This paper gives a full account of the dynamical properties of single-mode inhomogeneously broadened lasers. The study divides itself into two parts. First, the integro-differential ‘‘Maxwell-Bloch’’ equations, which describe such systems, are numerically solved for a large scan of values of the various control parameters that govern the dynamical evolution of self-pulsing lasers. The instability hierarchies, delimited with respect to the excitation parameter, reveal that, along with the various decay rates of the interacting variables, the chosen number of velocity components, which divides the polarization integral into discrete intervals, also plays an important role in the dynamical evolution of the system, especially in the self-pulsing regime of operation. The second part of this paper concerns another approach to modeling single-mode inhomogeneously broadened laser dynamics that largely circumvents the infinite-dimensional complexity of the medium’s polarization. A hierarchy of low-dimensional models, with increasing accuracy with respect to the infinite-dimensional ‘‘Maxwell-Bloch’’ equations, is constructed and adapted to describe correctly most of the properties of single-mode inhomogeneously broadened lasers.

A Hanbury Brown–Twiss experiment is described that is capable of demonstrating, in principle, the solitary behavior of a quantum soliton in an arbitrary fundamental soliton state. The relevant correlation functions are evaluated and show that the quantum noise does not cause a breakup of the solitons of the quantized nonlinear Schrödinger equation. For large photon numbers, the intensity autocorrelation function of the fundamental soliton becomes independent of certain momentum and photon-number distributions, which gives us a correspondence principle for the fundamental soliton. Whereas intensity-correlation measurements based on direct detection show essentially classical behavior for large photon numbers, homodyne-detection experiments can uncover quantum effects such as the generation of Schrödinger-cat solitons.

The energy-exchange process between the fundamental and its second-harmonic fields copropagating in an optical medium is facilitated by the spatially periodic dc poling field. The nonlinear dynamics of this system is investigated in the context of an effective Hamiltonian formalism. The explicitly included cross-modulation and self-phase-modulation nonlinear terms lead to the bifurcation instability interpreted as a new switching phenomenon in which both up- and down-conversion efficiencies can be precisely controlled by the external field. Experiments testing predicted effects are suggested.

A many-body theory of quantum fluctuations in the optical parametric oscillator is given. Dyson equations and diagrammatic representation of photon Green functions are derived from a combination of quantum Langevin and many-body techniques. Single-photon Green functions are used to compute dynamic spectra of the output using a self-consistent scheme which incorporates nonlinear, many-photon polarization effects. The latter scale with system size and their influence on the nonlinear quantum dynamics is addressed. We present results of dynamic output spectra and quantum-noise properties beyond the adiabatic approximation.

The nature of light scattered from a two-level atom, where the transition frequency between the two levels is a stochastic quantity, pumped by a strong monochromatic field is investigated. The optical Bloch equations, modified to include the stochastic nature of the atomic frequency, are solved using Monte Carlo techniques to include arbitrary strengths and bandwidths of the frequency noise. We find in the spectrum of scattered light a shift of the Rabi sidebands due to the stochastic nature of the transition frequency. We also find the height of the Rabi sideband first decreases and then increases with increasing strength of the noise. The intensity-intensity correlation function for the emitted fluorescence is observed to be sensitive to the time scale of the noise. The calculated line shapes for weak driving fields can be fitted to a superposition of Gaussian and Lorentzian lines.

The quantized center-of-mass (c.m.) motions of a single two-level atom or ion confined into a one-dimensional harmonic potential and interacting with a single-mode classical traveling-wave laser field are examined. We demonstrate that trap quantum states with remarkable nonclassical properties such as quadrature and amplitude-squared squeezing and sub-Poissonian statistics can be generated in this simple trap model when the c.m. motion is initially in certain coherent trap states. Our analyses also indicate that there exist some time regions where the production of nonclassical vibrational states is possible even if squeezing or sub-Poissonian statistics do not appear.

We investigate the photon distribution of a two-mode squeezed vacuum and show that the distribution of photons among the two modes depends on four parameters: two squeezing parameters, the relative phase between the two oscillators, and their spatial orientation. The distribution of the total number of photons depends only on the two squeezing parameters. We derive analytical expressions and present pictures for both distributions.

