The dynamics of quantum fluctuations in an atom interacting with a standing-wave field is studied. The spectrum of resonance fluorescence is calculated using a formulation based on optical Bloch equations for two-time correlation functions and continued-fraction methods. The spectra are calculated both under resonant and nonresonant conditions. The resonance condition in the context of a standing-wave field corresponds to a velocity-tuned or Doppleron resonance that in turn depends on the intensity of the pump. The Doppleron resonances are extracted from the positions of maxima in the total intensity of fluorescence. The spectral features are explained in terms of the eigenvalues of the appropriate ‘‘Floquet’’ matrix.

A criterion is evolved for testing the nonclassical character of the field even if it does not exhibit squeezing and sub-Poissonian statistics. An explicit example of a state of the field is given to demonstrate the utility of this criterion. The production of such a state by state-reduction methods is also shown. This criterion also enables us to study the nonclassical character of the Schrödinger cat state in regions where it does not exhibit sub-Poissonian statistics.

The screw operator is introduced in the system of the plane rotator and applied to the ground state of the mathematical pendulum. The resulting p state is studied from the viewpoint of the usual and modified statistical and uncertainty characteristics relevant to quantum optics and the quantum phase.

In the experiment described in this paper, a chopper serves as a source of neutron intensity pulses which pass through a perfect Si-crystal neutron interferometer (NI), where they are split coherently into two parts that recombine and interfere. As the occupation number of a single pulse is much smaller than unity, the results very clearly demonstrate the single-particle interference phenomena of neutron interferometry experiments. While traveling the pulses spread, with faster (slower) neutrons tending toward the leading (trailing) edge. The coherence length of the neutrons depends on the spectral width of their wavelength distribution. When a material with a neutron-nuclear optical potential is placed in one beam path in the NI, there is a loss of fringe visibility (contrast), which depends on the coherence length. By using time-of-flight techniques, we divide the pulse into time segments. Within a given time slice, the wavelength spectrum is narrower than in the pulse as a whole. As a result, contrast remains in the time slices even when it disappears in the overall pulse. We also observe an additional contrast modulation due to the overlap of neighboring pulses.

We consider a trilinear Hamiltonian in boson operators describing various physical processes such as frequency conversion, Raman or Brillouin scattering, or the interaction of N two-level atoms with a single-mode radiation field. Due to the fact that two independent integrals of motion can be found, the solution of the dynamics of the system is reduced to the diagonalization of a finite matrix (as was already shown by Walls and Barakat [Phys. Rev. A 1, 446 (1970)]). Performing a numerical diagonalization, we analyze the statistical properties of the field modes (sub-Poissonian statistics, anticorrelation, squeezing). We also pay attention to the appearance of collapses and revivals in the mean photon number of the modes. The relation of this model to the model of two coupled modes with an intensity-dependent coupling constant is pointed out.

Using a simple model of a ring cavity comprising a cubically nonlinear medium, we analyze dispersive optical bistability in the presence of more than one spectral component. We show the phenomenon of so-called competition for resonance. In addition to presenting cavity characteristics for the cases of two and three different frequencies, we also discuss the general method for finding steady-state solutions and checking their stability. A simple and efficient algorithm, based on a relaxation method, is devised to find steady-state solutions satisfying appropriate boundary conditions. The relaxation dynamics is physically related to a finite response time of the medium.

We consider the self-focusing in uniaxial gyrotropic media at axially symmetric geometry, i.e., when the wave beam and the gyration vector g are parallel to the principal axis. Dissipation is neglected and the nonlinearity is of the Kerr type. It is shown that when g is directed along the wave normal, i.e., g⋅n>0, there is a detrapping of the nonlinearly self-trapped wave beam. The detrapping increases with the narrowing of the beam and this results in the final defocusing of the wave. If g is antiparallel to the wave normal, (g⋅n)<0, there is no detrapping and finally a homogeneous wave beam is formed. The results obtained are beyond the theory based on the nonlinear Schrödinger equation.

We analyze the standard third-order model describing a laser gyroscope with backscattering in the two limiting cases of dissipative and conservative coupling. In both cases we discuss the steady-state and periodic solutions, determine their stability, and construct the locking diagram. In particular, in the dissipative coupling case, an exact periodic solution is found analytically. It is also proved that the concepts developed in the passive-cavity problem are useful tools to understand the dynamics of the laser gyroscope.

