Time-resolved secondary-radiation spectra have been calculated for a three-level system coupled with a reservoir under pulsed-light excitation. It has been found that a dip is observed in the time profile of the secondary-radiation intensity near the resonance-excitation condition, when the spectral bandwidth of the detection system is increased. If the secondary radiation is divided into the Raman and luminescence components that are, respectively, due to the mean value and fluctuation of the photoinduced emission dipole, the dip is observed only in the former. A simple analysis reveals that this dip originates from the quantum interference between the resonant and nonresonant contributions to the Raman scattering.

When three-photon atomic excitation is produced by two laser beams of angular frequencies ${\mathrm{\omega }}_{\mathit{L}1}$ and ${\mathrm{\omega }}_{\mathit{L}2}$, which are crossed at an angle θ, large cooperative pressure-dependent shifts can be produced in the peak position of the excitation line shape. Such shifts occur when the transition between states is dipole allowed in both one and three photons. When θ or ${\mathrm{\omega }}_{\mathit{L}2}$/${\mathrm{\omega }}_{\mathit{L}1}$ is small, these shifts are very large compared to the pressure broadened width of the line. Our analysis shows that for small θ or small ${\mathrm{\omega }}_{\mathit{L}2}$/${\mathrm{\omega }}_{\mathit{L}1}$, where the shift is large, the excitation is suppressed near the unperturbed resonance due to a destructive interference between the three-photon excitation by the laser and one-photon excitation due to the four-wave-mixing field, whereas the shifted resonance appears at the position where the atoms interact through ‘‘resonant’’ four-wave-mixing photons that are phase matched with the laser field. By studying an experimental situation in xenon we show that the theoretical predictions are in precise agreement with experiment for several angles and a wide range of pressures.

When atoms are placed in a static magnetic field, they undergo shifts of their energy levels and changes in their transition probabilities. These two effects must be taken into account when considering absorption profiles of alkali-metal D lines, which result from the contribution of many transitions influenced by the laser spectrum and Doppler broadening. The model presented here gives the D-line absorption coefficients of alkali-metal vapors in the presence of an arbitrary static magneitc field. They are evaluated considering various laser polarizations. Experimental measurements of D-line absorption profiles for ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$, and ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ isotopes show excellent agreement with theoretical predictions.

We have made a quantitative study of nuclear spin relaxation of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ atoms adsorbed on the surface of glass cells. By using highly asymmetric glass cells we have increased the wall-induced quadrupole splitting of the nuclear-spin sublevels of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ atoms by almost two orders of magnitude over previously reported values. These large surface interactions were used to extract quantitative information about the electric-field gradients experienced by the nuclei of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ atoms adsorbed on the glass surface and about the activation energies for surface adsorption. The experimental results indicate that the electric-field gradients at any surface site are nearly isotropic. The residual nonzero mean value of the fluctuating field gradient has cylindrical symmetry about the normal direction to the surface. The mean-field gradient along the surface normal direction is only 2.3% as large as the rms value. We find that silicone wall coatings, which slow down the relaxation of ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$ nuclear spins, speed up the relaxation of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ nuclear spins. This may be due to the nuclear quadrupole interactions of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ atoms dissolved in the relatively thick silicone wall coatings. Measurements of the temperature dependence of the coherent wall interaction show that the activation energy (≊0.03 eV) for the coherent wall interaction in well-cured, hydrogen-free cells is about three times smaller than the activation energy (≊0.10 eV) in hydrided cells.

The response of a quantum-mechanical multilevel system to external probe fields can often be formulated in terms of frequency-modulated oscillators. Experimental observation of the line shapes associated with a certain transition then gives information on the microscopic processes that are responsible for the frequency modulation. Model calculations have been very involved so far. We therefore present a model for the frequency modulation for which the response of the oscillator can be solved in closed form. The model is applied to the problem of microwave absorption of tumbling paramagnetic centra in liquid-crystalline systems. Explicit expressions for the absorption line-shape functions are derived, and their analytical structure in the frequency domain discussed.

The three-dimensional Coulomb system can be mapped onto the four-dimensional harmonic oscillator. Additional perturbations of the type ${\mathit{gr}}^{\mathit{p}}$ [r=(${\mathit{x}}^2$+${\mathit{y}}^2$+${\mathit{z}}^2$${)}^{1/2}$] translate into anharmonic perturbations λ(${\mathbf{x}}^2$${)}^{\mathit{p}+1\mathrm{}}$ (${\mathbf{x}}^2$=${\mathit{x}}_1^2$+${\mathit{x}}_2^2$+${\mathit{x}}_3^2$+${\mathit{x}}_4^2$) to the oscillator. We use this observation to relate the large-order behavior of perturbation series of the perturbed Coulomb systems to well-known large-order formulas for anharmonic oscillators. In this way, the leading behavior of Coulomb systems can be understood by simple scaling and symmetry arguments within the oscillator systems. Applications to more physical Stark- and Zeeman-type perturbations are briefly discussed.

