Exact analytical solutions for the problem of term crossing are obtained for decaying levels with the help of the Laplace contour-integral method. For the case of fast passage through resonance and for the case of slow decay, simple asymptotic expressions are found from the exact solution in terms of Whittaker functions.

A reasonably complete theoretical description of stimulated scattering in the presence of low-reflectivity external feedback is presented, based on an earlier treatment by Lu and Harrison [Europhys. Lett. 16, 655 (1991)] generalized to account for the integral effect of nonlinear refraction. Theoretical results show the Stokes signal to exhibit huge sustained or random bursts of quasiperiodic emission. Detailed comparisons with experimental findings on stimulated Brillouin scattering generated in single-mode optical fiber with weak external feedback by continuous-wave excitation give good agreement regarding both the dynamical features of the Stokes emission and their dependence on the physical control parameters, e.g., pump power, cavity reflectivity, and fiber length. Significantly, our results confirm the essential role of nonlinear refraction to the dynamical behavior and suggest that the noise structure of the initial spontaneous scattering has little influence on this behavior.

With the intent to explain the onset of a Rayleigh instability in a pure sodium cell driven by counterpropagating light beams, we report a theory that includes pump-depletion effects. A model is developed for fast-moving atoms that predicts the occurrence of a Rayleigh instability for sufficiently large concentration, which may explain the experimental observation.

The degenerate parametric oscillator operating above threshold exhibits bistability, and recent work suggests that it might also exist as a quantum-superposition state. We calculate the effect of the bistability on the two-time correlation function and the transmitted-field spectrum. The measurable steady-state probability distribution at the output of a homodyne detector is also calculated in a particular limit, in order to investigate whether one can experimentally distinguish between quantum-superposition and classical states.

Fock states and coherent states have been widely applied in analyses of quantum-optics experiments. In this paper, the application of a set of basis functions that consist of a product of displaced harmonic-oscillator states for the electromagnetic field and atomic states that are eigenfunctions of the momentum operator will be explored. For the case of a single mode, these states are the exact eigenfunctions in the limiting case where the electromagnetic-field mode frequency is much larger than the atomic transition frequency. This choice of basis functions will be used to analyze the interaction of a nonrelativistic, ‘‘two-level’’ atom with a single-frequency, quantized electromagnetic-field mode. Since in this basis the sign of the displacement of the electromagnetic-field state depends on the state of the atom, these new basis wave functions exhibit explicitly some aspects of atom-field correlations that are intrinsically quantum mechanical in nature. The analysis will be performed in the electric-dipole approximation for an atomic system that obeys the Δm=0 selection rule. The rotating-wave-approximation (RWA) terms cannot be made negligible through judicious choice of the field polarization for this system. The diamagnetic term, ${\mathit{e}}^2$${\mathbf{A}}^2$/2${\mathit{mc}}^2$, which is of the same order of magnitude as the RWA terms, is taken into account exactly by slightly modifying the traditional approach to quantizing the electromagnetic field. In this way the physical effects of the diamagnetic term are absorbed into a new electromagnetic cavity mode frequency.

An approximate expression for the combined system’s energy eigenvalues is found up to third order in the ratio of one-half the atomic transition frequency to the mode frequency. This expression indicates that inclusion of the RWA terms adds a small ‘‘ripple’’ on top of the smoothly varying energy eigenvalues when they are plotted as a function of the atom-field coupling constant. The ripple is interpreted as ‘‘interference’’ between two displaced oscillator-field states that represent the unperturbed state. When the Fock states are used as the basis for expanding the wave function of this system, a formidable five-term recurrence relation results. However, expanding the wave function in terms of the displaced harmonic-oscillator basis results in a less formidable three-term recurrence relation for the quantum coefficients.

We develop an analogy between the transverse modes of a class of aspherical laser resonators and the eigenstates of the stationary Schrödinger equation with a potential well directly related to the mirror profile. Using a perturbation method, the equivalence is shown to be valid for a short cavity length in comparison with the Rayleigh range of the fundamental mode, i.e., the most practical situation. Numerical examples with mirror profiles corresponding to a Pöschl-Teller potential confirm the validity of the model. The analysis also includes higher-order corrections for the case of a longer resonator length. The analogy with quantum mechanics should be useful for designing laser resonators with a high discrimination against higher-order transverse modes.

