Semiclassical quantization is incorporated into the average potential approach to atomic physics. The stationary energy functional is shown to be the sum of the Thomas-Fermi functional and a mainly oscillatory part. The latter turns out to be a small correction for sufficiently large atomic numbers, allowing perturbative treatment. Further, a detailed study of semiclassical spectra, with emphasis on energy degeneracy, is performed.

A heuristic microscopic two-level-atom model with fluctuations is developed to explore, theoretically, the effect of fluctuations on mirrorless optical bistability. In stochastic models, bistability appears as a bimodal distribution function. We show that the predictions of bimodality and bistability are the same in the heuristic and semiclassical (nonstochastic) microscopic models.

The excitation of an atom by a near-resonant-symmetric mode-locked multimode laser is solved in the two-state rotating-wave approximation. An analytic expression of an unusual new form of resonance is found and a simple experiment which could be used to observe the effect is suggested.

A phase-modulation technique for coherent Raman spectroscopy is used to measure both the real and imaginary parts of the third-order nonlinear susceptibility of gases. The Raman Q-branch resonance of ${\mathrm{D}}_2$ is calibrated by comparison to the Q-branch resonance of ${\mathrm{N}}_2$. By using ${\mathrm{D}}_2$ as an internal standard, the nonresonant electronic susceptibility of Ar and the sum of the electronic and molecular reorientation contributions to the nonresonant susceptibility of ${\mathrm{N}}_2$ are determined. The results of these measurements are compared to published data on the Q-branch Raman cross section of ${\mathrm{H}}_2$, to predictions from the theory of the optical (ac) Kerr effect, and to measurements of electronic hyperpolarizabilities. For the last-mentioned quantity, measurements from three-wave mixing, from field-induced second-harmonic generation, from third-harmonic generation, and from the electro-optic (dc) Kerr effect are intercompared and agreement at the 10% level is established. Formulas interrelating a number of different definitions of third-order susceptibilities found in the literature are presented.

Wideband calculations of the response of a homodyne detector to the outputs of various four-wave-mixer configurations are presented. It is shown that the noise-power spectrum of the homodyne detector output can exhibit regions where the noise is greatly reduced below the shot-noise level even at frequencies far from dc. Hence, in the detection of noise squeezing via homodyne detectors, 1/f noise and other low-frequency noise sources may be avoided by observing the homodyne detector’s noise power at frequencies far from dc.

Homodyne detection has been proposed as a means of detecting squeezed coherent radiation. Here the response of a balanced homodyne detector to wideband squeezed coherent states is presented. In order to carry out the analysis the theory of wideband photodetection is reviewed and in order to determine the ultimate performance limits of photoemissive detectors small terms of order Δω/${\omega }_0$ that are usually neglected, where ${\omega }_0$ is the optical carrier frequency and Δω is the electronics bandwidth, have been kept. It is shown that the ultimate noise reduction that can be achieved in the noise-power spectrum of a homodyne detector, detecting squeezed coherent radiation, is a factor of 2 worse when photoemissive detectors are used instead of power flux detectors.

We present the first space-resolved experimental determination of electronic density and temperature profiles in the transport region for plane target irradiation with 400–600-ps pulses at 0.53- and 0.26-μm wavelengths, and (1–3)×${10}^{14}$-W/${\mathrm{cm}}^2$ laser intensity. The experimental technique is x-ray spot spectroscopy on thin Al microdots deposited on a carbon substrate. A knife-edge imaging technique ensures a spatial resolution of 3 μm along the laser axis. The electronic density and temperature are deduced from Stark broadening and intensity ratios of ${\mathrm{Al}}^{11+}$ and ${\mathrm{Al}}^{12+}$ n=4 resonance lines, respectively. The experimental profiles are well reproduced by one-dimensional spherical simulations including nonlocalized thermal flux inhibition or very low inhibition.