Two-step photodissociation angular distributions are calculated by a coupled-equation approach for the 1 ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$→1 ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$→1 ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathit{g}}^{}{}_{}{}^{}$ transition in ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_2^{}{}_{}{}^{}$. The initial excitation is induced by a low-intensity visible laser in order to select the rovibrational state. The Π-Π transition is effected by an infrared laser that is varied from weak (perturbative) to intense (nonperturbative) regimes. It is shown that laser-induced orientation effects and laser-induced resonances (trapped states) considerably alter the angular distribution of the photodissociating fragments, creating anomalies in some instances at high intensities where a nonperturbative, numerical approach is essential.

We propose a new kind of correlated-spontaneous-emission laser in which the electromagnetic field is driven by coherently prepared atoms. Such a system constitutes a very simple correlated-emission scheme in that it involves only single-photon transitions, whereas all previous studies were based on correlated photon pairs. We find that for low intensities the fluctuations in the photon number can be reduced below the standard limit while the phase noise is unaffected by the atomic coherence. However, the amount of noise reduction crucially depends on the fluctuations of the pump mechanism. In the high-intensity limit the photon-number fluctuations can be reduced even further. It is possible to achieve a complete quenching of the spontaneous-emission noise and even squeezing, depending on the atomic coherence and the statistical properties of the pump mechanism. Additionally we find a large reduction in the phase fluctuations. In contrast to the amplitude noise, this reduction is independent of the pump noise.

We study angular correlations of the radiation emitted by spatially extended sets of atoms. Such correlations result from the fact that the photons are identical quantum particles. We show that the symmetry (or the antisymmetry) alone of the wave function for identical, indistinguishable particles always leads to significant angular correlations and that in full agreement with our intuition, bosons tend to travel in the same direction while fermions tend to travel in opposite directions. In order to quantify these intuitive notions, we introduce—as a measure of angular correlations—the average value of the cosine of the angle between the directions of the momenta of two particles. The angular correlation coefficient is calculated for simple, model wave functions and the results are compared with those obtained from an exactly soluble model describing radiating harmonic oscillators. We find that even though the interaction modifies the exact values of the angular correlation coefficient, the gross features can be obtained from quantum statistics, i.e., from the symmetry of the many-photon wave functions. Moreover, the angular correlations as measured by the average cosine exhibit an almost universal character, at least for a small number of emitting atoms. Finally, we compare angular correlations obtained in quantum electrodynamics with the correlations resulting from the phenomenologically introduced randomness of the phases in the classical description of the electromagnetic field.

A nonperturbative density-matrix formalism is used for the analysis of strong-field four-wave mixing, allowing the treatment of relaxation processes, including lifetime as well as dephasing. The combined role of proper dephasing and level saturation in the generation of extra resonances is studied. It is shown that, whereas in the absence of proper dephasing there is no pressure-induced resonance, there is always a nonzero contribution to the field-induced resonance. For increasing field intensity, a characteristic double saturation is predicted as a function of the field strength. The dependence on the various parameters is investigated, and the conditions under which these effects should be observable are identified.

An expression for the population inversion in the Jaynes-Cummings model and the most general initial state of the atom-field system is presented. States that maintain the same level of population inversion when the atom and the field are initially decoupled are found. When the atom is prepared in a coherent superposition of its states and the field is in an eigenstate of the Susskind-Glogower phase operator, for a certain choice of the relative phase between the atomic dipole and the field, coherent trapping occurs. The evolution of the squeezing of the field for these states is given, and the dependence on the phase and on the mean photon number of the field is studied.

Using a coupled-mode approach we numerically investigate the time-dependent properties of nonlinear periodic media of finite length. Based on time-independent considerations such media have been shown previously to exhibit bistable behavior and to support gap soliton excitations. Our calculations show that for low intensities the transition from a low-transmission to a high-transmission state occurs as expected, leading to an easy excitation of gap solitons. At higher intensities, however, periodic self-oscillations take place, which eventually turn chaotic.

We use the dressed-state representation to generate the full quantum-mechanical treatment of stimulated Raman scattering (SRS). Equations of motion and propagation are obtained from the Heisenberg equations of motion in the plane-wave limit and under conditions such that anti-Stokes and higher-order Stokes processes can be neglected. Equations for a stochastic model, based upon antinormal ordering and a quantum-classical correspondence are developed from them, suitable for numerical ensemble calculations for the study of amplified quantum fluctuations and spontaneously generated phase waves and solitons. Several alternative approaches, which have more general validity but present greater difficulty in numerical implementation, are also developed by introduction of quasiprobability functions and their associated Fokker-Planck equations from which corresponding stochastic equations of motion and propagation are derived. The Q representation, whose moments correspond to expectation values of products of antinormally ordered fields, and normally ordered atomic operators yield stochastic equations identical to the equations for the stochastic model developed directly from the Heisenberg equations for the same initial and boundary conditions, giving strong credence to the stochastic model. The Wigner representation, whose moments correspond to expectation values of symmetrically ordered operators, leads to a set of equations that are valid where the stochastic model fails, namely, where conditions are such that quantum fluctuations and nonlinearity are simultaneously important. The stochastic model, which is shown to be, by far, the simplest to implement in numerical calculations, is shown also to be valid for the conditions of SRS.

