The competition between the ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ nonlinearity of a resonant second-harmonic-generation (SHG) system and an added ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ nonlinearity shifts the Hopf bifurcation of the standard SHG towards higher photon numbers eventually completely stabilizing the system. Remarkably, perfect squeezing survives the stabilization. Two important consequences are discussed, namely, efficient bright squeezing generation and strong suppression of the excess noise which, for parameters corresponding to an experiment reported in the literature, can be reduced by two orders of magnitude without diminishing the squeezing. Possible experimental implementations are finally discussed.

At the most fundamental level of quantum electrodynamics, there is no such thing as two-body interactions between atoms. The potentials that describe these interactions are effective potentials resulting from a series of approximations whose validity depends on the precise situation at hand. Considering a one-dimensional geometry for simplicity, we discuss under which conditions the familiar form of the near-resonant dipole-dipole interaction is valid, paying particular attention to the effects of interatomic propagation of light, and to what extent it can be modified in the tailored electromagnetic environments provided by optical resonators. We find that once the atoms have established that they are inside a resonator, the dipole-dipole potential may or may not remain a useful concept, depending upon the strength of the atom-field interaction. In the weak-coupling regime, one finds a two-body dipole-dipole interaction that can be enhanced or inhibited by varying the atom-field detuning. In the strong-coupling regime, by contrast, the two-body dipole-dipole potential ceases to be meaningful.

The availability of relatively high intensity $(I>\mathrm{}{10}^9{\mathrm{W}\mathrm{}\mathrm{cm}}^{\mathrm{-}2})$ [but moderate $\left(\sim \mathrm{nJ}\right)$ total energy], femtosecond laser pulses with wavelengths ranging from the ultraviolet to the midinfrared has opened the doors for a serious investigation of the nonlinear optical properties of matter on ultrashort time scales in a new parameter regime. Even small intensity-dependent nonlinearities can begin to play a major role in the overall electrodynamics, and in determining the fate of the propagating pulse. It is shown that a femtosecond pulse propagating near a two-photon transition in a semiconductor waveguide can undergo a large blueshift.

The polarization state of the output of collisionally pumped soft-x-ray lasers is studied through the Maxwell-Bloch (MB) approach considering level degeneracy. We have used the MB theory, so as to account for the propagation of linearly polarized waves, in the laser-target conditions of two recent experiments on neonlike germanium. In the case where a linearly polarized x-ray beam is injected into an amplifying plasma, we conclude that the polarization state of the output will be basically unaltered by the amplifier. We have also investigated intrinsic polarization of the output of an amplified-spontaneous-emission system, i.e., in the absence of a seeded radiation. Applied to the $J=0\mathrm{}–J=1\mathrm{}$ lasing line, the calculations suggest that the emerging signal is not polarized. However, one of the experiments referred to above has shown a spontaneous polarization, but the mechanism invoked by the authors to interpret this result, namely a selective trapping of the resonance line, is shown to be negligible, especially when elastic electron-ion collisions are taken into account. The influence of these collisions on the polarization properties of the amplifier is investigated through the atomic orientation and alignment. A spontaneous contribution to the output polarization is obtained when a circularly polarized beam is injected in the amplifier in order to create the necessary population differences between the quantum states of each laser level.

The quantum-mechanical interpretation of the long-wavelength spatial beating of the light intensity in the Schwarz-Hora effect is discussed. A more accurate expression for the spatial period has been obtained, taking into account the mode structure of the laser field within the dielectric film. It is shown that the discrepancy of more than 10% between the experimental and theoretical results for the spatial period cannot be reduced by using the existing models. More detailed experimental information is necessary to clear up the situation.

The performance of the so-called superconvergent perturbation theory [W. Scherer, Phys. Rev. Lett. 74, 1495 (1995)] is investigated numerically in the case of the ground-state energy of a quartic anharmonic oscillator. It is shown that Scherer’s superconvergent approximation, which is rational in the coupling constant $\beta$, gives in the case of small coupling constants somewhat better results than the strongly divergent but asymptotic Rayleigh-Schrödinger perturbation series if it is truncated at the same order in $\beta$. However, the transformation of this truncated perturbation series into Padé approximants or into another class of rational functions by means of the sequence transformation ${\delta }_k^{\mathrm{}\left(n\right)\mathrm{}}\left(\zeta {,s}_n\right)$ [E. J. Weniger, Comput. Phys. Rep. 10, 189 (1989)] yields much more powerful rational approximants. Moreover, the performance of the superconvergent approximation can be improved considerably by Wynn’s epsilon algorithm [P. Wynn, Math. Tables Aids Comput. 10, 91 (1956)] or by ${\delta }_k^{\mathrm{}\left(n\right)\mathrm{}}\left(\zeta {,s}_n\right)$. Finally, it is shown that the other rational approximants provide much better approximations to higher order terms of the Rayleigh-Schrödinger perturbation series than Scherer’s superconvergent approximation.

The scaling properties of the exact correlation-energy functional are applied in the study of the general rational, polynomial, and logarithmic local forms (and their combinations) of the correlation-energy functional, which depend on the density. It is concluded that these forms cannot satisfy the uniform and nonuniform scaling properties at the same time; therefore, they would have to be modified to represent exact forms of the correlation-energy density functional, at least in the high- and low-density limits. These results are not affected by the application of the local spin density or the self-interaction correction procedures to the above functionals.