A quantum theory of stimulated Raman scattering is presented that takes into account three-dimensional propagation and collisional dephasing, allowing the study of the spatial and temporal coherence properties of the generated Stokes light. Maxwell-Bloch equations for the Stokes field operator and the collective atomic operators are solved analytically under low-signal-gain conditions, where the laser field and the atomic ground states remain undepleted. The intensity and the space-time autocorrelation function of the Stokes field are calculated. The Stokes field is expanded into a set of statistically independent ‘‘coherence modes,’’ which are determined explicitly for the case of a cylindrically shaped pumped volume. The Stokes pulse energy W is found to fluctuate from pulse to pulse. The probability distribution function for pulse energies P(W) is calculated for a range of Fresnel numbers of the excited volume and collisional dephasing rates. For small values of Fresnel number and dephasing rate, P(W) is a negative exponential distribution. For large values of either, P(W) narrows and approaches a Gaussian-shaped distribution. This occurs because many independent modes contribute to the Stokes emission, making it spatially and/or temporally incoherent.

We develop a quantum mechanical formalism which facilitates the study of interactions locally in semiconductors. It is based on the operators ${\psi }^{\mathrm{°}}$(m,x→,k→,t) and ψ(m,x→,k→,t) which are defined so as to create and destroy electronic wave-packet states having well-defined position x→ and crystal momentum ħk→ in a given energy band m of a crystal. We apply the formalism to develop local-operator equations of motion for semiconductor lasers.

Results of a computer simulation are reported for a lithium soft-x-ray laser pumped by synchro- tron radiation. Coherent stimulated emission of the photons of interest occurs in Li ii 1s2p→Li ii 1$s^2$ transitions. Calculated results include the dominant ion and photon densities and the laser gain.

If the angular and radial quantum numbers of states with the same binding energy satisfy a linear relation, as is the situation in the Coulomb potential, the spectrum is said to be linearly degenerate. We present a detailed study of the consequences of such linear degeneracy in atomic potentials. One of the results is a new, and more general, derivation of Scott’s correction to the Thomas-Fermi energy.

The emission of radiation from a spatially extended amplifying medium is shown to exhibit new coherence effects when the medium is modeled by inverted atoms which possess a degeneracy allowing Q(J) transitions. In particular, it is predicted that media of this type for which J=2 can emit leading pulses which are doubly peaked or asymmetric within both the regimes of superfluorescence and oscillating fluorescence. Dissipative processes can radically alter the character of the emission; an output consisting of two well-separated pulses appears feasible, but the precise behavior in the present model depends upon the magnitude of the field losses and the initiation statistics.

The many-mode Floquet theory (MMFT) recently developed by authors is extended to incorporate the irreversible damping mechanisms for the nonperturbative treatment of the dynamical evolution of dissipative three-level systems at two-photon or multiphoton coherent resonance trapping conditions induced by two strong linearly polarized monochromatic fields. It has been recently shown by several workers that under the rotating-wave approximation (RWA), population may be permanently trapped in the three-level system if the coherent monochromatic fields are exactly two-photon resonant with the initial and final states, decoupled from the intermediate decaying level. In practice, the inclusion of the non-RWA terms necessarily modifies the resonant trapping conditions and behavior. In this paper we extend the generalized Van Vleck (GVV) nearly degenerate perturbation theory to an analytical treatment of the non-Hermitian two-mode Floquet Hamiltonian. This reduces the infinite-dimensional time-independent non-Hermitian Floquet Hamiltonian to a 3×3 effective Hamiltonian, from which essential properties of the coherent population-trapping behavior as well as the dynamical evolution of the dissipative SU(3) coherence vector S→(t) can be readily obtained and expressed in terms of only three complex quasienergy eigenvalues and eigenvectors. The MMFT-GVV studies show that the RWA two-photon resonant trapping condition is substantially modified by the effects of non-RWA terms, and that the system can be ‘‘quasitrapped’’ for only a finite amount of time characterized by a small imaginary energy (width) associated with a coherent superposition state of the initial and final levels. Furthermore, it is found that the initially eight-dimensional coherence vector S→(t) evolves predominantly to a one-dimensional scalar at the two-photon or multiphoton resonant quasitrapping conditions. Detailed results and pictorial representations of the population trapping and SU(3) dissipative dynamical evolution are presented.

The spectrum of squeezing in the output field for the optically bistable system of an atomic medium in a coherently driven cavity is analyzed. Good squeezing is attainable only in certain limits of atomic parameters and cavity detuning.

