We show here that the model Hamiltonian used in our paper for an ion vibrating in a q-analog harmonic oscillator trap and interacting with a classical single-mode light field is indeed obtained by replacing the usual bosonic creation and annihilation operators of the harmonic trap model by their q-deformed counterparts. The approximations made in our paper amount to using, for the ion-laser interaction in a q-analog harmonic oscillator trap, the operator $F_q{=e}^{-(|\epsilon {|}^2/2)}{e}^{i\epsilon A^{†}}{e}^{i\epsilon A},$ which is analogous to the corresponding operator for an ion in a harmonic oscillator trap that is ${F=e}^{-(|\epsilon {|}^2/2)}{e}^{i\epsilon a^{†}}{e}^{i\epsilon a}.$ Here a and $a^{†}$ are the usual creation and annihilation operators, whereas A and $A^{†}$ are the q-deformed bosonic creation and annihilation operators. There is no problem with diagonalizing this operator using the basis states $|g,m〉$ and $|e,m〉,$ where m stands for the motional number state. In our paper we do not claim to have diagonalized the operator $F_q{=e}^{i\epsilon {(A}^{†}+A)}$ for which the basis states $|g,m〉$ and $|e,m〉$ are not analytic vectors.

We present a method for the deterministic generation of all the electronic Bell states of two trapped ions. It involves the combination of a purely dispersive with a resonant laser excitation of vibronic transitions of the ions. In contrast to other methods presented up to now, our proposal does not require differential laser addressing of the individual ions and may be easily implemented with present available techniques. It is further shown that this excitation scheme is highly adequate for the complete determination of the motional state of the ions.

The parameter that determines the nondipole correction to the angular distribution is calculated for Ar $1s$ and $3s$ subshells in the Hartree-Fock (HF) approximation and taking account of the multielectron correlations, using the random-phase approximation with exchange. In the photoelectron energy range 0–100 eV the parameter, which for s subshells is nonzero at threshold, is found for Ar $3s$ to be strongly affected by multielectron correlations. Results are also presented for He and Be in the HF approximation.

Closed-orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high-resolution spectral analyzer to obtain the semiclassical eigenenergies and transition matrix elements. The method is demonstrated for dipole transitions of the hydrogen atom in a magnetic field. This is an alternative semiclassical calculation of individual quantum transition strengths from closed-orbit theory.

Theoretical results from multistate semirelativistic Breit-Pauli $R$-matrix calculations are presented for electron-impact excitation of argon from the ${(3p}^{5}4s)$ $J=0,2\mathrm{}$ metastable states to the ${(3p}^{5}4s)$ and ${(3p}^{5}4p)$ manifold. In most cases, our results are in excellent agreement with those from the recent experiment by Piech et al. [Phys. Rev. Lett. 81, 309 (1998)].

We have performed a combined experimental and theoretical study of the charge transfer for 5-keV ${\mathrm{Na}}_n^{+}$ cluster-ion collisions with Na atoms in their ground and laser-excited states. The theoretical analysis of the laser-enhanced charge-transfer probability, based on a self-consistent treatment of both charge-transfer and collision-induced fragmentation, shows a crucial dependence on the energy content of the ${\mathrm{Na}}_n^{+}$ clusters before the collision. Quantitative information on this energy is obtained by comparing experimental data with theoretical results.

The ${1s2s}^2{}^{2}S$ resonance parameters in $e^{-}-\mathrm{He}$ scattering are calculated using the method of complex-coordinate rotation with Hylleraas functions. A fully correlated basis with all six interparticle coordinates between the three electrons and the nucleus is used to represent the wave function. The resonance energy and width are calculated to computational accuracies (relative error) of six parts in ${10}^6$ and 2%, respectively. A comparison is made with other calculations and high-resolution experiments.

Auger decay of the inner-shell doubly excited ${4d}^9{5p}^5{\mathrm{nln}}^{\prime }{l}^{\prime }$ states in Xe is studied by experiment and theory. The “single-participator,” “double-participator,” and “spectator” decay channels of the resonance states are calculated in a two-step approximation. The results are used to explain the observed resonance enhancement of the Xe ${5p}^4\mathrm{nl}$ photoelectron satellite intensities in the photon energy range 73–87 eV.

