The dynamical behavior of the polarization of a laser with one or two stable eigenstates subjected to the action of an ac longitudinal magnetic field with or without a dc longitudinal magnetic field is investigatged both theoretically and experimentally. In the case of an ac magnetic field only, the low-field linear and high-field nonlinear behaviors of the laser are isolated. For the low-field case, a typical cutoff frequency due to pure cavity effects is introduced. For the high-field case, two locations of the motion are isolated, depending on the amplitude and frequency of the ac magnetic field. This provides the tools used to understand the locking between the rotation of the polarization induced by the dc magnetic field and the vibration of the polarization induced by the ac magnetic field. In particular, thanks to the two dimensions of the polarization vector, it is shown that the ratio of locked frequencies depends on the number of stable polarization eigenstates. Unlike mechanical systems where coalescence of Arnold tongues is possible, our system, without any inertia, exhibits typical twisted Arnold tongues, for which a theoretical model provides a great precision and a good agreement between theory and experiment.

We examine a frequency-summation process where two nondegenerate inputs interact inside a cavity via a nonlinear crystal to create a field at a higher frequency, in an attempt to find a reduction of intensity fluctuations below the shot-noise level (squeezing). We find squeezing to be possible for the intensity sum of the input modes, a theoretical maximum of near 100% reduction of the quantum noise being predicted possible. Squeezing is also found in the higher frequency, where a theoretical maximum of 50% reduction below the shot-noise level is found.

Nonlinear optical systems using a Kerr slice and two-dimensional feedback are analyzed. A Neumann-series approach is used to study pattern formation. We show that interactions between spatial modes (rolls) occur in the form of ‘‘winner-takes-all’’ dynamics and cause formation of hexagon patterns.

We examine whispering-gallery-mode microdisk lasers, which have some potential for use in optical computing, in an attempt to determine their stability and switching properties. We solve the laser equations for a coupled-laser system and investigate the stability and switching properties of these solutions. We find that the lasers are stable and switch reliably in the absence of noise. If reasonable estimates of noise are included, spontaneous switching rates of the order of once a year can be arranged using physically reasonable parameter values.

In this paper, a quantum theory of an inversionless laser is presented. The gain medium is considered to consist of three-level atoms in a closed Λ configuration, with a lower-level microwave coupling. By deriving an equation of motion for the reduced density matrix for the two modes of the field, gain and diffusion are studied. In particular, two mechanisms through which inversionless amplification takes place in the context of this model, namely, the suppression of absorption and mode coupling, are discussed. Stable conditions for inversionless amplification and the attendant phase diffusion are discussed and a comparison is made with conventional, inversion-based lasers. It is shown that lasing without inversion does not necessarily result in a reduced linewidth compared to a conventional laser.

A theory is presented that describes collision-induced modifications of the grating stimulated echo (GSE) signal. In the GSE [B. Dubetsky, P. R. Berman, and T. Sleator, Phys. Rev. A 46, 2213 (1992)], a spatially modulated atomic population is created which undergoes Doppler dephasing and rephasing as a result of the interaction of the atoms with a number of input pulses. At low pressures, there is a rapid decay of the GSE signal owing to a collisional breaking of the dephasing-rephasing process. At high perturber pressures, however, there can be a revival of the GSE signal owing to a collisional inhibition of the Doppler dephasing. These collisional processes are described in detail, with a special emphasis given to the distinction between ‘‘open’’ and ‘‘closed’’ atom-field systems. The manner in which the GSE can be used to determine collision kernels and diffusion coefficients is also discussed.

We study the collective effects in the trapping states in a one-photon micromaser. We find that, for small photon numbers, the trapping states are difficult to detect experimentally due to these effects. On the other hand, for higher trapping conditions, the behavior of 〈n〉 is similar to the usual trapping states, except for the appearance of spikes and also large fluctuations of the photon number.

For a pulse with carrier frequency detuned less than an atomic plasma frequency but outside a narrow Lorentzian gain line, the group velocity will be negative. Unlike propagation at the center of an absorption line, the energy velocity is approximately equal to the group velocity, and is also negative. We show that a classical Gaussian pulse with such a carrier frequency will propagate at the negative group velocity for many atomic plasma wavelengths, before dispersion deforms the pulse shape. The peak of the transmitted pulse leaves the gain medium before the peak of the incident pulse enters, i.e., the pulse is transmitted superluminally. For a sufficiently long medium the exit pulse is well resolved from a comparison pulse traveling through an equal distance of vacuum. There is no conflict with causality, as numerical simulations with a switched-on Gaussian demonstrate. We propose an experiment to observe this kind of propagation by sending a pulsed probe beam through a Xe gas cell pumped to achieve inversion.

