For a three-level atom in the ssV configuration (i.e., having two excited states each dipole-coupled to a common ground state), we have found a particular linear combination of bare-atom states in which Rabi oscillations and their associated collapses and revivals do not occur. Moving to a dressed-state picture, we discover that this particular linear combination state is just that dressed state which is decoupled from all the field modes. It is a dressed state for which the transition dipole moments with the other dressed states are zero. The existence of this decoupled dressed state depends on the tuning of the dressing laser field, which in turn depends on the bare-atom excited-state dipole moments and energy-level separation. When we include spontaneous emission, the population decays from the other dressed states into this decoupled state and remains coherently trapped there, producing a system that experiences no dynamical behavior. This is exact for δ-function photon statistics (i.e., if there is no intensity uncertainty). The trapping becomes less perfect as the photon statistics are allowed to have a greater bandwidth. Also, if the applied field is tuned incorrectly, the spontaneous realignment of the atomic state amplitudes does not result in a totally decoupled dressed state, and the dynamics proceed normally.

Spontaneous Brillouin scattering in a micrometer-sized liquid droplet is analyzed from first principles, using the spherical-wave normal-mode basis. Instead of the conservation of linear momentum, this interaction is governed by a selection rule due to the conservation of angular momentum. The Brillouin spectrum is then calculated, both for observation at a given angle and for the sum over all angles, and compared with scattering in a bulk medium. Special attention is paid to the case where the incident and scattered radiation fall on an electromagnetic resonance of the droplet. The analysis lays the foundation for formulating stimulated Brillouin scattering in the same system.

Multiphoton detachment cross sections for a negative ion in a static, uniform magnetic field are obtained in the approximation that electron-atom interactions are ignored in the final state. The final state is described by the analytic momentum-space wave function for an electron in the combined field of a laser and a static uniform magnetic field. The effects of a static-field-induced electron-photon interaction are stressed. Three consequences of our general formulas are discussed. First, the ponderomotive shift is modified by the magnetic field. It goes through a resonance at the cyclotron frequency and becomes negative for smaller frequencies. Second, for N-photon detachment of an s-shell electron by a laser of arbitrary strength, the effect of a weak magnetic field can be described near threshold by two modulation factors, one for even N and one for odd N, which depend only on a scaled energy. Third, cyclotron resonances are shown to exist under certain conditions, as demonstrated here for the specific example of multiphoton detachment of ${\mathrm{H}}^{\mathrm{-}}$ by a weak laser in an arbitrarily strong magnetic field.

Data on the threshold ionization intensities of rare-gas atoms with 248-nm irradiation in the ${10}^{13}$–${10}^{16}$-W/${\mathrm{cm}}^2$ range of intensity are presented in the context of models involving tunneling ionization. Comparison is also made with the full Keldysh theory. It is shown that, although the experimental conditions fall well outside the tunneling regime as defined by the Keldysh theory, these relatively simple pictures accurately predict the threshold ionization intensities observed under the conditions studied. The main deviation of these results from the Keldysh theory occurs for the heavier elements at high charge states.

The quantum noise properties of injection-locked semiconductor laser oscillators are investigated. Included in the analysis are pump-noise suppression and squeezing of the injection signal. It is shown that the main effect of injection locking is the reduction of the phase noise of the outgoing laser light field. The influence that squeezing of the injection signal state has on the output state is shown to be strongly dependent on the value of the linewidth enhancement factor. In general, little or no noise reduction stands to be gained by squeezing the injection signal. It is also shown that under idealized conditions, the spectral uncertainty product of the outgoing field will approach, but never go below, the minimum uncertainty value given by the Heisenberg uncertainty relation.

The relativistic transform of electromagnetic fields and inductions in a nonlinear medium is studied theoretically, within the framework of classical electrodynamics. A covariant formulation of the electrodynamics of nonlinear media is presented. This theoretical formulation is of particular relevance to periodic systems since the spatial symmetries of a given medium, which determine most of its linear and nonlinear electromagnetic properties, as described by group theory are not conserved by the Lorentz transform (space-time symmetry). The Čerenkov radiation process is treated as an example in the rest frame of the interacting electron; it is found that in this case the linear refractive index of the dielectric medium becomes anisotropic and exhibits a singularity at the usual Čerenkov radiation angle.