Atomic-dipole squeezing in the presence of the Stark shift in two-photon Jaynes-Cummings model for an atom initially prepared in a coherent superposition of states, interacting with the coherent- or squeezed-vacuum-state field, is studied. Closed expressions for dispersive and absorptive components of the dipole for the coherent-field input under the large-n¯ approximation are derived. It is shown that atomic-dipole squeezing is sensitive to both the phase of the initial field and the relative phase between the two atomic levels. Our results show that, for certain choices of these phases, permanent dipole squeezing can be obtained.

The propagation of radiation from a source embedded in an inhomogeneous refractive medium is studied, using both mode-analysis and ray-tracing methods. Scaling laws for excitation strengths of the modes, the degree of spatial coherence, and the shift of the spectral line are derived.

A formalism is developed for evaluating the effects of pair correlations on cascading of the nonlinear susceptibilities of fluid dielectrics. The corresponding correlative and nonlinear alterations of the usual local-field corrections are determined. These corrections to the nonlinear susceptibilities when the polarization density is expanded in terms of the effective linear field are found to be significantly different from results previously reported in the literature. The consequences of the considerable field dependence of the susceptibility expansions on the local-field corrections and the cascading are pointed out, and a detailed comparison is made to previous work. A simple model (β media), in which only the second-order molecular polarizabilities are nonzero, is introduced in order to isolate the roles of the pair correlations and the intermediate electromagnetic propagators on the parts of the macroscopic third-order susceptibilities that result solely from cascading. In β media the exact macroscopic third-order susceptibilities are expressed in terms of so-called irreducible cascading coefficients, which are multidimensional multiple integrals involving known quantities. This model is extended to include intrinsic linear and third-order polarizabilities and the effects of pair correlations in the local-field-correction factors.

We investigate dark-wave solutions of the nonlinear parabolic equation with a nonlinearity of rather general type and nonzero boundary conditions at infinity. Traveling-wave solutions of some polynomial models are presented in the evident forms. The bistability of dark pulses as the possibility for two different waves to exist under the same boundary conditions is discussed. The consideration is supported by the numerical treatment of the polynomial nonlinearity allowing the bistability regime. It is found that some different boundary conditions can be coordinated with the nonlinear equation in the case of an ssN-shaped nonlinearity. In the small-amplitude limit the nonlinear Schrödinger equation is reduced to the Korteveg–de Vries equation. The stability of small-amplitude solutions is determined by both the kind of the nonlinearity and the intensity level at infinity. The occurrence of antidark pulses is pointed out.

We use the time-dependent Hartree approximation to obtain solutions to a quantized higher-order nonlinear Schrödinger equation. This equation describes pulses propagating in nonlinear-optical fibers and, under certain conditions, has femtosecond soliton solutions. These solitons travel at velocities that differ from those of the picosecond solitons obtained from the standard quantized nonlinear Schrödinger equation. Furthermore, we find that quadruple-clad fibers are required for the propagation of these solitons, unlike the solitons of the standard nonlinear Schrödinger equation, which can propagate in graded-index optical fibers. From the quantum solution, we find that the soliton experiences phase spreading and self-squeezing as it propagates.

A spatiotemporal instability is shown to occur in a dispersive nonlinear optical medium whose refractive index varies linearly with the optical intensity (the Kerr medium). The physical origin of the spatiotemporal instability lies in the simultaneous presence of diffraction and dispersion in nonlinear media. For a self-focusing medium the instability can occur for both normal and anomalous dispersion. In contrast, the instability exists only in the normal-dispersion region of a self-defocusing medium. A linear stability analysis is used to predict the initial growth rate of the spatiotemporal instability. Numerical simulations are used to analyze the behavior in the nonlinear regime where the results of the linear stability analysis become invalid. Our results show that the spatiotemporally modulated mode has a larger growth rate than that of the spatially homogeneous mode and is expected to dominate in practice. The periodic state eventually evolves into spatiotemporal chaos with further propagation inside the nonlinear medium.

