The forward peak resulting from electron capture to the continuum of bare projectiles is investigated within the impulse approximation in both its prior and post form. It is found that the asymmetry of the peak as well as the peak intensity increases if a larger number of interactions between the electron and the projectile is included in the calculation. For strongly asymmetric systems with light projectiles, a peaking approximation becomes valid which factorizes the capture cross section into the ionization cross section times the projectile Coulomb normalization. Thus capture from excited states is easily included, and the factorization allows for a fast evaluation not only of the electron spectra but also of the impact-parameter distribution and the alignment. The theory is also extended to capture into Rydberg states. The collision systems ${\mathrm{He}}^{2+}$+He, p+He, and p+Ne are investigated, and comparison is made with available experimental data.

We present partial-cross-section results for Si 2p and valence photoionization of ${\mathrm{SiF}}_4$ for photon energies in the vicinity of the Si 2p and 2s thresholds. The continuum shape resonances decay only to the Si 2p main line, in accordance with one-electron theory predictions. The Si $L_2$,3VV Auger spectrum was also measured, and was found to agree with earlier work. We propose that variations in hole-interaction energies are important in assigning the Auger final states. For the Si 2p discrete excitations, spectra obtained on the ${\sigma }^{\mathrm{*}}$($a_1$) resonances compare well with previous qualitative results and the above-threshold Si $L_2$,3VV Auger spectrum. Our results help to quantify the relative enhancement of satellites and main lines, emphasizing the dominance of spectator decay. Spectra obtained at several higher-energy Si 2p and Si 2s excitations also generally support spectator decay as an important mode of relaxation for these discrete states. The overall assignment of the Si 2p and 2s discrete excitations to molecular-orbital and Rydberg transitions is discussed.

Exact integral expressions and simple analytical estimates for the bound-bound, bound-continuum, and continuum-continuum dipole matrix elements are derived by use of the momentum-space eigenfunctions for a one-dimensional model of a hydrogen atom. These results provide the essential ingredients for the numerical study of the quantum mechanisms responsible for the chaotic ionization of highly excited hydrogen atoms in intense microwave fields. A specific numerical algorithm for solving the Schrödinger equation for a one-dimensional hydrogen atom in an oscillating electric field is described which uses these results for the dipole matrix elements along with a discrete representation of the continuum. In addition, the momentum-space representation of the Sturmian basis functions has been used to derive exact integral expressions and convenient analytical estimates for the projections of the Sturmian basis functions onto the hydrogenic bound and continuum states. These results are used to provide a direct comparison of numerical calculations for the ionization of one-dimensional hydrogen atoms using the hydrogenic and Sturmian bases.

The partial and total photoionization cross sections for the S(3$s^2$3$p^4$ ${}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$) ground state, leaving the residual ${\mathrm{S}}^{+}$ ions in the lowest three 3$s^2$3$p^3$ ${}_{}{}^4{}_{}{}^{}\mathrm{S}_{}^{\mathrm{o}}{}_{}{}^{}$${,}^2$${\mathrm{D}}^{\mathrm{o}}$${,}^2$${\mathrm{P}}^{\mathrm{o}}$ LS states, are calculated in both the dipole length and velocity forms. Extensive configuration-interaction wave functions are used to describe both the initial bound S state and the final continuum ${\mathrm{S}}^{+}$ states. The prominent features in the cross sections are the autoionization Rydberg series converging to ${\mathrm{S}}^{+}$(3${\mathrm{s}}^2$3${\mathrm{p}}^3$ ${}_{}{}^2{}_{}{}^{}\mathrm{D}_{}^{\mathrm{o}}{}_{}{}^{}$${,}^2$${\mathrm{P}}^{\mathrm{o}}$) excited-state thresholds. The parameters of these autoionizing levels are presented. The present results are compared with the available experimental measurements and other calculations.

The Stern-Gerlach magnetic deflection spectrum of a molecular beam of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$ cooled by supersonic expansion to its lowest rotational level (K=1) reveals nine spatially separated peaks within a span of 2 cm. These peaks readily are assigned from a calculation of the Zeeman energies of the K=1 spin-rotation sublevels characterized by $M_J$, and the assumption of a uniform field gradient within the deflecting magnet gap. However, the variable widths of the observed peaks and the decreasing deflection of certain $M_J$ peaks with increasing field above 14 kG require the explicit consideration of field-gradient inhomogeneities. The theory for this is developed and the spectral profiles again computed with field-gradient inhomogeneity and rotational temperature ($T_{\mathrm{rot}}$) as variables. Agreement of the theoretical shifts, bandwidths, and relative intensities with increasing field gradient when compared with the experimental spectra is very good, and $T_{\mathrm{rot}}$ is found to be 3.5 K. The deflection spectrum of a beam of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$ differs from that of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$, reflecting the population of the K=0 rotational level in the ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$ isotopomer. The oxygen dimer and trimer appear to be paramagnetic, but this result is tentative.