We investigate multiphoton ejection probability of strongly bound electrons in relativistically intense laser fields. A solvable model of a Klein-Gordon electron bound in a finite-range separaable potential and interacting with a circularly polarized plane-wave field is used for the analysis. For binding energies of the order of several keV the rates of electron ejection for ω=100 eV are found to be significant at relativistic intensities but are extremely small for ω=10 eV. For lower binding energies spectra are obtained for the available ${\mathrm{CO}}_2$ laser frequency (ω=0.117 eV) and Nd laser frequency (ω=1.169 eV). Numerical results show the stabilization effect for both relativistic and nonrelativistic intensities and subthreshold frequencies.

The cross sections for resonant two-color, two-photon detachment of ${\mathrm{H}}^{\mathrm{-}}$ with excitation of the degenerate H(2s) and H(2p) levels are calculated within a semiempirical adiabatic hyperspherical representation. The first photon, with energy ${\mathrm{\omega }}_1$=0.4017 a.u., is resonant with the well-known Feshback ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ resonance below the H(n=2) threshold. The second photon, with energy ${\mathrm{\omega }}_2$≥0.126 05 a.u., scans the energy region above the H(n=2) threshold over which long-range dipole-field-induced cross-section oscillations are predicted to occur. Such Gailitis-Damburg oscillations have not yet been observed experimentally. Results for various pairs of light polarization for the two photons are presented. Our resonant two-color, two-photon detachment cross sections are 8–9 orders of magnitude greater than the corresponding nonresonant, single-color, two-photon detachment cross sections obtained by Liu, Du, and Starace [Phys. Rev. A 43, 5891 (1991)]. Unmistakable evidence of long-range dipole-field effects is presented over the 5-meV energy range above the H(n=2) threshold. Furthermore, the differential cross sections for right- and left-circularly polarized, copropagating photons and especially the circular dichroism differential cross sections are shown to have nearly a full cycle of a greatly enhanced dipole-field-induced oscillation extending over the region from threshold to ≊34 meV above.

Transient statistics during the Q switching of two-mode gas ring lasers are studied, including the nonlinear regime. When both modes are well above threshold, explicit expressions for the transient intensity probability densities are obtained with the use of a quasideterministic theory. For similar pump parameters of the two modes, the intensity probability density of the secondary mode shows a polynomial tail due to mode competition. The main mode shows a symmetric tail and the probability density is peaked around its mean value (mode-partition noise). The anomalous fluctuations of the two modes are characterized by the maximum value of the probability density and by the time at which this maximum appears. We also consider the case of a very depressed secondary mode. An approximation is developed to describe the transient regime of the secondary mode. The transient probability densities and the side-mode excitation probability are obtained.

The squeezing properties of a system characterized by large ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ and ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ nonlinear susceptibilities and injected classical fields for the two relevant modes are studied as a function of the output power. A large reduction of noise levels well above threshold has been found and a remarkable dependence of the maximum squeezing on the input power has been shown. The possibility of an implementation with state of the art technology is demonstrated, enabling a practical realization of a laserlike source with a high degree of squeezing at high intensities.

An adiabatic-switch method for calculating harmonic generation under intense laser radiation is presented. The adiabatic switch is first applied to nonbound (i.e., ionizing or dissociative) time-periodic Hamiltonians when the energy spectrum is degenerate. Our derivation is based on the use of Floquet theory combined with complex scaling and of a generalized definition of the inner product for non-Hermitian operators. A model potential representing a Xe atom in the presence of a laser field is studied as an example to illustrate the numerical advantages of the present method and its stability.

The analytic solution of the steady-state density matrix is presented for a closed two-level atom with an arbitrary ground-state angular momentum ${\mathit{J}}_{\mathit{g}}$ and an excited-state angular momentum ${\mathit{J}}_{\mathit{e}}$ interacting with a linearly polarized laser field. From this solution, analytic formulas for the total rate of laser-atom scattering, the rate of coherent scattering, and radiative forces are derived. Interestingly, it is found that population inversion in true atomic states, as opposed to the population inversion in the dressed states, can occur under certain conditions. A method is proposed to take advantage of this inversion for light amplification. The mathematical formulation is built around the concept of the resolvent operator in Liouville space, with some conclusions that are generally applicable to any system with a unique steady state.