The quantum state for spontaneous parametric down-conversion was evaluated to include information about the transverse spatial characteristic of the down-conversion fields. This state was used to calculate the angular spectrum of down-conversion in the case of both single-channel and coincidence measurements, while retaining the characteristic nonclassical correlations. Actual transverse profiles for typical experimental parameters were evaluated numerically and measurements were performed with results that compared well with the numerical calculation. This theoretical spatial model was then applied nonrigorously to the case of induced coherence without induced emission. The theoretical results implied that there was a reduction in the degree of induced coherence due strictly to the spatial distribution of the down-conversion beams. This was interpreted as a result of increased distinguishability of the overlapping idler photons. Measurements were conducted which support these results qualitatively. In addition, the present theory explained an unexpected quantitative discrepancy between second- and fourth-order visibilities in previous induced-coherence experiments. This discrepancy was interpreted phenomenologically as a difference between intrinsic and nonintrinsic indistinguishability, and some implications towards quantum measurement theory and the role of the observer were suggested.

We present a general theory for the calculation of various characteristic properties of the beam of atoms emerging from a resonator in one-atom-maser experiments. The beam is described in terms of the statistics of the detector clicks. The evolution of the state of the maser photons between clicks is governed by a nonlinear master equation. The nonlinearity originates in the necessity to account for the atoms that escape detection. Despite the permanent reductions of the photon state, resulting from the detections, the steady state of the conventional linear master equation determines the statistics of the detector clicks. The whole process is ergodic, in the sense that a single run of the experiment contains all reproducible statistical data, provided the duration of the run is much longer than all relevant correlation times. The nonlinear master equation is used to calculate the distribution of waiting times between detector clicks. Other statistical properties of the clicks that are derived include correlation functions and variances of the counting statistics. The formalism is applied to standard one-atom-maser experiments and to parity measurements on both unpumped and pumped cavities. We find that, for the standard one-atom-maser operation, none of the said statistical properties is a simple immediate indicator for a sub-Poissonian variance of the photon number. For example, the detector clicks may be antibunched although the photon distribution has a super-Poissonian variance.

We show that in a two-photon correlated-spontaneous-emission laser with a fast-decaying intermediate relay level, it is possible to obtain the same degree of phase squeezing as when all levels have comparable lifetimes, but with a much higher gain coefficient.

For one-mode light described by the Wigner function of a generic Gaussian form with five real parameters, the photon distribution function is obtained explicitly in terms of the Hermite polynomial of two variables. The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. The first and the second statistical moments of the photon distribution function are calculated. The generating function for the photon distribution is discussed. Various special cases, including the shifted thermal states, correlated and squeezed states, coherent states, etc., are considered.

We have examined the effect of various phase-matching conditions on sum frequency generation in vapors. Using sodium vapor two resonant-enhancement routes for sum-frequency mixing (SFM) via a second-order magnetic-field-induced nonlinearity were explored. On one route the output is resonant with a quadrupole-allowed transition and the other a dipole-allowed resonance. We will show that the first route is preferential for SFM as phase matching on this route is easier to control and we present results detailing the important parameters and their effect in focused and unfocused cases. A second-order nonlinearity of 0.5–1 ${\mathrm{pmV}}^{\mathrm{-}1}$ is observed under optimum conditions. In the second route, variations in phase matching as one tunes across the transition may lead to a significant distortion of the spectroscopic line shapes. We show how the combination of different refractive-index sources can account for the different features seen.

We analyze how a decaying cavity field can lead to significant atomic cooling. This cooling can be intuitively understood by invoking the adiabatic theorem to characterize the dynamics of an atom dressed by a classical field. We find numerically that cooling can proceed well into the quantum regime where there are only a few photons left in the cavity, and where the adiabatic theorem ceases to be applicable. A physical interpretation of this final cooling stage is given.

