This paper presents a review of a few low-dimensional models which describe some of the dynamical properties of the single-mode inhomogeneously broadened, unidirectional ring laser, and points out the limits of their validity in comparison to the integro-differential equations from which they are derived. A 6D model that seems to circumvent the weaknesses of the other models is also proposed. A numerical analysis with parameter values that correspond to two-laser systems shows a good description of most of the qualitative dynamical aspects exhibited by these systems. The simplicity of our model will allow for a deep numerical investigation, and will yield a better insight into the physical mechanisms connected with single-mode inhomogeneously broadened laser dynamics.

In this paper we investigate the self-focusing of a Gaussian beam in a saturable nonlinear medium. We show that the dynamics of the incident Gaussian beam become progressively more complicated as the ratio of the Gaussian spot size to that of the ground-state solution is increased for a fixed energy flux. As this ratio is increased (or decreased) from unity, recurrence of the field is observed followed by a mixture of recurrence and azimuthal-symmetry breaking, and finally there is strong azimuthal-symmetry breaking resulting in beam breakup into solitary waves. In this last stage there is no evidence that the field will recur at larger propagation distances.

An active gravity-wave detector based on a two-arm optical parametric oscillator (OPO) is proposed and analyzed. The signal and idler waves of a nearly degenerate parametric oscillator are internally separated such that the signal beam propagates along one arm of the OPO and the idler beam along the orthogonal arm. By monitoring the signal-idler beat frequency, a sensitive measure is obtained of the differential path displacement in the two arms of this OPO interferometer. The phase noise of the output beat frequency is calculated and is shown to exhibit time-dependent squeezing. The detection sensitivity is limited by the signal-idler phase diffusion and photon shot noise, and is the same as that of the usual passive Michelson interferometer or active two-laser interferometer for a given apparatus size and detected optical power. Squeezed vacuum can, in principle, be used to improve the detection sensitivity.

We have derived the wave equation of electromagnetic field coupling with TO phonons in second-order nonlinear dielectrics. If the loss of the medium can be ignored, theoretical calculation shows that the propagation of electromagnetic pulses without distortion in the dispersive medium is possible due to the dependence of the index of refraction on the electromagnetic field. This electromagnetic field is governed by a Boussinesq equation that has soliton solutions. If the loss of the medium is sufficiently strong that the damping distance is much smaller than the signal width, we find electromagnetic shock-wave solutions. Possible experiments in ${\mathrm{LiTaO}}_3$ are discussed.

Lie-group methods are used for analyzing the photon number distribution of detuned two-mode squeezed states. The effects of the detuning on the vacuum and excited two-mode squeezed states are analyzed and found to be similar to those obtained previously for the degenerate case. Correlations between the radiations in the two modes are described and found to decrease as a function of the detuning parameters.

We study numerically ionization from a model atom induced by a strong high-frequency field. Both one- and two-dimensional models are considered. We discuss the physics of ionization suppression in strong fields and point out the differences between one- and higher-dimensional models. We also discuss the applicability of classical modeling.

The saturation effects of a single-mode laser containing both additive and multiplicative white noise are investigated. Analytic expressions of the mean, variance, and skewness of the steady-state laser intensity are derived. Compared with the experimental measurements of Young and Singh [Phys. Rev. A 38, 238 (1988)] and the third-order laser theory, good agreement is obtained in the threshold regime.

The dynamical properties of an optical parametric amplifier with an added fourth-order (Kerr-effect term) nonlinearity are studied by means of a computer simulation of a semiclassical nonlinear Langevin formulation. The transient statistics above threshold are analyzed in detail, and the relevance of the present results for the production of squeezed light in traveling-wave devices is finally discussed.

Hamiltonians attaining number-phase amplification are presented. The amplification is driven by a peculiar dependence of the polarization on the phase of the field in a limited frequency range.

We develop a semiclassical approximation method for calculating correlation functions of the outgoing field of dissipative quantum systems. The method is strictly valid for linear quantum systems, and can be extended consistently to the nonlinear case. It can be used even at bifurcation points where linearization is no longer possible. It is applied to the dc-pumped degenerated Josephson-junction parametric amplifier. We demonstrate that the linearized fluctuation analysis can severely overestimate the maximum obtainable degree of squeezing.

By applying microwave pulses to the two lower levels of three-level atoms in the ssV configuration, the collective state vector can be switched from forbidden to allowed transitions. This means that we can, in effect, switch the superradiant and subradiant processes from off to on and vice versa.