A simple experiment with ordinary interference of macroscopic laser beams is proposed which demonstrates that interference can be made to disappear and reappear, as in a ‘‘quantum eraser,’’ without using an entangled state.

In this report, our previous measured natural-radiative-lifetime values [G. Chuan et al., Phys. Rev. A 47, 1551 (1993)] of the perturbed Rydberg sequence 4${\mathit{f}}^{14}$6snp ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$ of Yb I have been analyzed using multichannel quantum-defect theory. The agreement between theoretical and experimental results is rather good.

Excitation energies and oscillator strengths from the ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ ground state to the first ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ excited states of Cd-like ions are calculated by using the multiconfiguration relativistic random-phase approximation including excitation channels from core electrons. The discrepancies among theories and experiments are much reduced but, in general, remain.

The electron-pair function h(u) of a finite many-electron system is not monotonic, but the related quantity h(u)/${\mathit{u}}^{\mathrm{\alpha }}$, α>0, is not only monotonically decreasing from the origin but also convex for the values ${\mathrm{\alpha }}_1$ and ${\mathrm{\alpha }}_2$, respectively, as has been recently found. Here, it is first argued that this quantity is also logarithmically convex for any α≥α’ with α’=max{-${\mathit{u}}^2$${\mathit{d}}^2$[lnh(u)]/${\mathit{du}}^2$}. Then this property is used to obtain a general inequality which involves three interelectronic moments 〈${\mathit{u}}^{\mathit{t}}$〉. Particular cases of this inequality involve relevant characteristics of the system such as the number of electrons and the total electron-electron repulsion energy. Second, the logarithmic-convexity property of h(u) as well as the accuracy of this inequality are investigated by the optimum 20-term Hylleraas-type wave functions for two-electron atoms with nuclear charge Z=1, 2, 3, 5, and 10. It is found that (i) 14<α’<20 for these atomic cases (we remark that α’≫${\mathrm{\alpha }}_2$≫${\mathrm{\alpha }}_1$) and (ii) the accuracy of the inequality which involves moments of contiguous orders oscillates between 62.4% and 96.7% according to the specific He-like atom and the moments involved. Finally, the importance of the logarithmic-convexity effects on the interelectronic moments relative to those coming from other monotonicity properties of h(u)/${\mathit{u}}^{\mathrm{\alpha }}$ are analyzed in the same numerical Hylleraas framework.

Fourth-order many-body perturbation-theory calculations of the spectroscopic constants of ${\mathrm{CaH}}^{+}$ are presented as an attempt to help identify possible astronomical or laboratory observations. The results for the rotational and vibrational constants are, respectively, 4.61 and 1511 ${\mathrm{cm}}^{\mathrm{-}1}$. Similar calculations are made on ${\mathrm{MgH}}^{+}$, where comparison with experimental values shows excellent agreement, indicating reliable results for ${\mathrm{CaH}}^{+}$

Various total cross sections and elastic differential as well as momentum-transfer cross sections for electron scattering by oxygen atoms are calculated for incident energies ${\mathit{E}}_{\mathit{i}}$=8.7–1000 eV. A partial-wave analysis of the local, complex, energy-dependent optical potential yields reliable total cross sections. Discrepancies between theories and experiment exist at low energies, but a reasonable energy-variation picture of various ${\mathit{e}}^{\mathrm{-}\mathrm{-}}$O cross sections emerges. The present total inelastic cross sections are similar to but higher than the recommended total ionization cross sections.

The kinetic-energy distribution of ${\mathrm{O}}^{+}$ ions produced from doubly ionized ${\mathrm{O}}_2$ by electron impact has been measured using a time-of-flight coincidence-detection method. Compared to other results, the signal-to-noise ratio has been increased and the kinetic-energy distribution shows some differences. Attempts have been made to assign the sources of the ions.