The detection of the phase shift between a single mode of the em field and a local reference oscillator is analyzed in the proper framework of quantum estimation theory. Such a fully quantum treatment clarifies the meaning of the ‘‘operational approach’’ suggested by Noh, Fougéres, and Mandel [Phys. Rev. A 45, 424 (1992)], in which different measurement schemes correspond to different phase operators. We show that the phase shift is actually measured in the form of the polar angle between two real output photocurrents, namely through a joint measurement of two conjugated quadratures of the field. This scheme is the only feasible one for detecting the quantum phase, and it is equivalently performed by either heterodyne detection or double-homodyne detection of the field. On the contrary, the customary homodyne detection (and, generally, any kind of measurement of a single phase-dependent variable) is more properly a zero-point phase measurement. As a definition of sensitivity we consider the output rms noise of the detection scheme, the only relevant one for actual experiments, in contrast with many other different notions currently adopted in the literature. We show that the rms phase sensitivity versus the average photon number n¯ is bounded by the ideal limit Δφ∼n${\mathrm{¯}}^{\mathrm{-}1}$, whereas for the feasible schemes the bound is Δφ∼n${\mathrm{¯}}^{\mathrm{-}2/3}$, in between the shot-noise level Δφ∼n${\mathrm{¯}}^{\mathrm{-}1/2}$ and the ideal bound.

The latter can acutally be achieved by single homodyne detection of the suitable squeezed states, but only in the neighborhood of a fixed zero-phase working point. The phase sensitivity bound Δφ∼n${\mathrm{¯}}^{\mathrm{-}2/3}$ can be reached using coherent states with only 2% of squeezing photons, in contrast with the homodyne-detection bound Δφ∼n${\mathrm{¯}}^{\mathrm{-}1}$ which is reached with 50%. The uncertainty product of two conjugated phase quadratures largely exceeds the Heisenberg limit, even for the ideal joint measurement. We also show that no sizeable improvement in sensitivity is found for detection schemes which involve wideband states, at least for the case of nonentangled states. At the end of the paper we give an extensive table of asymptotic sensitivities at large n¯ for both ideal and feasible schemes.

Optical switching between bistable soliton states of the second kind is demonstrated numerically when two parallel, straight optical fibers are evanescently coupled. The numerical switching study is supplemented by a variational analysis which provides a preliminary guide to what ranges of input parameters should be chosen for the switching simulations.

If the quantized field has initially a small mean number of photons (n¯∼2), quantum inversion displays distinct revivals, provided the detuning between the field and the atom is large as compared to the coupling constant [(g/Δ${)}^2$≪1]. However, the amplitudes of these revivals are very small. For long times, individual revivals partially overlap to form fractional revivals, and for even longer times superrevivals (revivals of the revivals) appear. These phenomena result from the beating of modes of the quantized field that are not nearest neighbors. The envelope of the electric field associated with the oscillating atomic dipole exhibits similar superstructures, but with a period twice that for the atomic inversion.

It is shown that for the scalar analog of electrodynamics in one dimension, the quasinormal modes of a leaky cavity form a complete set inside the cavity, provided the cavity is defined by a discontinuity in the refractive index. This condition is sufficiently general to apply to a number of interesting examples. The quasinormal modes are also orthogonal under a modified definition of the inner product. The completeness and orthogonality hold even though the cavity is not a Hermitian system by itself. These properties allow the discrete quasinormal modes to be used as the basis for dynamics of the scalar wave in the cavity.

If a cavity is leaky, its ‘‘modes’’ are quasinormal modes (QNM’s) with complex frequencies, and they do not constitute a Hermitian system. Nevertheless, the time-independent perturbation arising from a small change of the dielectric-constant distribution can be formulated in terms of these discrete QNM’s, resulting in a generalization of the usual perturbation scheme to a non-Hermitian situation. In particular, shifts for the imaginary parts of the eigenvalues are obtained as well. This paper presents this theory for scalar waves in one dimension.

A relativistic density-functional theory for ensembles of unequally weighted states is formulated. This is a relativistic generalization of the formalism proposed by Gross, Oliveira, and Kohn [Phys. Rev. A 37, 2805 (1988); 37, 2809 (1988); 37, 2821 (1988)]. Application of the theory is illustrated by a simple relativistic local-density (Xα) calculation.