We report on detailed studies of the effect of resonant light pressure on the optical response of an atomic gas to a single monochromatic laser field. In this very elementary situation of laser spectroscopy, the redistribution of atomic velocities that is induced by spontaneous light pressure leads to a novel contribution to the optical dispersion curve of the medium. This light-pressure-induced dispersion phenomenon displays a pronounced nonlinear dependence on the laser intensity. Moreover, for a given intensity, its strength is closely related to the laser beam diameter. As most important feature, this light-pressure-induced dispersion displays an even symmetry with respect to the optical detuning from line center. As a result, the total Doppler-broadened dispersion curve of the gas can become asymmetric, and a significant shift of the dispersion line center can occur. In addition to a detailed theoretical description of the phenomenon, we report on its experimental investigation on the λ=555.6 nm ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$${\mathrm{-}}^3$${\mathit{P}}_1$ transition in atomic ytterbium vapor with the use of frequency-modulation spectroscopy. The experimental findings are in good quantitative agreement with theoretical predictions.

A detailed account of a formal mathematical description of the interaction of relativistic charged particle beams with electromagnetic waves, within the frame of classical electrodynamics, is presented. The standard system of eight equations (Maxwell and Lorentz gauge conditions and fluid dynamics) in the four-vector potential ${\mathit{A}}_{\mathrm{\mu }}$ and the four-vector current density ${\mathit{j}}_{\mathrm{\mu }}$ is reduced, after linearization, to a canonical system of four coupled partial differential equations in the electromagnetic field perturbation δ${\mathit{A}}_{\mathrm{\mu }}$. Both electromagnetic and dynamical quantities are treated as fields, according to the Eulerian formalism. This new system is very general, and different beam-wave interactions are characterized by different fluid equilibria and boundary conditions for δ${\mathit{A}}_{\mathrm{\mu }}$ and its derivatives. Finally, the equations are used, as an example, to study the dispersive characteristics of space-charge waves propagating in a cylindrical waveguide, along a relativistic electron beam confined by an axial magnetic field. The problem is treated in a fully relativistic way, for arbitrary values of the axial guide field and any degree of azimuthal symmetry.

Radiative coupling between identical atoms sharing an excitation is studied in media where dispersion creates photonic band gaps, i.e., forbidden bands of light propagation for all directions and polarizations. Photonic band gaps can exist in media whose dielectric index exhibits strong three-dimensionally periodic modulations (‘‘photonic crystals’’) or in bands of polaritonic media. It is shown that the resonant dipole-dipole interaction as well as cooperative fluorescence of two-atom systems can be strongly enhanced or suppressed, to the extent of being essentially eliminated, by one of the following mechanisms: (a) dependence on location of the atoms within a unit cell of a photonic crystal, i.e., sensitivity to the spatial variation of the field normal modes; (b) dependence on the density of normal modes in allowed bands and on the density of virtual (evanescent) modes in band gaps. The ability to suppress the dipole-dipole interactions at interatomic separations characterizing quasimolecules would have far-reaching implications on their dissociative or collisional dynamics, spectroscopy, and rates of energy transfer.

Linearization of the self-induced transparency equations reduces the problem to a single linear integro-differential equation for the perturbation field of a soliton. The adjoint system is introduced to establish orthogonality relations that lead to the relations between the perturbed field and perturbed scattering data. The commutation relations of the perturbation field provide the quantization rules for the perturbed ‘‘scattering data.’’ The quantized solitons are described by operators for photon number, phase, momentum, and position. The evolution and detection of these fluctuations are studied. The contribution of the continuum part can be suppressed by suitable detection schemes.

The minimal-coupling Hamiltonian that describes the quantum-mechanical interaction of charged matter and electromagnetic fields, implies the existence of an optical analog of the Aharonov-Bohm effect that may be observable as a resistivity change in mesoscopic conductor loops. In superconducting quantum interference devices (SQUID’s) the ponderomotive potential adds to the chemical potential, altering the Josephson oscillation frequency. These interactions do not involve the absorption or random scattering of quanta, but merely the mutual nonlinear phase shift of matter and electromagnetic waves, and thus (in principle) support back-action-evading measurement schemes. The well-known electrostatic Aharonov-Bohm effect can be used to detect potentials produced by optical rectification, another back-action evading process. Only the SQUID implementation seems likely to produce back-action-evading readouts of quantum amplitude fluctuations larger than Johnson noise.

The commonly used Keldysh multiphoton ionization rate is shown to follow from the zeroth-order approximation of an exact expression, based on the formal time-independent theory of scattering. The formulation is applied to the loosely bound ${\mathrm{H}}^{\mathrm{-}}$ system; good agreement is obtained with a recent experimental measurement.

An expression for the multiphoton ionization rate, recently derived nonperturbatively from formal time-independent scattering theory, has been employed to study the effect of the final-state interaction in strong-field photodetachment of ${\mathrm{H}}^{\mathrm{-}}$. The first-order improved distorted-wave Born approximation in the binding potential has been evaluated. The calculation further improves agreement with experiment.