We discuss the classical dynamics of a model SU(1,1) Hamiltonian system that may have some application in many-boson systems. A ground-state phase transition is shown to exist in this model, and the energy surface is shown to undergo a qualitative change at this transition.

The $L_2$-$L_3$ Coster-Kronig transition probability $f_{23}$ in Nd was measured using multiparameter K-vs-L x-ray coincidence techniques. The Nd x rays were obtained from a radioactive source of ${}_{}{}^{145}{}_{}{}^{}\mathrm{Pm}$. High-energy-resolution germanium and silicon detectors were used to detect the K and L x rays, respectively. A method is described to correct for the very important contribution of K${\alpha }_1$ x rays to the K${\alpha }_2$ x-ray peak as well as for the small contribution of K${\alpha }_2$ x rays to the K${\alpha }_1$ x-ray peak. The contribution of Lη x rays to the measured K${\alpha }_2$-(Lα+Lη) coincidences was calculated and subtracted. The value obtained, $f_{23}$=0.146±0.005, is lower than that predicted (0.170) by the latest theoretical calculations, confirming a trend of deviations from theory recently observed in atoms of higher atomic number. It differs, however, from another recently reported value of 0.123±0.013. .AE

The $O_u^{+}$${(}^3$${\Pi }_u$)←${\mathrm{XO}}_g^{+}$${(}^1$${\Sigma }_{\mathit{g}}^{+}$) excitation spectrum of ${\mathrm{Zn}}_2$ van der Waals molecules produced in a molecular beam employing free-jet supersonic expansion, crossed with a pulsed dye-laser beam, was studied using Ar as the carrier gas. A well-resolved structure arising from transitions between the vibrational levels of the lower and upper states was recorded at various carrier gas pressures. An analysis of the spectrum yielded the vibrational constants, bond strengths, and equilibrium internuclear separations of the molecule in the two electronic states.

The relaxed-core Hartree-Fock (RCHF) approach to the calculation of K-shell photoionization cross sections is analyzed and applied to K-shell single-hole ionization in CO. A direct method based on the Schwinger variational principle and single-center-expansion techniques is used to generate the continuum orbitals associated with the motion of the photoelectron in the direct and exchange potential of the relaxed ion. A method is presented for evaluating the N-electron transition moment, a step that has posed a considerable computational obstacle due to the lack of orthogonality between the frozen and relaxed orbitals in the initial and final N-electron states, respectively. Besides being very practical and efficient, this formulation establishes the distinction between the ‘‘direct’’ and ‘‘conjugate’’ part of the transition moment, introducing bound-free dipole and overlap integrals, respectively. Whereas for large photoelectron energies the conjugate terms can be neglected, they become important near threshold, contributing, for example, up to 30% to the 1s cross sections in CO. An analysis by means of low-order perturbation theory shows that the RCHF model correctly describes the effect of ionic relaxation, that is, essentially the screening of the 1s hole by the valence electrons. As a consequence the ${\sigma }^{\mathrm{*}}$ shape resonance is substantially shifted to higher energy and broadened compared with the frozen-core Hartree-Fock picture where the more attractive unscreened 1s-hole potentials are used. The remaining discrepancies with the experimental results are attributed to the neglect of target polarization in the RCHF model.

A systematic way of simultaneously handling relativistic and many-body effects for electric dipole transition probabilities is introduced. Relativistic many-body wave functions are generated using a relativistic configuration-interaction (RCI) approach, where the virtual space is represented by screened hydrogenic functions whose effective charges are determined during the RCI process. It is shown that the number of ‘‘parents’’ that must be kept in a first-order wave function may be minimized, using a procedure called reduce. The relativistic form of the first-order theory of oscillator strengths is used to determine which configurations are crucial. Application is made to the ${\mathrm{Tl}}^{+}$ 6$s^2$→6s6p ${}_{}{}^1{}_{}{}^{}$,3${\mathrm{P}}_1$ transitions for which both nonorthonormality and core excitation effects are found to be crucial. For the allowed transition, our results (length and velocity) are in excellent agreement with experiment.

An inhomogeneous radiofrequency electric field can couple the cyclotron and axial modes of a single ion in a Penning trap. The classical equations of motion are the same as those of a driven quantum-mechanical two-level system. We discuss an analog of the π pulse, which can exchange mode actions, and an analog of the avoided crossing. Experimental illustrations are presented.

