The problem of correlated diagonal fluctuations is treated in the particular case of a dimer. Specifically, we analyze the influence of the correlation existing between the fluctuations on different sites. The local fluctuations induce a frequency modulation on the individual monomers. When these fluctuations are correlated, the internal dynamics of the dimer is altered. As a consequence, these intersite correlations give an additional contribution to the linear and nonlinear optical responses of the dimer. While this process has been discussed previously for δ-function-correlated Gaussian-Markovian processes, we consider here the non-δ-function-correlated case. The linear absorption spectrum and the third-order susceptibility in a degenerate-four-wave-mixing experiment are considered in order to emphasize the role of the correlated fluctuations in the linear and nonlinear regimes, respectively.

We propose that the threshold of a laser is more appropriately described by the pump power (or current) needed to bring the mean cavity photon number to unity, rather than the conventional ‘‘definition’’ that it is the pump power at which the optical gain equals the cavity loss. In general the two definitions agree to within a factor of 2, but in a class of microcavity lasers with high spontaneous emission coupling efficiency and high absorption loss, the definitions may differ by several orders of magnitude. We show that in this regime the laser undergoes a transition from a linear (amplifier) behavior to a nonlinear (oscillatory) behavior at our proposed threshold pump rate. The photon recycling resulting from the high spontaneous emission coupling efficiency and high absorption may in this case result in lasing without population inversion, and coherent light is generated via ‘‘loss saturation’’ instead of gain saturation. This mechanism for lasing without inversion is very different from lasing without inversion using a radiation trapped state.

We present a many-body theory of nonlinear atom optics, and discuss some of its physical implications in the coherent regime. Considering a system of N identical two-level atoms interacting with classical and quantum-mechanical electromagnetic fields, we derive a Fock-space many-particle master equation. Introducting a Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy and a Hartree-Fock factorization to truncate this hierarchy, we obtain an effective nonlinear single-particle master equation that forms the basis of nonlinear atom optics. In the second part of the paper, we concentrate on the coherent part of that master equation, and derive an effective single-atom nonlinear Schrödinger equation. This equation leads to the prediction of a number of effects, and, in particular, several kinds of atomic solitons. We discuss and numerically study two such kinds of solitons, Thirring solitons and gap solitons. Finally, the axial containment of an atomic gap soliton is illustrated.

The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in atom-field coupling. The coupling coefficient is assumed to fluctuate in phase and/or in amplitude. The phase fluctuations are described by a Wiener-Levy process and the amplitude fluctuations by a colored Gaussian noise. A secular approximation and the theory of the multiplicative stochastic processes are invoked to derive the master equation for the density operator averaged over both phase and amplitude ensembles. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.

We use the theory of cascaded open systems to calculate the transmitted photon flux for a weak beam of photons focused onto a single, resonant two-state atom in the narrow-bandwidth limit. We study the dependence of the transmitted flux on the quantum statistics of the incident light. Sources of coherent, chaotic, squeezed, antibunched chaotic, and antibunched coherent light are considered. We find that the second-order correlation function and frequency dependence in the wings of the spectrum of the incident light must be considered to explain the results.

The full saturation effects of a two-mode ring laser are investigated. An analytic expression for the steady-state laser intensity distribution function is derived. The auto and cross correlation of the two-mode intensities are calculated for different pump parameters for the two modes. Compared with third-order laser theory and with experimental measurements, good agreement is obtained when the laser is operated below threshold. However, when the laser is operated above threshold, noticeable deviations occur between third-order and full saturation laser theories.

We show how a collection of noninverted two-level systems, under the action of a quasiresonant pump field, can produce an exponential amplification of a probe signal through the mechanism of a dynamical instability with spatial self-bunching in a way very similar to that experienced by a high-gain free-electron laser. We offer a detailed description of this phenomenon, specify the conditions under which it takes place, and sketch possible experimental parameters for its observation in a gaseous medium.

An alternative way of diagonalizing the Jaynes-Cummings Hamiltonian is proposed and allows the definition of annihilation operators and coherent states for this model. Mean values and dispersions over these states are computed and interpreted. Limiting cases which are physically interesting are also examined.

We investigate the nonlinear dynamics of dual-frequency-pumped four-wave mixing in both the normal- and the anomalous-dispersion regime of optical fibers. We compare the exactly integrable dynamics of a truncated system of nonlinear ordinary differential equations for the first four modes of the multiwave mixing interaction with the phase-plane projections of the numerical solutions of the nonlinear Schrödinger equation.

The linewidth of a Λ-type noninversion laser is calculated on the basis of a c-number Langevin approach in lowest order of the laser field. It is shown that the system behaves in general—that is, also in the good-cavity limit—nonadiabatically. In the nonadiabatic regime a substantial deviation of the laser linewidth from the Schawlow-Townes formula is found and a simple interpretation is given.

We consider an atom in interaction with a massless scalar quantum field. We discuss the structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom through the quantum vacuum. Our main intention is to identify and to analyze quantitatively the distinct contributions of vacuum fluctuations and radiation reaction to the spontaneous excitation of a uniformly accelerated atom in its ground state. This gives an understanding of the role of the different physical processes underlying the Unruh effect. The atom’s evolution into equilibrium and the Einstein coefficients for spontaneous excitation and spontaneous emission are calculated.