Metastable states of atomic hydrogen in an ideal linearly polarized laser have been shown to exist. These states, in the laboratory frame, have the electron oscillating with a large amplitude. The electron will radiate both even and odd harmonics of the laser frequency at a rate calculated here. The electron may also radiate nonharmonic radiation, thereby leaving the atom in an excited state. This process contributes to the width of the ground state. Both processes are evaluated at an upper limit of intensity imposed upon the theory by the dipole approximation.

We use resonance ionization involving two colors in single-pass and retroreflected geometries to study the suppression of excitation of a four-photon resonance by an interference involving four-wave sum-frequency generation occurring near an intermediate three-photon resonance. The 6p[1/2](J=0) state of xenon is excited by three blue photons plus one infrared photon. One beam, focused to ${\mathit{I}}_1$≃7×${10}^9$ W/${\mathrm{cm}}^2$, is nearly three-photon resonant with the 6s[3/2](J=1) resonance; the second, unfocused beam (${\mathit{I}}_2$≃2×${10}^7$ W/${\mathrm{cm}}^2$) is tuned to maintain exact four-photon resonance with the 6p[1/2](J=1) state. One additional blue photon ionizes from the four-photon level. Third-harmonic light is generated by the first, nearly three-photon-resonant beam by four-wave sum-frequency mixing. One third-harmonic photon plus one photon from the second laser form a second excitation pathway to the four-photon level; destructive interference between the two pathways results in a reduction in the observed ionization. The degree of reduction depends on the xenon density and the detuning (both positive and negative) from three-photon resonance. This interference may be overcome by retroreflecting the nearly three-photon-resonant beam to provide an additional excitation pathway which generates no third harmonic.

The study provides detailed information on the pressure-dependent range from exact resonance over which the familiar three-photon cancellation effect is operative; it shows that the interference occurs in high- and low-energy regions about three-photon resonance; and it establishes that interference is produced for large values of the phase mismatch even if the absorption of the interfering field is low. We compare our measurements of the reduction in ionization with predictions published by us elsewhere [M. G. Payne, J. C. Miller, R. C. Hart, and W. R. Garrett, Phys. Rev. A 44, 7684 (1991)]; excellent agreement is observed. We also report the observation of suppression of pressure-induced wing absorption into the three-photon state observed in a classic ‘‘hybrid’’ resonance mode of excitation.

The near-zero threshold and the very high gain of the active optical microlaser are investigated both theoretically and experimentally. These properties are found to be determined by the synergy of several quantum-statistical processes taking place in the condition of extreme field confinement provided by the peculiar Casimir-type topology of the optical microcavity. The determination of the microcavity mode structure leads to a detailed study of the process of merging of the spontaneous emission with stimulated emission (StE) and of the consequent anomalous onset of the collective atomic behavior at very low excitation levels. An excitation threshold of about 50 pJ has been determined experimentally with a molecular oxazine microlaser excited by a femtosecond-pulse source. The relevance within the overall StE dynamics of the processes of mode-competition fluorescence loss, interatom transverse Bose correlations, and periodic excitation are investigated both theoretically and experimentally. A discussion of the overall process in terms of a second-order phase transition in a nonequilibrium statistical problem is given. The extension of the microcavity dynamics to quantum-dynamical systems such as the ‘‘microscopic’’ parametric oscillator and to Raman and Compton scattering is also considered.

Photons spontaneously emitted from single atoms are necessarily antibunched in time. The statistics of the photon time record, however, can show sub-Poissonian or even super-Poissonian statistics and depend strongly on the time interval used for analysis. In this work we have analyzed photon arrival times from resonantly excited barium atoms in an atomic beam observed under single-atom conditions. The time-interval dependence of photon statistics is presented, showing the connection between antibunching and sub-Poissonian statistics (at times comparable to the spontaneous-decay lifetime of the atom) as well as the evolution of the statistics in the long-time limit.