We show that in a large class of nonlinear optical processes which are used to generate the squeezed states of the radiation field, the quantum state of the generated radiation is given by a Gaussian Wigner function. This is so even when losses in the medium are included. The photon-number distributions for such fields are evaluated. The number distributions exhibit oscillatory character for the range of parameters for which the field is squeezed.

A nonlinear quantum theory of the quantum-beat laser is developed using a ‘‘dressed-atom–dressed-mode’’ master-equation approach. The theory is valid under the detuning conditions which led to correlated spontaneous emission in a linear theory. It is shown that the quenching of the quantum noise remains valid in the nonlinear theory and this operation is stable above threshold.

We show that if we inject three-level atoms, at a low rate, through a double cavity, with the two upper levels strongly coupled, and if, in the theoretical analysis, one makes the rotating-wave approximation, this problem is formally equivalent to the ordinary two-level micromaser. We also obtain the relevant master equation and the photon statistics.

We show that in a three-level system, if the atoms are initially prepared in a coherent superposition of the two upper states, as in Hanle experiments, the spontaneous-emission events from these two states to the lowest one can, under certain conditions, be strongly correlated, with a vanishing diffusion constant for the relative phase. The conditions under which correlated spontaneous emission occurs in a Hanle laser remain essentially unchanged if atomic motion is included.

A single three-level atom with the ground state strongly coupled to an excited state and weakly coupled to a third intermediate state exhibits a telegraph signal of fluorescent emission when driven by laser light at the strong coupling frequency. The ‘‘on’’ periods correspond to normal resonance fluorescence, whereas the ‘‘off’’ periods correspond to the atom being ‘‘shelved’’ in the intermediate state. Such a system has interesting statistical properties. The photon statistics during the ‘‘on’’ periods correspond to two-level behavior and are close to Poisson in nature. However, the photon number distribution of a succession of ‘‘on’’ periods exhibits Bose-Einstein statistics. Thus the three-level system can exhibit both ‘‘quiet’’ and ‘‘noisy’’ behavior. The mathematical connection between the two cases is established, and an atomic beam experiment is described which records a mixture of the two statistical extremes. The composition of the mixture is varied, and the data are shown to be well represented by an analysis based upon the model developed.

Calculations of the single and multiphoton ionization of xenon valence-shell electrons are reported for several wavelengths and laser intensities. The model follows a single valence electron in the field of an effective core potential, the remaining valence electrons, frozen in their ground-state orbitals, and a linearly polarized laser field. Ionization rates and cross sections are determined using a direct numerical solution of the time-dependent Schrödinger equation using a finite-difference technique. Excellent agreement with experimental rates and previous theoretical cross sections has been obtained. Bound states, shifted into resonance by the ac Stark effect, are found to affect the ionization dynamics. Departures from perturbation theory at high intensities are demonstrated and discussed.

A quantum analysis of the intensity fluctuations is given for the nondegenerate parametric oscillator both above and below threshold. Theoretical analysis and experiments by Heidmann, Horowicz, Reynaud, Giacobino, and Fabre [Phys. Rev. Lett. 59, 2555 (1987)] have shown that a noise suppression below the vacuum level is possible in the difference of the intensities of the signal and idler modes. The effect of nonequal cavity decay rates and intracavity losses is shown to modify significantly the fluctuation spectra for the difference in the intensity of the signal and idler beams. The results of exact nonlinear solutions for the internal cavity modes are discussed. We demonstrate that a very sensitive absorption detector may be made by operating the oscillator near threshold.

Cooperative effects on squeezing in resonance fluorescence from a finite number N of atoms are examined. Analytical expressions for the spectrum of squeezing and a quantity Q(T) related to the photon-counting statistics of the squeezed states are presented for N=1 and 2. These expressions are obtained by invoking the high-field approximation of the relevant master equation. The analytical results are supplemented by the numerical solutions of the exact master equation for N≤10. It is shown that for intense fields or large detunings, squeezing in resonance fluorescence is predominantly due to the quantum nature of the sidebands of the Mollow triplet. As a manifestation of cooperative effects, squeezing present in the total as well as the sideband radiation increases with the number of atoms. This is further confirmed from the behavior of the photon-statistics function Q(T).