The Coulomb explosion of ${\mathrm{H}}_2\mathrm{O}$ in laser pulses of 50 fs and intensity of $3\times {10}^{16}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ has been investigated using an ion momentum-imaging technique to determine the shape of the exploding molecule. The molecule is found to straighten substantially during the ionization process with the bend distribution at a maximum between $130°$ and $180°.$

We propose a method of measuring diffusion of the relative phase between two Bose-Einstein condensates occupying different nuclear or electronic spin hyperfine states coupled by a two-photon magnetic-dipole transition via an intermediate level. Due to the macroscopic quantum coherence the condensates can be decoupled from the electromagnetic fields. The rate of decoherence and the phase collapse may be determined from the occupation of the intermediate level or the absorption of radiation.

We study the transverse effects in a degenerate optical parametric oscillator with a saturable absorber. We focus on the analysis of two-dimensional stationary and time-dependent localized patterns. The homogeneous steady-state solution is destabilized by a Hopf bifurcation to periodic states with finite wave number and a Turing bifurcation. These bifurcations are close enough that they interact. This leads to localized structures consisting of a sharp peak emitting concentric rings of alternating high and low intensities.

We consider a two-level atom driven by an ideal degenerate optical parametric oscillator. For squeezing bandwidths of the order of the natural width $\gamma ,$ and smaller, we report remarkable spectral profiles for the scattered light. We also consider a system where the atom is driven by arbitrarily correlated light of arbitrary bandwidth. Employing analytic and numerical solutions, we find different spectral features depending on the classical or nonclassical nature of the driving field. The spectral linewidth can be both subnatural and narrower than the incident field linewidth, an effect that does not require nonclassical light. However, nonclassical light is essential for the appearance of a narrow hole at line center. It is a unique signature of the quantum nature of the field, and for ideal squeezing, the fluorescence at line center vanishes.

We demonstrate efficient phase conjugation in an inhomogeneously broadened rare-earth doped crystal using electromagnetically induced transparency. The observed frequency conversion efficiency of the phase conjugate in energy over a backward pump beam is as high as 10% with ∼1/4 of maximal Raman coherence. This efficient phase conjugation has potential applications of nonlinear optical processes such as frequency up-conversion and Raman excited spin-echo optical memory.

We show that the tendency of a laser beam to break into a filamentary structure in passing through a nonlinear optical medium can be largely suppressed by proper tailoring of the vacuum field that interacts with the laser beam.

We consider exact time-dependent analytic solutions to the Schrödinger equation for tunneling in one dimension with cutoff wave initial conditions at $t=0.\mathrm{}$ We obtain that as soon as $t\ne 0$ the transmitted probability density at any arbitrary distance rises instantaneously with time in a linear manner. Using a simple model we find that the above nonlocal effect of the time-dependent solution is suppressed by consideration of low-energy relativistic effects. Hence at a distance $x_0$ from the potential the probability density rises after a time $t_0{=x}_0/c$ restoring Einstein causality. This implies that the tunneling time of a particle can never be zero.

We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically without the usual five-dimensional extension and shown to be equivalent due to the supersymmetry of the action. They correspond to a projection on the mass of the particle either continuously or at the end of the time evolution. It is shown that the supersymmetry transformations are generated by shifting and scaling the supertimes and the invariant difference of two supertimes is given for the general case. A nonrelativistic reduction of the relativistic propagator leads to a three-dimensional path integral with the usual Pauli Hamiltonian. By integrating out the photons we obtain the effective action for quenched QED and use it to derive the gauge-transformation properties of the general Green function of the theory.

A quantum parametric harmonic oscillator with a unitary evolution but not invariant under time reversal, is shown to be unitarily equivalent to a quantum generalized harmonic oscillator. As a consequence the phase properties of the two systems, in particular their geometric phases, are identical. Equivalent results for the corresponding classical systems are deduced from the study of the time evolution of the appropriate squeezed coherent states.

We address the problem of chaos in quantum systems in terms of the sensitivity of the evolution of individual quantum states to errors in measurements. Specifically, we generate quantum trajectories of the quantum kicked top by considering discrete measurements on individual states as they evolve. If an error occurs when recording the results of the measurements we can calculate the difference between the true quantum state and the state inferred from the measurement results. Not surprisingly, the results depend on the strength of the measurement back action and also on whether the initial state is centered in a regular or chaotic region of the corresponding classical phase space. For measurements with a strong back action we find that the initial chaotic state shows sensitivity to measurement errors, but an initial regular state does not.