Recently several methods have been proposed for generation of superposition (Schrödinger-cat) states in microwave cavities. At microwave frequencies, thermal photons can significantly affect statistical properties of superposition states. In the present paper we study the influence of a thermal heat bath on nonclassical properties of quantum superposition states. We show that at nonzero temperature the loss of coherences is much faster than at zero temperature. Using the formalism of quasiprobability distributions and solving the corresponding Fokker-Planck equations, we describe the time evolution of the super-position states in phase space and derive the rate of the decay of quantum coherence. This decay rate depends on the separation between the component states and on the temperature of the heat bath. Moreover, we discuss in detail how the interaction with a nonzero-temperature heat bath leads to a transformation of a nonclassical state to a classical state. We show that the sensitivity of the quantum coherence to the presence of thermal photons can lead to some difficulties in the preparation of Schrödinger-cat states in microwave cavities unless the temperature of the microwave cavity is sufficiently low.

We consider an array of N coupled class-B lasers in a ring geometry. We analyze the stability of the steady-state solutions for small values of the coupling strength and small damping. The problem is motivated by recent studies of laser-diode arrays, but analytical results on the possible instabilities remain limited to the case N=2. We consider N arbitrary and use the coupling strength as the bifurcation parameter. As this parameter increases from zero, we show that the first instability leads to a preferential mode of oscillations. For N even, we study this bifurcation to a time-periodic standing-wave solution and determine the direction of bifurcation. We discuss the bifurcation possibilities in terms of the parameter α, known as the linewidth-enhancement factor, in semiconductor lasers. Increasing α destabilizes phase locking between adjacent lasers but leads to a smooth bifurcation to periodic solutions. Inversely, decreasing α stabilizes the laser array, but the first bifurcation leads to a hard transition to time-dependent solutions. The predictions of our analysis are in agreement with the results of a numerical study of the laser equations.

The statistical properties of the mirrorless-laser output radiation field, E(r,t), and its spectrum, E(r,ν), are studied. The study is based on the analysis of the cross-spectral density integrated over a band of frequencies of width B; ${\mathit{M}}^{\mathit{B}}$(r,r,’ν)≡${\mathcal{F}}_{\nu \mathrm{-}\mathit{B}/2\mathrm{}}^{\nu +\mathit{B}/2\mathrm{}}$dν’’ ${\mathcal{F}}_{\nu \mathrm{-}\mathit{B}/2\mathrm{}}^{\nu +\mathit{B}/2\mathrm{}}$dν’〈Ẽ(r,ν’)E${\mathrm{̃}}^{\mathrm{*}}$ and of the power spectrum ${\mathrm{\Lambda }}^{\mathit{B}}$(r,ν)≡${\mathit{M}}^{\mathit{B}}$(r,r,ν). The relation between the spectral properties and the spatial correlations is characterized by the ratio between measurements in a narrow band near the atomic line center and measurements in a band of frequencies much larger than the atomic linewidth, namely by the ratios a(r)≡${\mathrm{\Lambda }}_1^{\mathit{B}}$≪Γ(r,0)/${\mathrm{\Lambda }}_2^{\mathit{B}}$≫Γ(r,0) and b(r,r’)≡${\mathit{M}}_1^{\mathit{B}}$≪Γ(r,r’,0)/${\mathit{M}}_2^{\mathit{B}}$≫Γ(r,r’,0 ). It is shown that, for systems with small spatial variations in the atomic population-inversion density, both the ratios a and b are independent of the observation points r,r’ and their value equals the ratio between the bandwidth ${\mathit{B}}_1$ and the gain-narrowed atomic linewidth. For systems with a strong spatial variation in the population inversion, it is shown that the ratio b depends on the observation points r,r’ and is larger than the ratio between the bandwidth ${\mathit{B}}_1$ and the gain-narrowed atomic linewidth. This effect is demonstrated by a detailed numerical calculation for a mirrorless laser with a Lorenzian atomic line shape.

We investigate theoretically the noise properties of the amplification of a weak probe beam in an atomic vapor pumped by an intense nearly resonant pump field. For the case of gain via the three-photon effect, we find that only in the limit in which collisional broadening is absent can the system operate as an ideal quantum-noise limited optical amplifier for the probe wave. For the case of gain via stimulated Rayleight scattering, we find that the minimum noise figure is four times that of an ideal optical amplifier, and that it occurs when the atomic system is predominantly collisionally broadened.