Members of the 6$p_j$${\mathrm{nf}}_{j\mathcal{’}}$ autoionizing series in barium have been observed experimentally using multistep laser excitation. The recorded spectra exhibit extremely broad profiles for n values ranging from 7 to 30. We have fitted the spectra using an energy-independent multichannel quantum-defect theory model that reproduces the data reasonably well in spite of the fact that the full widths at half maximum of the excitation profiles are comparable in magnitude to the energy spacings between adjacent states. Experimental quantum defects and autoionization rates are presented along with the parameters determined from the theoretical fit.

The WKB method is commonly used in semiclassical approximations to the wave function in both the classically allowed and the forbidden regions of a one-dimensional potential. In a multidimensional space, the method can be adapted to construct wave functions in an ‘‘allowed’’ region from classical trajectories or wave normals. However, in the ‘‘forbidden’’ region the WKB wave function is in general specified by two sets of wave fronts, the equiphase and the equiamplitude surfaces or equivalently by two sets of paths defined to be normal to these surfaces, respectively. We present a Huygens-type construction for obtaining these wave fronts and paths, which reveals that for non-normal incidence the paths are coupled to each other. The analysis enables us to answer some of the basic questions concerning tunneling in multidimensional nonseparable potentials. A special and important case occurs when the incident wave is normal to the turning surface. We show that for normal incidence the path equations are decoupled and are equivalent to Newton’s equations of motion for the inverted potential and energy.

We discuss some recent developments in the implementation of the Schwinger multichannel method for electron-molecule collision calculations. The evaluation of matrix elements involving the operator ${\mathrm{VG}}_P^{\mathrm{}(+)\mathrm{}}$V, previously accomplished by insertion of a Gaussian basis on either side of $G_P^{\mathrm{}(+)\mathrm{}}$, is now done by direct numerical quadrature. This approach avoids the necessity of very large Gaussian basis sets, allowing the size of the basis to reflect only the dynamical requirements of the scattering wave function. We find that the reduction in the required basis size results in improved efficiency, in spite of the additional numerical effort of performing the quadrature. Trial applications to electron-${\mathrm{CH}}_4$ scattering in the static-exchange approximation and to electronic excitation of ${\mathrm{H}}_2$ illustrate the excellent convergence characteristics of the procedure.

This paper analyzes the transient state of a bunched electron beam traversing a narrow beam pipe under the influence of transverse resistive-wall effects. Because the electron beam in the wigglers of future free-electron lasers (FEL’s) is required to travel in pipes with small diameters, this study is relevant in determining the beam stability in these FEL’s. The analysis is restricted to the case in which the first mode dominates. First, an integral representation of the single-mode solution is obtained. Second, the transient-state solution is obtained for the case in which the focusing force dominates the resistive-wall force. The maximum transient amplitude is derived for the case in which a single bunch is off-axis. Third, this result is used to compute the maximum transient amplitudes when the bunches enter the system with random and with equal initial displacements, respectively. These analytic expressions of maximum transient amplitudes are useful in predicting when the transient could become significant. They are compared with earlier derivations and with numerical simulations. These expressions are also applied to various proposed FEL’s. Results showed that the transverse resistive-wall instability could not pose a problem in the operation of these FEL’s.

We derive the equation of motion for the field density matrix of the degenerate two-photon laser under conditions of two-photon resonance starting from the full microscopic Hamiltonian. Our results are compared with the corresponding quantities obtained from the standard effective Hamiltonian. As we have shown for the nondegenerate case, the full diagonal density-matrix equations tend to the effective Hamiltonian density-matrix equations in an appropriate limit, but the equations of motion for the off-diagonal elements do not coincide. The equations obtained using a more accurate form of the effective Hamiltonian, in which Stark shifts are included, do agree. In this paper we concentrate on the photon-number distribution and the nature of the phase transition that takes place in the neighborhood of the two-photon lasing transition threshold. We determine the steady-state mean photon numbers and consider the stability of the solutions. A solution is found where the mean photon number is zero, but this is found to be a stable solution only for sufficiently weak pumping, whereas in the standard effective Hamiltonian approach it is always stable. As the pumping strength is increased, a range of detunings is reached in which there are two stable solutions. The amplitude of the zero-photon peak diminishes very rapidly as the pumping strength increases. Finally, for sufficiently large detunings, a single, stable, steady-state solution is obtained. The nature of the phase transition is illustrated by presenting plots of the photon-number distribution against detuning and pumping rate. The photon-number fluctuations about the mean are also discussed.

Numerical simulation of a nonlinear interface has shown that remarkable improvement in switching quality is theoretically possible by hard-limited saturation of the nonlinearity. We report the results of simulations investigating the effect of different types of soft saturation on nonlinear-interface switching behavior. The calculated predictions are consistent with recent experimental findings and show surprisingly little difference between hard and soft saturation. Significant softening leads to contrast reduction.