Thermal light-scattering fluctuations are examined as a fundamental noise source inherent in nonlinear optical processes involving Kerr and artificial Kerr media. Stochastic models are introduced to simulate noise in optical phase conjugation via degenerate four-wave mixing, and in signal amplification via nondegenerate two-wave-mixing processes. Significant noise fluctuations in the amplitude and phase components of the processed signals are shown to occur even with incident signal powers in the milliwatt range. For time-dependent processes, including nondegenerate two-wave mixing, the fluctuation-dissipation theorem is shown to generalize a previously derived static susceptibility relation between light-scattering and nonlinear optical response to media exhibiting both power dissipation and nonlocal interaction.

We analyze in detail the quantum-nondemolition (QND) scheme of Brune et al. [Phys. Rev. Lett. 65, 976 (1990)]. It is shown that the quantum treatment of the scheme based on the density-matrix formalism is fully equivalent to an information-theoretical description. In this context, it is explicitly seen that the scheme works well even with a low detection efficiency. We show further that a careful choice of the atomic velocities can significantly reduce the number of atoms needed to perform a measurement. It is also possible to use a monoenergetic atomic beam, although in this case the number of atoms needed increases. Finally we discuss how the results are modified if the atomic velocities are only known approximately.

The photodetachment of a model one-electron ion simulating ${\mathrm{H}}^{\mathrm{-}}$ in the presence of a low-frequency field is analyzed. Two different geometries are considered in order to get information on the effect of the ponderomotive energy shift Δ on the photodetachment cross section. Our calculations suggest that a correspondence may be established between the ponderomotive shift and the photodetachment cross section, when the ejected electron may exchange only a few low-frequency photons. This is in qualitative agreement with recent experimental observations. When a large number of processes are open in which the detached electron may exchange low-frequency photons with comparable probability, it is impossible to make any connection between ponderomotive threshold shift and photodetachment cross section which, instead, may be described in terms of a field picture.

Numerical simulations of mode locking in synchronously pumped ${\mathrm{Tl}}^0$(1) color-center lasers are presented. An asymmetric response with respect to cavity mismatch and the origin of large-scale fluctuations in spontaneous-emission noise are described. It is shown that quasistationary pulse trains may be obtained on cavity tuning without a degradation in pulse quality.

In this paper, we have investigated the time evolution of the phase operator of the radiation field in the Jaynes-Cummings model with and without the rotating-wave approximation, making use of the phase formalism of Barnett and Pegg [J. Mod. Opt. 36, 7 (1989); Phys. Rev. A 39, 1665 (1989)]. We verify by an analytical method that the atomic Rabi oscillation leads to phase dissipation of the radiation field, and also that the effect of the virtual-photon field can exhibit quantum fluctuations in the atom-field-coupling system and lead to a frequency shift of the radiation field.

Resonances in the interaction of a saturable two-level system with stimulated Brillouin scattering are discussed. These resonances appear due to the coupling between the two-level system and the resonant acoustic waves that are excited in the host substance by a coherent electromagnetic field of two mutually detuned, counterpropagating laser beams. Results for sodium vapor mixed with nitrogen buffer gas are presented.

An open quantum system is usually characterized by a reduced ensemble density matrix, the dynamics of which is governed by a generalized Master equation. Transforming this equation of motion into the instantaneous diagonal basis of the corresponding reduced density matrix, we can separate the coherent and incoherent part of the dynamics: The coherent dynamics is incorporated in the time development of the diagonal basis states, while the coupling to the reservoirs leads to simple rate equations. Interpreting these rate equations as a stochastic point process allows one to simulate the stochastic time evolution (random telegraph signals, ‘‘quantum jumps’’) of single-quantum systems. The diagonal representation can be considered as a generalization of the dressed-state picture of open quantum systems. Numerical simulations (‘‘quantum Monte Carlo’’) allow one to derive various dynamical properties (including correlation functions) of single-quantum systems. This concept is applied to different two- and three-level scenarios (λ and ν configuration), and its limitations are discussed.

Atomic coherences and squeezing of the resonance fluorescence are investigated for three-level atoms of the Λ configuration. An experimental scheme is proposed for direct observation of the atomic coherence in the lower states, based on switching the phase difference of the pump lasers. Squeezing of the resonance fluoresence of three-level atoms is predicted even when long-lived atomic coherences exist.

We describe a simple approximate nonperturbative method for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian.