We describe selection and dynamics of transverse patterns in a nonlinear feedback cavity with a rotated beam. The symmetry of the patterns, described by composite modes, is determined by the image rotation angle within the loop. Complex quasicrystalline patterns sustained by resonant interactions arise under conditions when wave and Turing composite modes are excited simultaneously. It is shown that the excited patterns may be saturated even by the action of quadratic (three-wave) interactions only. Exact resonance involves three composite modes, and may exhibit periodic amplitude modulation on a slow time scale. Another possibility is a strained resonance leading to stabilization of the pattern in a wider parametric domain. Finally, wave-Turing resonance may be complemented by resonance among Turing triplets.

We introduce a dressed-state Monte Carlo wave-function technique to describe resonance fluorescence in a broad class of non-Markovian reservoirs with strong atom-reservoir interaction. The method recaptures photon localization effects which are beyond the Born and Markovian approximations, and describes the influence of the driving field on the atom-reservoir interaction. Using this approach, we predict a number of fundamentally new features in resonance fluorescence near the edge of a photonic band gap. In particular, the atomic population exhibits inversion for moderate applied field intensity. For a low external field intensity, the atomic system retains a long-time memory of its initial state.

We use the operational theory of homodyne detection, introduced by Banaszek and Wódkiewicz [Phys. Rev. A 55, 3117 (1997)], to express a generic quantum phase space quasiprobability distribution (in the sense of Cahill and Glauber) of an electromagnetic field in terms of the photocount moments. We adapt the method of degenerate parametric (pre)amplification of a signal, within the operational theory, in order to overcome the drawback of nonunit efficiency of the detector. Simulations show that as the gain parameter of the amplification is increased, the quasiprobability distribution goes closer to the original one, even for an efficiency lower than 0.5. We also express the mean value of an arbitrary observable in terms of the same photocount moments.

The quantization of atomic center-of-mass motion is considered within the context of cavity QED with particular emphasis on the dynamics of localized wave packets. “Well-dressed” states are introduced as an eigenbasis that incorporates both the quantized atom-field interaction and the external bound states of a potential well. The interplay of internal and external time scales generates qualitatively new dynamics such as novel “collapses” and “revivals.”

An operator is defined that is analogous to the time translation operator except that it translates every component of a state in energy by an amount ɛ. A prescription for measuring expectation values of this operator is described. These measurements provide phase information that is not obtainable by other means. The similarity of this treatment with the treatment of recurrence spectroscopy in the time domain is presented. Two examples from atomic systems are described, but the usefulness of this operator is not restricted to atomic processes.

We use the Lewis and Riesenfeld invariant method to obtain the exact Schrödinger wave functions for a time-dependent harmonic oscillator with and without an inverse quadratic potential. As a particular case we also obtain the wave functions for the Caldirola-Kanai oscillator.

We apply renormalized perturbation theory by the moment method to an anharmonic oscillator in two dimensions with a perturbation that couples unperturbed degenerate states. The method leads to simple recurrence relations for the perturbation corrections to the energy and moments of the eigenfunction. We generalize the approach and systematize its application to excited states.

A Stern-Gerlach setup for the measurement on a quantum system (spin-$$$\frac{1}{2}$) with a macroscopic quantum apparatus (the particle trajectory) produces a Schrödinger-cat-like superposition in which the spin states correlate with wave packets centered around macroscopically distinguishable positions and momenta. When an interaction with an environment is included, the pure density matrix of the system-apparatus combination reduces to a statistical mixture in the spin space, and exact solutions show that the decoherence time for this reduction goes inversly as the macroscopic separation between the two parts of the superposition correlating with up- and down-spin states. This is consistent with Zurek’s approximate result for the decoherence time, and the persistence of system-meter correlations at large times makes it an interesting candidate to look at experimentally.

Recoil corrections to the atomic decay rate are considered up to the order $Zm/M$. The expressions are treated exactly without any expansion over $Z\alpha$. The expressions obtained are valid both for muonic atoms (for which they contribute on the level of a few percent in high $Z$ ions) and for electronic atoms. Explicit results for Lyman-$\alpha$ transitions with low $Z$ of the order $\mathrm{}(Zm/M)(Z\alpha {)}^2$ are also presented.

We prove the validity of a propensity rule for populating magnetic substates by electron capture processes in the intermediate and high-energy range by using the eikonal impulse approximation. This rule says that if the quantization axis is chosen to be perpendicular to the scattering plane, the $M=-l$ final substates are predominantly populated. A scaling rule in terms of the projectile charge is used to display results of the eikonal impulse and the continuum distorted-wave methods.

Core-excited ions have been produced using charge exchange between metastable ion beams and alkali-metal atoms. The technique used permits an unambiguous discrimination between lines of doubly excited states and those of singly excited states. Other lines have been determined in the quartet system of lithiumlike nitrogen (N${\mathrm{V}}^{\mathrm{*}\mathrm{*}}$). Among them are transitions from high-lying levels (${1s2ln}^{\prime }{l}^{\prime }$ with $n^{\prime }>~6$) and an electric-quadrupole $\mathrm{}\left(E2\mathrm{}\right)\mathrm{}$ transition. The spectroscopic source can be useful for a wide range of applications.

We report results of theoretical calculations for the dispersion coefficients associated with the long-range interaction of two ${}^{39}$K atoms in the states ${}^{39}$K$\mathrm{}\left(4s\right)\mathrm{}$-${}^{39}$K$\mathrm{}(5d,6d,7s)\mathrm{}$. These results have been found by Wang et al. [Phys. Rev. Lett. 78, 4173 (1997)] to be in a good agreement with their measurements.

The scheme of Clauser and Dowling [Phys. Rev. A 53, 4587 (1996)] for factoring $N$ by means of an $N$-slit interference experiment is translated into an experiment with a single Mach-Zehnder interferometer. With dispersive phase shifters, the ratio of the coherence length to wavelength limits the numbers that can be factored. A conservative estimate permits $N\approx {10}^7$. It is furthermore shown that sine and cosine Fourier coefficients of a real periodic function can be obtained with such an interferometer.

One-dimensional laser cooling based on velocity-selective coherent population trapping (VSCPT) on a $2_g\to 1_e$ transition has been investigated numerically through the solution of the optical Bloch equations. As in the work of G. Morigi et al. [Phys. Rev. A 53, 2616 (1996)], it has been found that for a large set of atomic and laser parameters, the VSCPT cooling process may be described through scaling-law relations. The scaling laws are based on the relations between the loss rates at large atomic momentum and their dependence on the momentum around zero value. The role of the laser detuning on the VSCPT trapping efficiency has been examined and scaling laws including the detuning have been derived.

We present a study of the time evolution of wave packets excited in optical lattices. Our model shows that, after a sudden change of the potential well depth, a breathing oscillation is created, in agreement with recently performed experiments. We predict that this motional wave packet should subsequently collapse and revive, with a rich intermediate structure comprised of fractional revivals. Moreover, we estimate the rate of damping of the oscillations due to the interaction of the atoms with light and other experimental constraints.

The demonstration that there exists “entangled entanglement” is called into question because the argument that establishes nonlocality using a Bell inequality ceases to hold when applied to subsequences of the type considered.

Expounding an argument that we have stated in Sec. IV of our paper [Phys. Rev. A 54, 1793 (1996)], we demonstrate that according to our understanding Schafir’s conclusion [preceding Comment, Phys. Rev. A 56, 4335 (1997)] is based upon a premise that is not tenable.

An algebraic model in terms of a local harmonic boson realization was recently proposed to study molecular vibrational spectra [Zhong-Qi Ma et al., Phys. Rev. A 53, 2173 (1996)]. Because of the local nature of the bosons the model has to deal with spurious degrees of freedom. An approach to eliminate the latter from both the Hamiltonian and the basis was suggested. We show that this procedure does not remove all spurious components from the Hamiltonian and leads to a restricted set of interactions. We then propose a scheme in which the physical Hamiltonian can be systematically constructed up to any order without the need of imposing conditions on its matrix elements. In addition, we show that this scheme corresponds to the harmonic limit of a symmetry-adapted algebraic approach based on u(2) algebras.

The problem of removing the spurious components from the vibrations of a polyatomic molecule is discussed in this paper. The scheme proposed in the Comment [R. Lemus et al., Phys. Rev. A 56, 4337 (1997)] for constructing the physical Hamiltonian is a standard method in group theory, but not the simplest one due to multiple applications of Clebsch-Gordan coefficients. A simpler and more general scheme for removing the spurious degree of freedom from both the configuration space and the Hamiltonian is explained in this paper.

We point out formal correspondences between thermodynamics and entanglement. By applying them to previous work, we show that entropy of entanglement is the unique measure of entanglement for pure states.