We investigate the effect of a spatially varying field mode on the squeezing generated by two-level atoms interacting with a single mode of an optical cavity. The mode structure is incorporated into a quantum theory that does not employ adiabatic elimination of field or atomic variables. Thus we are able to consider the regime in which cavity and atomic decay rates are approximately equal as well as the good- and bad-cavity limits. Calculations show that squeezing is reduced by the inclusion of a Gaussian transverse mode profile and a standing-wave structure for a particular value of atomic cooperativity C. The model is consistent with recent measurements of squeezing. The degree of squeezing reduction depends on the ratio of cavity and atomic damping rates, in the regime where they are similar in size.

At low intensities the rate of two-photon transitions in an atom driven by parametrically down-converted light may be linear in intensity. Such a violation of the usual perturbative law arises from strong correlations between pairs of photons.

The purpose of this paper is to develop a singular perturbation expansion for the linear optical cavity modes in a micrometer-sized droplet. Closed-form expansions for the eigenmodes are given, as well as for the eigenfrequencies. The leading terms are usually accurate to within a few percent. Bessel functions of large argument and/or order are not required, nor are spherical harmonics of large l and m. With this expansion it becomes possible to evaluate analytically the linear and nonlinear evolution of such modes under a variety of conditions.

The off-resonant electronic third-order optical susceptibility is derived in the dipole approximation using the method of averages. These results are studied in detail for the two-, three-, and N-level model to determine the origin of the susceptibility with symmetry considerations. If the matrix elements are independent, the third-order susceptibility is shown to be maximized in centrosymmetric structures in the two-level model while, for the general N-level system, weak coupling between the excited states is also required. To address the interdependence of the matrix elements, a two- and three-level system is perturbed to make the molecular potential asymmetric or more asymmetric, and the conditions on the matrix elements for maximizing the third-order susceptibility are derived. The dependence of the third-order susceptibility on the asymmetry of a harmonic oscillator and particle in a box are also discussed.

The time-dependent Schrödinger equation was solved numerically, as a set of coupled equations, for an electron moving in three spatial dimensions, bound initially in the ground state of a hydrogen atom, and acted upon by a linearly polarized, single-frequency, classical electromagnetic field, turned on abruptly at t=0. Characteristic photoionization times ${\mathrm{\tau }}_{\mathrm{PI}}$ were computed for a wide range of laser intensities, at a photon energy of 5 eV. Comparison was made with the predictions of two widely used analytic expressions for ${\mathrm{\tau }}_{\mathrm{PI}}$. Emitted electron energy spectra and angular distributions were computed. The spectrum of radiation emitted during ionization was also determined.

We explore the bifurcation diagrams of self-coupled unidirectional single-mode ring lasers. We focus our attention on nearly identical lasers with an intermediate coupling and in the limit where the atomic polarizations can be adiabatically eliminated. We determine analytically the domains of a stable steady state, bounded by Hopf bifurcations. We study the stability of the emerging branch of periodic solutions and in one case determine the presence of a secondary Hopf bifurcation leading to quasiperiodic solutions. These results are complemented by a set of numerically determined bifurcation diagrams that display the behavior of the solutions far from the bifurcation points.

We analyze the photoelectron energy spectrum that results from near-threshold ionization of atomic hydrogen, initially in the 2s state, by a sharply turned on intense field. We demonstrate the existence of resonance structure close to threshold. The structure derives from transitions between degenerate ns and np states; opposite parity, degenerate states in the hydrogen atom are mixed by the nonadiabatic turn-on; at higher energies further structures in the photoelectron energy spectrum are generated through the action of counterrotating terms in the atom-laser coupling. We confirm the existence of a Rydberg series structure and investigate the possibility of q reversals in the line shapes.

We demonstrate that, for a simple model of the damped oscillator, both the wave packet in the position representation and oscillator expectation values are insensitive to the rapid decay of off-diagonal coherences. This rapid decay is, however, seen in the von Neumann entropy for the oscillator and the wave packet in the number representation.