We study spontaneous emission near the edge of a photonic band gap. Instead of a simple exponential decay in the vacuum, spontaneous emission displays an oscillatory behavior. A single photon-atom bound dressed state exhibits a fractional steady-state atomic population on the excited state. For a three-level atom we evaluate the spectral splitting and subnatural linewidth of spontaneous emission. In the presence of N-1 unexcited atoms we show that the collective time scale factor is equal to ${\mathit{N}}^{\mathrm{\phi }}$, where φ=2/3 for an isotropic band gap and φ=1 or 2 for anisotropic two-dimensional or three-dimensional band edges, respectively.

We examine a model of two-channel cavity quantum electrodynamics (QED) consisting of three-photon and one-photon absorption processes, i.e., we present a cavity-QED version of a nonlinear optical balance. We give detailed numerical results for the evolution of the atomic populations and the number of photons at the fundamental and third harmonic frequencies. We also show the behavior of the system if the fields are treated semiclassically, and we find the quantum effects to be rather dominant.

The optical Schrödinger-cat states are simple realizations of quantum states having nonclassical features. It is shown that vibrational analogs of such states can be realized in an experiment of double-pulse or chirped-pulse excitation of vibronic transitions. The possibility of conversion of vibrational Schrödinger-cat states to chemical-cat states is discussed.

It is shown that various variants of the deformed Jaynes-Cummings model (JCM) correspond to the JCM with an intensity-dependent coupling characterized by two additional phenomenological parameters (p,q). The standard JCM is obtained for p=q=1. The quantum collapse and revival effects and the squeezing properties of a particular variant of the (p,q)-deformed Jaynes-Cummings model are studied numerically. The model is based on the q-deformed oscillator algebra ${\mathit{AA}}^{\mathrm{°}}$-${\mathit{qA}}^{\mathrm{°}}$A=1 that interpolates between Fermi-Dirac and Bose-Einstein statistics. If the cavity field is prepared initially in a q-deformed coherent state, the quantum collapse and revival effects are observed only for q≊1. For q>1, the atomic inversion 〈${\mathrm{\sigma }}_3$(t)〉 exhibits chaoticlike behavior, which is a feature observed also in other q-deformed JCM’s. Strong squeezing is observed only for small positive and small negative q values. If q≊1, the squeezing is very weak. In the limit q=1±ɛ with ɛ≪1, the algebra can be interpreted as describing a small violation of Bose-Einstein statistics in the JCM.

The coupled-systems approach of Gardiner [Phys. Rev. Lett. 70, 2269 (1993)] and Carmichael [Phys. Rev. Lett. 70, 2273 (1993)] is used to study the effects of driving systems by a variety of kinds of nonclassical light, namely, squeezed light, two-mode squeezed light, antibunched light from a two-level atom driven by either coherent light or finite-bandwidth thermal light, and the light from a single atom in a very-high-Q cavity. The method is shown to be very efficient and complete. It is also shown that the photon-counting properties of light from an atom driven by antibunched light are not determined solely by the antibunching of the driving light.

When two optical waves at frequencies ${\mathrm{\omega }}_1$ and ${\mathrm{\omega }}_2$ interact in a medium with cubic nonlinearity, multiple four-wave-mixing processes can generate pairs of sidebands. A conservation law that connects the amplitudes of the pump waves and sidebands is shown to arise from the Manley-Rowe relations and from the infinite set of conservation relations of the nonlinear Schrödinger equation. The conservation relation is examined theoretically and verified experimentally for a variety of input pump power levels and asymmetries. It can be used as a diagnostic measure to determine if nonlinearities of higher order than cubic are present.

We investigate the interaction of atoms through two-photon resonant transitions, with quantized cavity radiation, in the framework of a lossless micromaser theory. Taking advantage of the fact that the atomic inversion is quasiregular in time in this model, with quite precise revivals, we find a very strong amplification of the average photon number. At the two-photon revival time, the atom leaves the cavity in an almost pure state. This leads to an essentially noise-free process that results in a shift of two photons of the initial photon distribution each time an atom passes through the cavity, while the width of the photon distribution remains constant. This leads to strongly sub-Poissonian field statistics.

A minimal model for a laser with delayed feedback is analyzed. The model is motivated by two independent studies of a laser controlled by a fully optical feedback [Otsuka and Chern, Opt. Lett. 16, 1759 (1991)] and a laser with an optoelectronic feedback [Loiko and Samson, Opt. Commun. 93, 66 (1992)]. By reformulating the original laser equations in terms of dimensionless quantities, we obtain a simpler problem which is valid for both lasers. We then investigate the limit of small-amplitude feedback and small damping and determine a bifurcation equation for all periodic solutions. We analyze this condition in terms of increasing values of the delay time and show that each branch of solutions emerges from the basic state and becomes isolated as the delay time is progressively increased. The overlap of bifurcating and isolated branches of solutions explains the coexistence of nearly harmonic and pulsating solutions. Pulsating solutions may change stability through period-doubling bifurcation. We determine a simple approximation for this bifurcation point and study its validity numerically.

The normal modes of electromagnetic fields satisfying three different boundary conditions are constructed systematically. For each of these cases, cavity quantization of the electromagnetic fields is carried out explicitly. It is possible, using normal modes, to perform a unitary transformation of the minimal-coupling Hamiltonian of an atom inside the cavity to a multipolar form. It is shown that the boundary condition plays an important role in the transition rates for the spontaneous emission by the atom. Some explicit calculations are carried out for several different boundary conditions. These results become consistent with those for free space in the large-box limit.