A variationally stable, adiabatic hyperspherical treatment of two- and three-photon detachment of ${\mathrm{H}}^{\mathrm{-}}$ is presented. Results are compared with analytic predictions of a zero-range potential model of ${\mathrm{H}}^{\mathrm{-}}$. Detailed comparisions are made also with other theoretical results which include the effects of electron correlations. We predict analytically (and demonstrate numerically) an extreme sensitivity of the theoretical predictions to any errors in the value of the electron affinity employed. In an Appendix we show that the low-intensity limit of the Keldysh treatment [Sov. Phys. JETP 20, 1307 (1965)] of detachment of an electron bound in a zero-range potential agrees with the results of a perturbative treatment.

In this paper, we develop a linear stability analysis of stationary nonlinear guided waves in self-focusing and self-defocusing Kerr-like layered media. The analysis is applicable to the general problem of the stability of stationary nonlinear guided waves in layered structures including one or more self-defocusing media, a previously unsolved problem. Further, as a demonstration of its use, the technique is applied to the case of the fundamental dark surface wave (FDSW), a wave guided near the interface between two dissimilar defocusing media. We obtain results consistent with a numerical stability analysis of the FDSW performed previously [J. Opt. Soc. Am. B 8, 2265 (1991)]. Finally, the generalization of this technique to arbitrary layered structures of Kerr-like media is discussed.

We show that well above threshold the use of linearized Ito quantum stochastic differential equations allows a systematic description of all quantum stochastic properties of laser light including the phase properties. This is accomplished by the use of mixed field-atom operators which are phase independent and around whose finite mean values we may linearize. As a consequence we are able to derive an equation for an operator describing the phase properties of the laser light. We illustrate our method by applying it to three different models for sub-shot-noise lasers.

The theory of lasing in an ensemble of driven two-level atoms is shown to agree satisfactorily with the experimental observation of lasing without inversion by Grandclément, Grynberg, and Pinard [Phys. Rev. Lett. 59, 40 (1987); 59, 44 (1987)]. It is demonstrated that the lasing is dominated by the multiphoton amplification processes induced in the medium.

We have analyzed a model which describes a laser with an injected signal (LIS). We have used a simplified model, keeping only the complex-field equation. By means of standard mathematical methods, we have investigated the vicinity of a Hopf bifurcation point that it presents, and derived the normal form of the laser response. The parameter plane is fully analyzed in terms of the periodic-solution stability. A second branch of periodic solutions is also shown to be present in the system. Numerical simulations are carried out following the parameter-plane analysis and lead to the full set of bifurcation diagrams that this model can present. Finally, a global and complete view of the LIS dynamics is deduced.

In the preceding paper [H. Zeghlache and V. Zehnlé, Phys. Rev. A 46, 6015 (1992)], the analytical study of a simple model for a laser with injected signal has been developed. The existence and stability of self-oscillating periodic solutions of small amplitude in the vicinity of a Hopf bifurcation have been analyzed. Time-periodic perturbation of these solutions is considered here. When the amplitude of the injected field is modulated, the system exhibits the well-known behaviors currently found in coupled nonlinear oscillators. Among these behaviors, we focus our attention to the study of locked solutions and perform an analytical development in the case of small modulation amplitude. The entrainment region in the parameter plane spanned by the amplitude and the frequency of the modulation is analyzed in the particular cases where the modulation frequency is close to the system self-oscillating frequency or twice this value. A detailed analysis of the corresponding 1/1 and 1/2 resonances is performed.

The effect of detuning on squeezing of coherent light is studied in the Jaynes-Cummings model and in the large-N (mean photon number) limit. Analytical formulas for quadrature variances are obtained both in the one-photon and two-photon transition cases. In the former case, small detuning only has a small (unfavorable) effect on squeezing. In the latter case, however, the effect of detuning is significant. No squeezing will occur at resonance, and by the presence of detuning, there will be a series of minima appearing in the suppressed quadrature variance during time evolution as happens in the one-photon transition case, with the limit of this series tending to zero. The explicit expressions for the kth minima are also given for fairly large k.

Squeezing of a coherent light field in a cavity by repeated interaction with atoms is studied in the resonance Jaynes-Cummings model. The least quadrature variance δ is calculated for different values of N (mean photon number), t (interaction interval for each time), and K (number of times of interaction). In the one-photon-transition case, δ could be reduced by this process to a certain extent for suitably chosen t. The squeezing becomes worse if K is too large. δ as a function of t and K (for fixed N) has a minimum, which becomes smaller when N increases. The situation of the two-photon-transition case is similar, the only new feature is that δ(K,t) varies with t periodically when N is large. With a favorably chosen value of t (half of the period), analytical formulas for δ(N,K) are obtained in the large-N approximation. These formulas show definitely, both for atoms initially in the upper or lower level, the least quadrature variance δ goes down when K increases up to a quite large value (for atoms in the upper level it is of order ${\mathit{N}}^{3/2}$, while for atoms in the lower level it is of order N) and the achievable minimum value of ${\mathrm{\delta }}^2$ is of order 1/ √N . Moreover, the light fields so obtained are nearly in pure states with minimum uncertainty product ${\mathrm{\delta }}_1$${\mathrm{\delta }}_2$=1/4.

A unitary Fock-space operator that leaves the canonical quantization rule for fermions covariant is introduced. The defining equation of a canonical fermion coherent state retains the symmetry under this unitary transformation. This fact mandates that the coherent state must accompany a partner state, and that the form of a state in the pair is related to the partner state by the symmetry. A careful definition of the phase in the extended fermion Fock space is crucial for the uniqueness of the normalized fermion coherent state. Also the proper choice of the phase renders the canonical fermion coherent state equal to a displaced-vacuum state.

Self-adjoint extensions of the usual Hamiltonian are studied for a charged particle moving in the x-y plane in the presence of an infinitely thin thread of magnetic flux along the z axis. This is done by starting with a square-well potential and taking its zero-range limit. The wave function for such an extended Hamiltonian is, although square integrable, singular at the origin. There are interesting differences between the cases with and without the magnetic flux.

Based on the close relations between statistical properties of quantum dissipative systems and scattering systems, we conjecture that for quantum chaotic scattering the distribution of the resonance poles of the S matrix is generic and follows the predictions of Ginibre’s ensemble of random (non-Hermitian) matrices. This will be demonstrated on a simple example of a single particle being scattered by (a fixed number of) point obstacles distributed randomly in two dimensions.

It is observed that the well-known shifted large-N technique proposed by Imbo, Pagnamenta, and Sukhatme [Phys. Rev. D 29, 1669 (1984)] fails to yield the correct behavior of the bound-state wave function for the Morse oscillator. To remove this inadequacy, we propose a modified approach which not only restores the exact analytic expressions for the energy eigenvalues and eigenfunctions for the Morse oscillator but also predicts quite accurate results for the rotating Morse oscillator.

A p-version finite-element method is applied within the Moller-Plesset formalism [Phys. Rev. 46, 618 (1934)] to calculate accurate second-order pair and total correlation energies. Radial limits of the second-order correlation energy up to l=12 are given, and careful angular-extrapolation procedures have been applied to obtain results which are expected to be accurate to ±2×${10}^{\mathrm{-}5}$ hartree.

An autoionization spectrum of the ${\mathrm{H}}_2$S molecule has been identified from the comparison between the Auger electrons recorded by means of high-resolution electron-beam and monochromatic Al Kα exciting sources. Due to the high energy resolution the measured kinetic energies can be used for a precise assignment. Our results support a model of a fast dissociation of the core-excited ${\mathrm{H}}_2$${\mathrm{S}}^{\mathrm{*}}$ (2p${)}^{\mathrm{-}1}$(6${\mathit{a}}_1$${)}^1$ and (2p${)}^{\mathrm{-}1}$(3${\mathit{b}}_2$${)}^1$ states into core-excited ${\mathrm{HS}}^{\mathrm{*}}$ (2p${)}^{\mathrm{-}1}$(2π${)}^4$ followed by autoionization decay into the ${\mathrm{HS}}^{+}$ radical. Vibrational structures are resolved and assigned to the ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{}^{\mathrm{-}}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{\Delta }$ final states in the ${\mathrm{HS}}^{+}$ radical. No participator Auger process in ${\mathrm{H}}_2$${\mathrm{S}}^{\mathrm{*}}$ could be identified. However, contributions from the spectator process in ${\mathrm{H}}_2$${\mathrm{S}}^{\mathrm{*}}$ might be present.

Padé approximants are used to derive the Gamow-Siegert wave function by back rotation of its complex rotated forms. This provides an unambiguous way to normalize a resonance wave function.

Different expressions for the transmittance in wave-packet scattering in one dimension are examined. Special attention is paid to the difficulties when the initial packet ρ(0) has negative momentum components. A general formula is provided for this case, and the domain of applicability of a simple approximate expression is indicated. A model calculation illustrates the results.

Measurements of spin-resolved elastic electron-sodium scattering have been carried out at incident energies of 4.1 and 12.1 eV, and the ratio of triplet to singlet scattering cross sections has been obtained at each energy. The ratio is used to provide a determination of not only the magnitudes of the triplet and singlet amplitudes, but also the cosine of the relative phase difference between them. These determinations of magnitude and relative phase represent the most detailed characterization to date of electron-atom scattering from a ‘‘one-electron’’ target.

The photoabsorption cross section near the K edge in krypton gas has been measured using synchro- tron radiation. Several features for simultaneous multielectron excitations were detected and analyzed by the use of the shakeup and shakeoff probabilities and their dependence on the photon energy. Previous observations of the [1s3p], [1s3d], and [1s4p] transitions have been confirmed. A transition is found between [1s3p] and [1s3d] multiple excitations and identified as a three-electron excitation [1s3d4p].

We have investigated the geometry as well as the equilibrium bond lengths for a number of possible structures of the ${\mathrm{Sb}}_4$ cluster by the Hartree-Fock procedure. The tetrahedral structure is shown to exhibit higher stability than several planar structures studied. No stability could be found for a square in the singlet spin configuration, in keeping with considerations based on the Jahn-Teller theorem. For the ${\mathrm{Sb}}_4$ tetrahedron, good agreement of the calculated ionization potential with the observed value is found.

The consequences of sudden frequency changes of a quantum oscillator from ${\mathrm{\omega }}_1$ to ${\mathrm{\omega }}_2$ and back is considered. A strong dependence of squeezing on the time interval between the frequency jumps is found. It is shown that a high degree of squeezing can be achieved by a series of sudden frequency changes.