We study the spontaneous emission of atoms coupled to frequency-dependent photon-mode reservoirs, and find atomic emission spectra qualitatively different from those of free space. Frequency-dependent photon-mode reservoirs are found in a variety of physical situations (e.g., in waveguides, microcavities, dielectrics, systems with photonic spectral gaps, etc.), and are shown to lead to nonexponential decay and concomitant complicated non-Lorentzian emission line shapes. By studying Autler-Townes spectra in the presence of a frequency-dependent photon-mode density, we present simple examples of dynamical modifications of spontaneous decay properties.

The Kroll-Watson [N.M. Kroll and K. M. Watson, Phys. Rev. A 8, 804 (1973)] theory for electron scattering in the field of a low-frequency laser has been extended by L. Rosenberg [Phys. Rev. A 23, 2283 (1981); 28, 2727 (1983)] to apply to higher intensities. That result is rederived in another way so as to make the correction second order. The correction terms are obtained and shown to be small in the high-intensity low-energy regime in which the original theory is weakest. The special case of a Coulomb potential is analyzed and shown to present special peculiarities in the extended theory just as in the original Kroll-Watson theory.

Experimental and theoretical investigations of a multimode, standing-wave, cw dye laser have been carried out. The optical spectrum of the dye laser was found to evolve by discrete transitions with increasing pump power, between spectra composed of three stable modes and spectra composed of many modes whose amplitudes fluctuate strongly. The variation of the intensities versus time of individual modes of the multimode laser was measured. For pump powers where the spectrum consisted of modes with strongly fluctuating amplitudes, we found that the intensities of individual modes have a correlation time that decreases, and a variance that increases, with increasing pump power. In addition, the fluctuations were found to be deterministically chaotic. This rules out quantum noise as the origin of the fluctuations, a mechanism that had been assumed in many previous studies. We also have carried out numerical simulations of this laser, using a semiclassical model based on third-order, coupled-mode laser theory, which includes population oscillations, four-wave mixing in the gain medium, spatial hole burning, and spontaneous-emission noise. The behavior of the optical spectrum and the fluctuations of single-mode intensities are well modeled for low pump powers. The modeling indicates that four-wave mixing and spatial hole burning are responsible for the discrete transitions in the optical spectrum, and that four-wave mixing drives the strong fluctuations of the individual mode intensities.

A mathematically rigorous treatment of the Weisskopf-Wigner model of atomic spontaneous emission is presented. For the first time to the authors’ knowledge, it is shown that in the correct asymptotic treatment with a cutoff frequency at which the dipole approximation breaks down, the main contribution to the long-time deviation from the exponential decay is of the order of 1/(t ${\ln }^2$t). This contradicts the results of previous authors who have obtained a long-time behavior of the order of 1/$t^2$ by nonrigorous mathematical treatment of the same model in the dipole approximation. However, we will show that the result 1/$t^2$ can still be obtained if the retardation effects are taken into account, i.e., if no dipole approximation is made.

We have studied theoretically the effect of laser intensity on (2+1)-photon resonance-enhanced multiphoton ionization of the ${\mathrm{H}}_2$ molecule via both the inner-well and the outer-well vibrational levels of the double-minimum E,F ${}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}$ state. The branching ratios for the vibrational distribution of the ${\mathrm{H}}_2^{+}$ ion, the photoelectron angular distribution, and the corresponding asymmetry parameters have been calculated as functions of laser intensity ranging from ${10}^7$ W/${\mathrm{cm}}^2$ to 5×${10}^9$ W/${\mathrm{cm}}^2$ (peak intensity). For ionization via the vibrational levels $v_E$ of the inner well, it has been found that the branching ratios depend on laser intensity, the peak of the distribution being at Δv=0, i.e., $v_E$=$v_{\mathrm{ion}}$ transition, and our results are in good agreement with experiment. For ionization via the outer-well levels $v_F$ we have shown that the lower the value of $v_F$, the more the ion yield is shifted towards higher $v_{\mathrm{ion}}$ levels. We find that the photoelectron angular distribution remains unchanged over the whole intensity range studied in this work.

This paper investigates the angular momentum effect of the relativistic electron beam with large orbits in the electron cyclotron maser, where the electrons are injected axially and their equilibrium rotation is supported by a combination of an axial magnetostatic and a radial electrostatic field. Nonlinear simulation shows that the conversion efficiency of the kinetic energy of the electron beam may be enhanced by a proper radial electrostatic field.

The natural linewidths of a laser with a saturable absorber and of a dye laser have been calculated using a Fokker-Planck approach.