A study of the forced Duffing equation is reported, with particular reference to a region of the parameter space where five different attractors coexist. This coexistence, reported in some recent experiments, is called generalized multistability. The role of external noise in bridging the otherwise disjoint basins is explored. Noise-induced couplings are shown to be ruled by simple kinetic equations under a general assumption for the geometry of the boundaries. These kinetic equations yield low-frequency power spectra in qualitative agreement with the experimental results.

The spectrum of a laser-produced plasma of tantalum in the range 4.4–4.8 Å is interpreted as spin-orbit-split arrays of the 3d-5f transitions for ${}_{73}{}^{}{}_{}{}^{}\mathrm{Ta}$ xlvi. The excellent agreement between model and experiment indicates the possibility of use for plasma diagnostics.

The velocity autocorrelation function for the hard-sphere fluid is computed for ten values of the volume ranging from 25 to 1.6 times the close-packed volume $V_0$ for systems of from 108 to 4000 hard spheres, using a Monte Carlo, molecular-dynamics technique. The results are compared with the theoretical predictions of the mode-coupling theory, modified to take into account the finite size of the system and the periodic boundary conditions. The data are found to be in good agreement with the theory, evaluated using Enskog values for the transport coefficients, for values of the time greater than roughly 15 to 30 mean free times (depending on density), for volumes as small as 2$V_0$. The higher-density results do not agree with the theory, unless the actual transport coefficients (evaluated using molecular dynamics) are used in the theory. The latter version of the theory, however, fails to fit the data at lower densities, except at very long times. To answer the recent critique by Fox, the data are further compared with the theory over time intervals for which the molecular-dynamics trajectories retain some measure of accuracy. The agreement between the data and the theory is largely unaffected, except at a volume 1.8$V_0$ for which there is a marginally significant difference at very long times only.

The quantum-mechanical motion of a free particle coupled to a linearly dissipative environment is analyzed in the Hamiltonian formalism. The total Hamiltonian is diagonalized and its eigenstates displayed. These results are used to discuss the role of initial conditions on the subsequent motion. A widely used initial condition—heat bath uncoupled from particle—is compared with another one in which the initial off-diagonal coherence of the reduced density matrix is comparable to that in the state of thermal equilibrium of the coupled system. Different transient behaviors, on time scales longer than the inverse cutoff frequency of the bath are found. The mean-square momentum of the particle in the steady state is found to depend on this highest bath frequency. An analysis of the correlated states of particle and heat reservoir shows that the latter behaves in some sense like a position-measuring apparatus.

The kinetics of a number of prototypical diffusion-controlled reactions are studied, primarily through the application of scaling approaches. Our goal is to investigate the effects of spatial inhomogeneities in the particle densities on the reaction kinetics. In general, we find that there exists an upper critical dimension below which the kinetics cannot be described by a rate-equation analysis, an approach which gives the kinetic laws of a mean-field approximation. Below the upper critical dimension, spatial inhomogeneities in the particle densities give rise to new fluctuation-dominated kinetics. For irreversible reactions, with bimolecular decay A+B→inert being a simple generic example, universal kinetic laws are obtained which are a function only of the spatial dimension, the number of particles needed to initiate a reaction, and the nature of the particle-conservation laws for the system. We also consider the generalization of bimolecular decay to a multistate process where particles of variable ‘‘heights’’ and traps of variable ‘‘depths’’ react. This phenomenologically rich example serves as an illustrative testing ground for scaling ideas. The introduction of a small reaction probability on bimolecular decay provides an example of a dramatic crossover from an initial mean-field decay to the fluctuation-dominated decay law at large times. When the possibility of a reverse reaction is allowed in bimolecular decay, the available evidence suggests that there is a power-law approach to the equilibrium state, rather than an exponential approach predicted by the rate equation. Many of our new theoretical predictions are tested by extensive numerical simulations.

Experimentally determined level populations of hydrogen excited states from a low-density Z pinch are used as initial conditions in a simulation to derive electron-velocity distributions. These velocity distributions show excess electrons in the high velocity end of the distribution when compared to a Maxwellian velocity distribution. The non-Maxwellian velocity distributions are used to find the nonequilibrium structure factors which are a main component in the plasma line broadening of hydrogen lines. The line profiles generated using the structure factors show plasmon satellites on the wings of the Balmer-α- and -β-line profiles.