We discuss the optical bistable behavior of a system of N two-level atoms pumped by a coherent input field and coupled to a squeezed vacuum field by treating the optical bistability of such a system as an input-output problem. We consider the equation of motion for atomic dipole moments, coupled to the cavity field and the squeezed vacuum, and the boundary condition connecting the input and output fields with the atomic lowering operator. A simple analytical expression for the influence of the squeezed vacuum input on the bistable behavior of the output field is derived by this method. The results indicate a strong influence of the squeezed vacuum input on optical bistability. The squeezed (stretched) vacuum input field tends to increase (decrease) the range of optical bistability.

We find that a ${\mathrm{CO}}_2$ laser oscillation can be transferred from the chaotic state into the periodic pulsation state by introducing a small-amplitude sinusoidal modulation on an intracavity absorption. The proposed rate-equation model successfully reproduces these characteristic behaviors of the laser system. The numerical calculations based on the present model predict that the periodic window on the bifurcation diagram as a function of a normalized intracavity absorption coefficient shifts in two ways by the modulation: towards the lower absorption side when T<${\mathit{T}}_0$ and towards the higher absorption side when T>${\mathit{T}}_0$, where ${\mathit{T}}_0$ is the period of the laser pulsation in the window without the modulation and T is the period of the modulation. In the windows the laser pulsation is locked to the modulation signal, but the relative phase between them is different by π in the two cases stated above.

It is shown that optical pulses in dispersive media with dissipation and saturable broadband gain experience frequency self-shifting toward the point of zero group-velocity dispersion. The decreasing dispersion leads to a strong compression of the pulses at constant pulse energy. The ultrashort pulses that result from this evolution have a duration limited only by the third-order group-velocity dispersion of the medium. A set of solitonlike pulses is found that has a continuous spectrum of velocities, and a selection rule is presented to determine the unique solution established from an arbitrary initial pulse form.

Coherence properties of quantum optical solitons in the normalized fundamental soliton states are discussed in terms of the integrated two-point field and intensity autocorrelation functions, which are the relevant quantities in the quantum description of soliton interference experiments and in the Hanbury-Brown and Twiss experiment, respectively. Both the spatial and the temporal correlation properties are considered. The correlation functions are shown to be stationary in general, which demonstrates the solitary behavior of quantum fundamental solitons and indicates their stability in propagation. Explicit evaluation of the correlation functions in some limit cases enables us to make comparisons between the classical and the quantum-mechanical results. Conditions leading to the classical limit are derived and the intrinsic quantum phenomena are identified. Of great importance is the contribution of the momentum superposition, which can make the quantum results differ significantly from the corresponding classical ones.

The sum-frequency generation process using strong-field coupling and quantum interference is described systematically using atomic hydrogen both in theory and experiment. It is shown that strong coupling at the 3p-2s transition creates destructive interference to reduce the linear susceptibility at the resonant 3p←1s transition. Simultaneously, two-photon coupling of the 2s and 1s states produces constructive interference to resonantly enhance the nonlinear susceptibility for sum-frequency generation at the 3p→1s (Lyman-β) transition. Experimental results clearly demonstrate the theoretical predictions. When the Rabi frequency for the 3p-2s coupling exceeds the Doppler tail of the medium, the photoion signals on resonance are suppressed significantly because of induced transparency. The generated Lyman-β radiation grows rapidly by a factor of 250 at an atom density of ${10}^{15}$ ${\mathrm{cm}}^{\mathrm{-}3}$ and interaction length of 3.5 cm, resulting in a conversion efficiency of 2×${10}^{\mathrm{-}4}$.

The photon-number distribution for the gray-body radiation given by Bekenstein and Schiffer [Phys. Rev. Lett. 72, 2512 (1994)] is used to study its nonclassical effects. It is shown that as the absorptivity varies from 0 to 1, the gray-body state changes from an extremely nonclassical state to an extremely classical one. The critical point of this transition is located. It is discovered that the negative binomial state is a special case of the gray-body radiation at the transition point; hence, it is an example of borderline states such as the coherent state. The explicit expressions for the factorial moments, the Q parameter, the P function, and the nonclassical depth of the gray-body state as functions of absorptivity and temperature are derived.

We prove a theorem linking the phase associated with the ballistic evolution of a coherent state of a harmonic oscillator about a jumping vertex to that associated with its adiabatic migration along straight lines connecting the initial and the final points of each ballistic arc to the vertex on which the arc is centered. This equivalence allows one to determine the ballistic phase by Berry’s prescription. The method facilitates both the visualization and the calculation of modulation effects (quantum beats) in photon-echo experiments.

A general anaylsis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4,openR). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

The concept of the classical-like Wehrl entropy is shown to be a very sensitive and informative measure describing the time evolution of a quantum system. Its applications to the Jaynes-Cummings model reveal relevant aspects of the field dynamics. The Wehrl entropy provides a compact one-parameter description giving, among other things, a clear signature for the splitting of the Q function. It gives also a clear indication of the phase randomization of the coherent electromagnetic field states during the interaction with a two-level atom.

Optimal schemes for the creation of a transient population inversion between the ground and excited states of an ion in a subpicosecond-pulse laser-produced plasma are discussed. First results on experimental investigations of possible amplification in the soft-x-ray spectral region on transitions to the gorund states in O ii, O iii, C iii, and N iii ions are reported. Ions are produced due to optical field ionization of ${\mathrm{O}}_2$, ${\mathrm{CO}}_2$, and ${\mathrm{N}}_2$ gases in an intense Ti:sapphire laser field. Amplificaiton on the 2p3s${(}^3$P)-2${\mathit{p}}^2$${(}^3$P) transition (λ=374.12 Å) in O iii ions and on the 2${\mathit{p}}^2$3s${(}^2$P)-2${\mathit{p}}^3$${(}^2$D) transition (λ=616.56 Å) in O ii ions has been observed.

