This paper analyzes the resonantly photopumped Na-Ne x-ray-laser scheme that has been studied experimentally on Z pinches for the last five years. By modeling as an x-ray source the Na Z-pinch output obtained on the Saturn generator experiments at Sandia National Laboratories, the time-dependent properties of the Ne lasant are studied. Our model yields a maximum gain, approximately 0.2 ${\mathrm{cm}}^{\mathrm{-}1}$, with a full width at half maximum duration of 18.5 ns, on the 4f→3d transition at 231 Å under the conditions of the Saturn experiments. We investigate the effects of varying parameters such as the ion density of the Ne lasant and the linewidth of the Na pump line. The impact of radiation trapping on the gain of the various laser lines is considered in a one-dimensional slab geometry.

A semiclassical theory of a resonant periodic-gain (half-wave spatially periodic-gain segments) laser in the context of a semiconductor medium is presented using an oversimplified picture. Terms arise in the polarization of this periodic-gain medium that lead to enhanced light-matter interaction, doubling the gain coefficient, and enhancing mode-pulling effects. Discussion of the physical processes is extended to include a comparison with the ring-cavity correlated-emission laser, which also utilizes a periodic-gain medium and exhibits a vanishing phase fluctuation between the degenerate counterpropagating modes. A simple physical picture of radiations from a half-wave-periodic, radiating dipole array illustrates the common mechanism and important relationship between these lasers.

We introduce self-similar variables in the stimulated Raman scattering (SRS) problem and discuss a class of analytic solutions of the SRS equations in the nonlinear transient regime. The distribution of intensities, energies, and passage times are discussed and analytically calculated in the nonlinear regime.

An interference experiment with signal and idler photons produced by parametric down-conversion in two nonlinear crystals is described and analyzed theoretically. It is found that when the idlers for the two crystals are superposed and aligned, the idler photon from the first crystal can induce coherence between the two signals, but without inducing any additional emission. Blocking the first idler wipes out the interference. The implications for the interpretation of the quantum state vector are discussed, and this leads to the conclusion that the state reflects not only what is known, but to some extent also what is knowable in principle.

A cavity-damped Jaynes-Cummings model with a Kerr-like medium filling the cavity is investigated in the rotating-wave approximation. We introduce six operators with respect to the light field whose equations of motion are transformed to six coupled partial differential equations using the s-parametrized quasiprobability distributions of Cahill and Glauber [Phys. Rev. 177, 1882 (1969)]. Equations of motion for expansion coefficients of the distribution functions are solved by a Runge-Kutta procedure for vector tridiagonal relations. Starting with an initial coherent state for the cavity field and the atom in its upper state, we find that revivals of the atomic inversion are more pronounced for a given damping constant compared to the case of no Kerr medium. Also, quadrature squeezing is less affected by weak cavity damping and thermal noise compared to the standard Jaynes-Cummings model. The effect of damping on interesting non-Gaussian structures is also discussed.

We investigate a system through which a variety of competitive dynamics can be optically realized. The interaction between the dynamical variables, in this case the intensities of resonator modes, can be controlled and even programmed. Photorefractive media are used to establish the coupling between the optical modes. We illustrate the properties of such a system through two different instances. The first is a ‘‘winner-takes-all’’ system in which the mutual competition between the modes leads to multiple stable fixed points in which one mode oscillates while the other ones are suppressed. The second system employs circular coupling between the modes giving rise to a dynamically recalled sequence of modes, often referred to as ‘‘voting-paradox’’ dynamics.

Intensity maps from an experiment on a laser with a saturable absorber, in the case of strong dissipation, are compared with theoretical one-dimensional (1D) maps. These 1D maps are derived in the limit of infinite dissipation, starting from 2D maps for a dissipative saddle cycle with stable and unstable manifolds approaching a quadratic tangency and giving rise to a structurally unstable homoclinic orbit. They are multibranched, each branch corresponding to a particular number of turns around the saddle cycle. The good agreement between theory and experiment indicates that the origin of the complicated behavior of a laser with a saturable absorber is a saddle cycle. A multibranched structure is also present in maps of time of flight between planes in phase space. Depending on the choice of these planes, it is possible to obtain time-of-flight maps that give the same symbolic dynamics of the intensity maps.

Photoionization of atomic hydrogen by a linearly polarized laser is numerically studied using a method based on an expansion of the wave function in angular-momentum components. The numerical method presented is quite efficient to compute photoionization of three-dimensional atoms. Moreover, the main advantage of the method is that it allows a clear comparison with one-dimensional models. As a consequence, we propose a family of models that have the same complexity as a one-dimensional model, but that are closer to real atoms.

Stochastic theories have been used for a long time to describe relaxation as well as line-shape functions. Since the pioneering work of Kubo, these theories have gained considerable interest in the application to optical processes. While previous theories focused on stochastic descriptions of the relaxation, our emphasis is on the dynamics induced by stochastic interactions in a system undergoing relaxation and dephasing processes, including pure dephasing. All the theories based either on the Hilbert-space representation, or on the Liouvillian-space representation, but requiring spectral decomposition methods, are unable to describe these effects simultaneously. In this paper, the implications of the statistical properties of the stochastic variables on the dynamics are elucidated, and the general time evolution of a stochastic N-level system is established in the particular Markovian or weakly colored noise cases.