Angle-separated pair photons emitted in spontaneous parametric fluorescence are superimposed at a beamsplitter and detected by coincidence techniques. The coincidence disappears when the photon path lengths to the beamsplitter are equal to within their inverse bandwidth due to fourth-order interference. The photon bandwidth is set by wide apertures placed to satisfy phase-matching conditions at the nonlinear crystal. The resulting broadband photons are short (39-fs full width at half maximum) and show an oscillatory tail resulting from the hard-edge apertures. Two-color photons are created by blocking the central portion of the apertures leading to strong oscillations of the coincidence rate as a function of path-length difference. Both effects are predicted by the theory of fourth-order interference coupled with the detailed phase-matching conditions in the nonlinear crystal used as a source. The two colors overlap at different positions on the beamsplitter. We show how this could be used as a test of local realistic theories by formulating a Bell inequality based on relative phases between the colors.

A Raman-coupled model, in which a single atom is coupled to a single cavity mode by Raman-type transitions, is treated. Taking damping of the cavity mode into account, we first transform the equation for the density operator into equations for quasiprobability densities. It is shown that these equations can be solved analytically. Various plots of the inversion and of quasiprobability distributions are presented and discussed.

Various quasiprobability distributions have been developed in the past using the Hilbert space of the single-mode light field. The development of a quasiprobability distribution associated with a phase operator has previously been impossible because of the absence of a unique Hermitian phase operator defined on the Hilbert space. Recently, however, Pegg and Barnett [Europhys. Lett. 6, 483 (1988); Phys. Rev. A 39, 1665 (1989)] and Barnett and Pegg [J. Mod. Optics 36, 7 (1989)] introduced a new formalism that does allow the construction of a Hermitian phase operator and associated phase eigenstates. In this paper we develop a quasiprobability distribution associated with the number and phase operators of the single-mode light field in the new formalism. The new distribution, which we call the number-phase Wigner function, has properties analogous to the Wigner function. We also derive the number-phase Wigner representation of number states, phase states, general physical states, coherent states, and the squeezed vacuum. We find this new representation has features that are related to the number and phase properties of states. For example, the number-phase Wigner representation of a number state is nonzero only on a circle, while the representation of a phase state is only nonzero along a radial line.

The waves reflected from a resonator must obey the commutation relations of waves in free space. This fact alone, regardless of whether the medium in the resonator is linear or nonlinear, imposes commutation relations on the internal noise sources. The minimum linewidth of an oscillator can be derived from this fact alone. This paper analyzes the special cases of a nondegenerate parametric oscillator and diode laser oscillator and shows how the physical noise sources satisfy the commutation relations and how the linewidth is determined from them.

The steady-state free-induction decay (FID) has been investigated in samples of crystalline and amorphous quartz containing paramagnetic two-level electron spin centers (S=1/2). We report experimental data on the dependence of the FID rate on the Rabi frequency χ induced during the preparative stage. Our results confirm that the decay of the FID signal is much slower than expected on the basis of the conventional Bloch equations. The range of χ investigated here is wide enough to show the whole transition from Bloch-type behavior to the high-power Redfield limit, in which the FID rate is determined only by χ. The experimental data are compared with theoretical results recently obtained by hypothesizing Gaussian-Markovian fluctuations of the resonance frequency. Even if agreement is poor, the comparison suggests by itself the possibility that more than one source of fluctuations may be effective. Other possible origins of the failure of the Bloch equations as well as of the stochastic theories are examined.

A linear theory of two-photon amplification by three-level atoms in the cascade configuration is developed, where a coherence is induced between the top and bottom levels, by an external classical driving field. It is shown that this system becomes an ideal parametric amplifier for sufficiently strong driving field, whereas for a weak driving field it is a phase-insensitive amplifier. In between these two extremes, one finds phase-sensitive amplification as well as squeezing for a certain range. The system does not, however, reduce to a model studied previously where the atomic coherence was treated as an initial condition. The system is also studied in a cavity configuration: It is predicted that the oscillator may behave as a two-photon correlated emission laser, i.e., its phase diffusion coefficient vanishes.