We study the resonance fluorescence emitted by two laser-driven coupled identical two-level atoms and allow for an arbitrary separation between the atoms and an arbitrary orientation of the interatomic axis in the laser field. Quantum beats arise in the resonance fluorescence intensity profile when an interatomic axis orientation is not perpendicular to the driving field propagation direction and are well resolved for an interatomic separation comparable to the resonant wavelength. These beats vanish for noninteracting atoms as well as for atoms separated by distances much smaller than the resonant wavelength. We also consider the time-dependent resonance fluorescence photon statistics that also exhibit quantum beats. Sub-Poissonian photon statistics occur for large interatomic separations and, for small separations, sub- and super-Poissonian statistics arise depending on the atomic orientation in the external driving field.

For a leaky cavity driven by an active medium, we clarify the connection between the concepts of single-quasimode squeezing (for the intracavity field) and spectral squeezing (for the input and output fields). Our analysis is based on a rigorous construction of the Fox-Li quasimodes of an empty cavity by a superposition of the true modes of a perfect, large (infinitely large in the limit) cavity which fully subsumes the leaky cavity. To illustrate the physical importance of spectral squeezing (as defined here and as used by other authors), we consider a novel model of a microscopic system that is sensitive to the generalized quadratures of the field. We obtain a simple picture of the reasons why the quantum-noise reduction is in general different inside and outside the cavity. An important special case of our picture is that if the intracavity field is perfectly squeezed, then the output field shows no squeezing at all. Our considerations apply to a wide class of systems, examples of which are discussed in the companion paper.

In the preceding paper we developed a formalism based on the true modes of the universe containing a leaky cavity to analyze the relationship of quantum noise inside that cavity to that outside. We illustrate this formalism here by studying several active systems. We analyze both an ordinary laser and a laser operating in the phase-locked regime. We calculate the extracavity quadrature variances for the phase-locked laser and find that the spectrum of noise reduction in the squeezed quadrature is Lorentzian. Our formalism is also applied to a two-photon correlated-spontaneous-emission laser. We find the familiar result that with 50% squeezing in the phase quadrature of the field inside the cavity, one has nearly 100% phase squeezing outside the cavity. However, under different conditions the phase quadrature of the intracavity field is nearly perfectly squeezed, but the extracavity field shows almost no squeezing in its phase quadrature. We also analyze the effect of finiteness of measurement time on the extracavity quadrature variances.

A theory is presented for forward- and backward-stimulated Raman scattering of colored chaotic light in dispersive media. Both amplification of a coherent Stokes seed and spontaneous generation are treated. It is shown that group-velocity dispersion reduces the gain for the average Stokes intensity, while the intensity fluctuations in the pump enhance it. For a given bandwidth, chaotic light is scattered more efficiently than coherent light when its average intensity exceeds the critical intensity for overcoming the decorrelating effects of group-velocity dispersion on the pump and Stokes waves. The figures presented demonstrate the asymmetry in the intensity of forward and backward Raman scattering of nonmonochromatic light.

We have found the gain of a Raman amplifier to be almost completely suppressed when the amplifier is pumped by a multilongitudinal mode laser and seeded with an initially uncorrelated Stokes beam that is nearly as intense as the pump. This effect is predicted by a plane-wave model of Raman amplification that accounts for multimode pump and Stokes fields. Our experiments have also demonstrated that the beam quality of the pump is maintained to the extent that the amplification is suppressed.

The purpose of this paper is to investigate intrinsic restrictions of quantum mechanics put on the correlation function $g^{\mathrm{}\left(2\right)\mathrm{}}$ by values of lower-order moments, which characterize noise in interferometric measurements. Some general consequences regarding the relation between antibunching and squeezing are obtained. The class of fields with the minimum value of $g^{\mathrm{}\left(2\right)\mathrm{}}$ for given noise is specified and the relation of such states to the Kerr medium is emphasized. The concept of noise minimum states can replace number-phase minimum uncertainty states.

A quantitative transient multiwave-mixing theory is developed to analyze recently observed picosecond-laser-amplification effects in silicon. Our calculations and comparison with experimental data show the importance of accounting for side diffractions (even in regions of large phase mismatches) and the temporally vastly changing self- and mutual-phase-modulations, besides other physical, material, and optical parameters.

The statistical properties of the third-order nonlinear dissipative oscillator, which evolves from any state, are derived on the basis of the exact solution to the master equation. Some important features of the nonlinear oscillator model, such as the recurrences of the initial state, are related to the properties of quasidistributions connected with the phase of the complex field amplitude.