In the preceding paper we have developed a formal theoretical approach to describe the dynamics of stochastic systems in nonlinear optics. The main emphasis has been on the description of the equation of motion of the free system, since the optical fields are usually treated by perturbation expansion. Here we explicitly develop the dynamics of complex models, which should be helpful in realistic situations. Two different models are considered. The dynamics of a stochastic three-level system is introduced first. Then the case of two configurations stochastically coupled is explicitly treated. This last model is of interest in order to understand the effects of nonradiative transitions on the nonlinear-optical properties of stochastic systems.

It has been shown that a coherent preparation of atoms can, under certain conditions, lead to noise-free amplification and almost 50% phase squeezing in a two-photon correlated-emission laser. In this paper, we study the effect of phase fluctuations in the injected atoms on the phase noise of the field in these systems. We discuss the conditions under which squeezing is preserved in the two-photon linear amplifiers. We also show that, even for very large phase fluctuations in the injected atoms, almost 50% phase squeezing can be achieved. The corresponding gain is, however, significantly reduced.

We discuss the generation of quantum noise in interferometers. A heuristic model is described that enables different characteristics of the noise to be understood and calculated. In particular, the effects of modulation on signal and noise in interferometers are discussed. It is seen that the mixing in of quantum noise from different modes of the vacuum can degrade the signal-to-noise ratio of a measurement in a variety of apparently different physical situations. Michelson interferometers with both internal and external phase modulation are specifically considered, but the results are easily extendable to any type of interferometer. We also comment upon some implications for the use of squeezing in interferometers. For examples, we argue that it is possible, even in lossy narrow-band interferometers, for squeezing to reduce significantly the effective quantum-noise power.

We consider a parametric amplifier driven by a periodically pulsed pump field inside a cavity containing a Kerr nonlinearity. The dynamics of the device is modeled as a kicked nonlinear system. The pulsed parametric amplifier constitutes the kick. In between kicks the dynamics is determined by the Kerr nonlinearity and damping. In the absence of damping, a classical description of the device exhibits a rich phase-space structure including fixed points of multiple period and chaos. We contrast the classical behavior of the mean intensity with that predicted by quantum dynamics. The mean photon number inside the cavity is shown to undergo regular collapse and revival in the regular region of the phase space and irregular revivals in the chaotic region. When damping is included, the quantum recurrences are rapidly suppressed, and the classical behavior is restored. In this case a stable steady state is possible. The damping represents the effect of photon-number measurements on the system. We also discuss the photon statistics in the steady state.

Several models of partial differential equations describing the dynamics of lasers with transverse effects are introduced by using the center manifold theorem for the elimination of irrelevant variables. By taking advantage of the different time scales associated with the relaxations of the variables, we first eliminate the polarization and later the population inversion. We show that in contrast with the plane-wave models, the use of center manifold techniques is necessary to properly describe the spatiotemporal behaviors of lasers. In particular, we characterize unsuspected Hopf bifurcations for the model obtained from the adiabatic elimination of the polarization and discuss the presence of diffusive terms induced by the interaction of radiation and matter after the elimination of the population inversion. A complex Ginzburg-Landau equation is also obtained in the small-field limit.

We show that by using second-order differential operators as a realization of the so(2,1) Lie algebra, we can extend the class of quasi-exactly-solvable potentials with dynamical symmetries. As an example, we dynamically generate a potential of tenth power, which has been treated in the literature using other approaches, and discuss its relation with other potentials of lowest orders. The question of solvability is also studied.

The exact solutions of the generalized Killingbeck potential that are obtained for specific values of the quadratic coupling are shown to provide excellent estimates of the energy levels of the Coulomb plus linear potential problem.

We derive the virial theorem for Hamiltonians whose domain of definition is not invariant under spatial dilatations. This generalization is important for problems where the support space is noncompact.

The electron-beam ion trap at Lawrence Livermore National Laboratory is used to excite levels selectively in lithiumlike ${\mathrm{Cr}}^{21+}$, ${\mathrm{Mn}}^{22+}$, ${\mathrm{Fe}}^{23+}$, ${\mathrm{Ni}}^{25+}$, and ${\mathrm{Ge}}^{29+}$ that possess two radiative-decay branches in the x-ray regime. High-resolution spectroscopic measurements of the relative x-ray intensities are made to infer the radiative branching ratio. Results are compared with theoretical values and demonstrate the importance of relativity in the determination of level structure and mixing coefficients in configuration-interaction calculations.

The existence of an approximate recursion relation among the expansion coefficients in a modified Dunham expansion of potential energy-distance relations has been directly verified for diatomic molecules. The recursion relations uniquely determine the functional structure of diatomic potentials, which provides a sound physical basis for the proposition of a ‘‘universal’’ diatomic potential reported recently [Phys. Rev. A 42, 6497 (1990)].

To clarify some essential discrepancies between experimental and recent theoretical studies of the photoionization cross section of excited 6s6p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ barium, we present experimental data of the relative photoionization cross section of the 6s6p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ state of barium in the energy range between the ${\mathrm{Ba}}^{+}$ 6s and ${\mathrm{Ba}}^{+}$ 5${\mathit{d}}_{3/2}$ thresholds.