dependence of the effects observed in our experiments to be understood and lays the foundation for future studies of nonlinear propagation.

We propose and analyze the possibility of performing two-photon continuous-wave Doppler cooling of hydrogen atoms using the $1S-2S$ transition. “Quenching” of the $2S$ level (by coupling with the $2P$ state) is used to increase the cycling frequency, and to control the equilibrium temperature. Theoretical and numerical studies of the heating effect due to Doppler-free two-photon transitions evidence an increase of the temperature by a factor of 2. The equilibrium temperature decreases with the effective (quenching-dependent) width of the excited state and can thus be adjusted up to values close to the recoil temperature.

The frequency of the calcium ${}^3{P}_1{-}^1{S}_0$ intercombination line at 657 nm is phase-coherently measured in terms of the output of a primary cesium frequency standard using an optical frequency comb generator comprising a sub-10-fs Kerr-lens mode-locked Ti:sapphire laser and an external microstructure fiber for self-phase-modulation. The measured frequency of ${\nu }_{\mathrm{Ca}}=455\mathrm{}\hspace{0.5em}986\hspace{0.5em}240\hspace{0.5em}494\hspace{0.5em}276$ Hz agrees within its relative uncertainty of $4\times {10}^{-13}$ with the values previously measured with a conceptually different harmonic frequency chain and with the value recommended for the realization of the SI unit of length.

The dynamical version of the so-called “interaction-free” measurement [Phys. Rev. Lett. 74 (1995) 4763] is presented, in which the object called “bomb” is replaced with the atom evolving coherently. It is pointed out that, due to the quantum Zeno effect, the “explosion” symbolized by the absorption of a photon by the atom will never take place. It is shown, however, that this is accompanied by a strong modification of the involved evolution which now has a highly entangling character. Properties of the new evolution are discussed. It is also proved that beyond the quantum Zeno effect regime there is a natural possibility of conditional (i.e., followed by the sequence of some, but not necessarily frequent, probes) freezing of the evolving system in a maximally entangled state. An explanation of the effects as well as some general conclusions are provided.

This paper presents a simple model for repeated measurement of a quantum system: the evolution of a free particle, simulated by discretizing the particle’s position. This model is easily simulated by computer and provides a useful arena to investigate the effects of measurement upon dynamics, in particular the slowing of evolution due to measurement (the quantum Zeno effect). The results of this simulation are discussed for two rather different sorts of measurement process, both of which are (simplified forms of) measurements used in previous simulations of position measurement. A number of interesting results due to measurement are found, and the investigation casts some light on previous disagreements about the presence or absence of the Zeno effect.

We study the effect of the environment on the process of the measurement of a state of a microscopic spin-half system. The measuring apparatus is a heavy particle, whose center-of-mass coordinates can be considered at the end of the measurement as approximately classical, and thus can be used as a pointer. The state of the pointer, which is the result of its interaction with the spin, is transformed into a mixed state by the coupling of the pointer to the environment. The environment is considered to be a gas reservoir, whose particles interact with the pointer. This results in a Fokker-Planck equation for the reduced density matrix of the pointer. The solution of the equation shows that the quantum coherences, which are characteristic to the entangled state between the probabilities to find the pointer in one of two positions, decays exponentially fast in time. We calculate the exponential decay function of this decoherence effect, and express it in terms of the parameters of the model.

We report on an experimental investigation of the tension between quantum nonlocality and relativity. Entangled photons are sent via an optical fiber network to two villages near Geneva, separated by more than 10 km where they are analyzed by interferometers. The photon pair source is set as precisely as possible in the center so that the two photons arrive at the detectors within a time interval of less than 5 ps (corresponding to a path length difference of less than 1 mm). One detector is set in motion so that both detectors, each in its own inertial reference frame, are first to do the measurement! The data always reproduces the quantum correlations, making it thus more difficult to consider the projection postulate as a compact description of real collapses of the wave function.