The spontaneous emission of photons by an atom placed near the dielectric slab is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (traveling) and the modes trapped to a waveguide formed by the slab (trapped). To describe angular properties of spontaneous emission a parametrization of the traveling modes by the outgoing waves has been proposed. Angular characteristics of the traveling photon emission, distributions of the trapped photon emission, as well as global decay rates have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error in an earlier paper by Khosravi and Loudon [Proc. R. Soc. London Ser. A 436, 373 (1992)] affecting thin slabs and results near waveguide-mode thresholds has been improved.

We study degenerate two-photon micromasers pumped by cascade three-level atoms, where each atomic energy level has a different linewidth. Our model allows us to recover the ordinary two-photon micromaser situation when these widths vanish. In the limit of large linewidths we obtain a two-photon laser model. We show that trapping states are extremely sensitive to atomic decay, even when the decay time is small in comparison to the transit time through the cavity. Unlike the one-photon micromaser, they are sensitive to the linewidth of the upper, as well as the lower energy level. We have also studied the effects of atomic decay on the starting time of micromasers and on the noise. We found that there is a significant difference between the behavior of two-photon micromasers and lasers as we change the ratio of the widths of the upper and lower levels.

Any quantum device that amplifies coherent states of a field while preserving their phase generates noise. A nonlinear, phase-invariant amplifier may generate less noise, over a range of input field strengths, than any linear amplifier with the same amplification. We present explicit examples of such nonlinear amplifiers and derive lower bounds on the noise generated by a nonlinear, phase-invariant quantum amplifier.

It is shown that the mutual trapping of the fundamental and second-harmonic beams in a diffractive (or dispersive) medium with quadratic nonlinearity can support a family of two-wave (2+1)-dimensional solitons of circular symmetry. The stability analysis shows that these (2+1)-dimensional solitons are stable in the physically important region of parameters, although unstable solitons are also revealed and their instability dynamics is analyzed numerically. Phase-dependent and, in some cases, nondestructive collisions of these solitons are also considered.

In the first part of the paper we define the spatial spectrum of squeezing following an operational procedure, and we show in general how the spatial structure of squeezed states can be described in terms of correlation functions of quadrature components of the electric field. In the second part we formulate an appropriate quantum model for a degenerate optical parametric oscillator (OPO) with plane mirrors, and we analyze it extensively below the threshold for signal generation. The correlation length diverges when the OPO approaches threshold; this picture provides an ideal completion of the analogy with critical phenomena in second-order phase transition at equilibrium. The spatial configuration of the correlation function exhibits the phenomenon of ‘‘quantum image:’’ the signal field, which is purely generated by quantum noise, shows an ordered spatial structure which is observable via the spatial correlation function.

In the recently developed microlaser, a single two-level atom interacts with a single mode of the optical resonator to generate coherent radiation. The resonator mode is in the form of a standing wave. We present an analysis of the standing-wave features, based on an approximate solution of the fully quantized microlaser equations. The result explains the rapid increase in the observed signal when the average number of atoms in the cavity is of the order of 1.

We consider a model for nondegenerate cavity fields interacting through an intervening boson field. The quantum correltaions introduced in this manner are manifest through their higher-order correlation functions, where a type of squeezed state is identified.

We find the intrinsic Hermitiean phase operator associated with the Noh-Fougères-Mandel apparatus. This is achieved by first identifying the corresponding phasor basis. Previous, alternative approaches are shown to be equivalent. Quantum analogs of trigonometric functions are discussed with the aid of their Glauber and Wigner representations.

The influence of many-body, nonequilibrium, and cavity effects on the emission characteristics and carrier dynamics of semiconductor microcavity lasers is investigated. The nonlinear coupled equations for the carrier kinetics and the laser dynamics are derived. Numerical solutions for vertical cavity surface emitting lasers show that the electron-hole plasma population has strong nonequilibrium character under many realistic conditions, exhibiting plasma heating and/or kinetic hole burning. It is shown that the desired threshold reduction through increased spontaneous emission coupling is accompanied by a significant increase in the laser linewidth and deviations from the usual Schawlow-Townes line narrowing. Assuming optical excitation with femtosecond pulses, the delayed onset of laser action and the dynamical emission characteristics are computed.

A four-level model which takes account of the polarization of the laser field by including the spin sublevels of the conduction and valence bands of a semiconductor allows us to introduce vector rate equations which account for the polarization degree of freedom of the laser emission. Analysis of these rate equations and their extension to include transverse degrees of freedom provides important physical insight into the nature of polarization instabilities in surface-emitting semiconductor lasers. In the absence of transverse effects the model predicts a marginally stable linearly polarized state. The type of dynamical response of the polarization degrees of freedom is linked to the relative time scale of spontaneous-emission and spin-relaxation processes. With transverse effects included, we predict the existence of stable transverse spatially homogeneous intensity outputs with arbitrary direction of linear polarization in the transverse plane. The stability of the off-axis emission solutions to long-wavelength perturbations is investigated and, in addition to an Eckhaus instability associated with a global phase, we predict a polarization instability associated with a relative phase of the complex field vector. The role of phase anisotropy in the laser cavity is explored close to threshold and we predict that it stabilizes two preferred orthogonal directions of polarization, which, however, are discriminated in their stability properties by transverse effects.