Nuclear-size corrections of order $(Z\alpha {)}^5$ and $(Z\alpha {)}^6$ to the $S$-state levels of hydrogenic atoms are considered. These nuclear-elastic contributions are somewhat smaller than the polarizability (nuclear-inelastic) corrections for deuterium, but are of comparable or larger size for the hydrogen case. For deuterium the (attractive) nonrelativistic $(Z\alpha {)}^5$ correction to the $2S$-$1S$ transition is 0.49 kHz, while the (repulsive) relativistic $(Z\alpha {)}^6$ contribution is $-$3.40 kHz. For the proton the corresponding corrections are 0.03 kHz and $-$0.61 kHz, respectively. The $(Z\alpha {)}^5$ contribution largely cancels the Coulomb-retardation part of the nuclear-polarization correction.

The scalar and tensor polarizabilities of the cesium $(10\mathrm{}–{13)D}_{3/2,5/2}$ states were found with uncertainties of less than 0.3%. This experiment measured the voltage required for atoms excited by a laser beam in an electric field to be simultaneously in resonance as atoms excited by a frequency sideband of the laser in a field-free region. The results are in reasonable agreement with theoretical calculations.

The WKB approximation for the Bogoliubov equations of the quasiparticle excitations in Bose gases with a condensate is worked out in the case of spherically symmetric trap potentials on the basis of the resulting quantization rule. The excitation spectrum is calculated numerically and also analytically in certain limiting cases.

The use of mixed gases of working atoms with a much higher density of hydrogen has been proposed in recombination type x-ray lasers excited by high-intensity ultrashort pulse lasers. Hydrogen was chosen as the most suitable material to supply low-energy electrons in the optical-field ionization. Numerical analysis shows that a maximum gain can be expected for lithiumlike neon at a relatively low neon density of $9\times {10}^{17}{\mathrm{cm}}^{\mathrm{-}3}$ with 60 times higher hydrogen density.

We predict the possibility of using two-photon coherent propagation effects for generating pulses at the difference frequency with duration significantly shorter and intensity higher than those of the input pump and injection pulse.

A certain class of parametric down-conversion Bell-type experiments has the following features. In the idealized perfect situation it is in only 50% of the cases that each observer receives a photon; in the other $50\%$ one observer receives both photons of a pair while the other observer receives none. The standard approach is to discard the events of the second type. Only the remaining ones are used as the data input to some Bell inequalities. This raises justified doubts about whether such experiments could ever be genuine tests of local realism. We propose to take into account these “unfavorable” cases and to analyze the entire pattern of polarization and localization correlations. This departure from the standard reasoning enables one to show that the experiments are indeed a true test of local realism.

A semiempirical calculation of the $6s-7s$ Stark amplitude $\alpha$ in Cs has been performed using the most accurate measurements and calculations of the electromagnetic amplitudes available. This is then used to extract the parameters of the electroweak theory from experimental data. The results are $\alpha {=269.0\mathrm{}\left(1.3\right)a}_0^3$, weak charge of Cs $Q_W=-{72.41\left(25\right)\mathrm{}}_{\mathrm{expt}}{\mathrm{}\left(80\right)\mathrm{}}_{\mathrm{theor}},$ deviation from the standard model $S=-{1.0\left(.3\right)\mathrm{}}_{\mathrm{expt}}{\mathrm{}\left(1.0\right)\mathrm{}}_{\mathrm{theor}}$ and the limit on the mass of the extra $Z$ boson in the SO(10) model $M_{Z_x}>550\mathrm{}$ GeV.

The fine-structure intervals separating $n=9\mathrm{}$ and 10, $L=5\mathrm{}–8$ Rydberg levels of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2,$ bound to the $v=0,R=0\mathrm{}$ ground states of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+},$ are measured with microwave spectroscopy and used to determine the isotropic dipole polarizabilities of both ion ground states. The results ${\alpha }_s({\mathrm{H}}_2^{+}{)=3.1659\mathrm{}(8)a}_0^3$ and ${\alpha }_s({\mathrm{D}}_2^{+}{)=3.0667\mathrm{}(8)a}_0^3$ are more precise than existing theoretical predictions, and their explanation will pose a substantial challenge to the theory of this fundamental ion.

We build amplitude, i.e., absorptive masks, for neutral atoms using light, reversing the roles of light and atoms as compared to conventional optics. These masks can be used both to create and to probe spatially well-defined atomic distributions. The resolution of these masks can be significantly better than the optical wavelength. Applications range from atom lithography to fundamental atom optical experiments.

We describe the calculation of singly differential (energy-sharing) cross sections for electron-impact ionization. First, using exterior complex scaling, we calculate the outgoing portion of the scattering wave function without explicit use of asymptotic boundary conditions. Once that wave function is known for a finite region of space, the outgoing flux can be calculated and extrapolated to large distances according to behavior that is specific to the ionization problem. The differential cross section is proportional to the outgoing flux in specific directions of a hyperspherical angle in the coordinates. Calculations on the singlet $s$-wave radial limit (Temkin-Poet and collinear) models of electron-hydrogen atom ionization are presented.

We have observed the production of ${\mathrm{HeH}}^{+}$ ions by the bombardment of gaseous mixtures of ${\mathrm{H}}_2$ and He with slow positrons and measured its dependence on the positron energy. The formation is believed to involve vibrational excitation of ${\mathrm{H}}_2^{+}$ via positronium formation, followed by proton transfer from ${\mathrm{H}}_2^{+}$ to He. The significance of these results with respect to astrophysics is discussed.