We study analytically and numerically a very simple nonlinear optical system, a thin slice of Kerr material with a single feedback mirror. Theoretical analysis shows that for both a focusing and defocusing medium the plane-wave solution is unstable above a certain input intensity and a hexagonal pattern of bright spots should form. The amplitude equations for this system are three coupled Ginzburg-Landau type equations. Numerical analysis confirms these results; moreover by further increasing the input intensity, the hexagonal solution becomes itself unstable and turbulent motion sets in.

Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)] have proposed a formalism for a Hermitian optical phase operator, constructed from the so-called phase states. In this paper we give an alternative derivation. We begin by defining a unitary phase operator $e^{i\hat{\phi }}$ from the relationship $\hat{a}=e^{i\hat{\phi }}R\left(\hat{N}\right)$ ($\hat{a}$ is an annihilation operator for a single-mode boson field), but borrow the idea of a finite- (but arbitrarily large) dimensional space from Pegg and Barnett. Finally, we comment on an experiment to determine quantum phase uncertainty. Our analysis uses the operator $e^{i\hat{\phi }}$, which we feel is a more natural choice than $\hat{\phi }$. The use of $e^{i\hat{\phi }}$ also avoids the multivalued problems associated with $\hat{\phi }$.

We discuss the geometric phase accumulated by the wave function of an atom ionizing in the presence of a bichromatic field as physical parameters are varied adiabatically around a closed circuit. As an illustration we calculate the geometric phase for a hydrogen atom in the presence of 355-nm light and its third harmonic when the phase and intensity of the two components are varied. The wave function need not be single valued after one complete circuit—two circuits may be necessary to map the original eigenray onto itself. Furthermore, the geometric phase may be complex, and may therefore modify the ionization yield calculated from the width of the instantaneous quasienergy.

The connection between proposed experiments involving a micromaser and the Ramsey technique of separated oscillatory fields is explored, specifically with regard to possible experiments to measure the phase-diffusion linewidth of the maser. A method of detecting the trapping states and a setup to identify the two-level system as being a true spin-1/2 system are presented. In addition, a pictorial view of the time evolution of the atomic Bloch vector is given.

The formalism of Englund and Bowden [Phys. Rev. A 42, 2870 (1990)] is used to conduct a detailed investigation into the statistics of spontaneously generated Raman solitons and their origin in phase waves. Two approaches are adopted. In one, a Monte Carlo simulation of the stochastic differential equations describing stimulated Raman scattering is carried out, with quantum noise entering through the Stokes vacuum. The other involves determining analytically the field statistics in the quantum-initiation regime, finding the corresponding phase-wave statistics, and determining numerically the class of phase waves that appear in the nonlinear regime as solitons. Computations involving quasi-Gaussian and rectangular pump-pulse profiles consistently indicate soliton yields of roughly 10% and 4%, respectively; differences in the distributions of soliton delay times and peak intensities are also indicated. The Monte Carlo method is adapted to the experimental parameter values of MacPherson et al. [Phys. Rev. A 40, 6745 (1989)], and gives yields and distribution in good accord with the experiment.

Unlike classical and quantum particles rolling down a potential slope, quantum waves on a lattice are confined in bound states on the potential hill. For the linear potential there is an equidistant spectrum of these states. The well-known Bessel functions ${\mathit{J}}_{\mathrm{\alpha }}$(kr) with the integer index α as a discrete spatial coordinate (not r as usual) play the part of the bound-state wave functions—standing waves between the potential hill and the invisible boundary of the upper forbidden zone. This exactly solvable model elucidates some peculiar features of more realistic systems, particularly, the interchannel wave motion where α means the discrete channel number.

We have used classical dynamics to study high-field-intensity ionization of atoms for various parameters and different potentials. The numerical calculations establish evidence that the ionization probability P vanishes in the limit of large field amplitude and small Kramer’s parameter A/${\mathrm{\omega }}^2$, where A is the field amplitude and ω is the frequency. We also show that the reported suppression of P for large values of A at fixed frequency ω in quantum dynamics is consistent with results from the corresponding classical ensemble, depending upon the potential, and within the context of comparison. These results, combined with other data, indicate that the classical-ensemble initial conditions, together with the modulation of the potential by the externally applied field, play a significant role in the classical picture of photoionization.

We use classical-ensemble dynamics to study multicolor, laser-field-induced, atomic photoionization from the ground state. It is shown that multicolor laser excitation can enhance ionization, a trend that is shown to persist for two distinct one-dimensional potentials. Maximum Lyapunov exponents and corresponding power spectra for bound orbits are used to illustrate that although chaotic temporal evolution may be manifest in predissociation dynamics, it is not a sufficient condition for dissociation. Correlation is obtained between the magnitude of the maximum Lyapunov exponent and the tendency to ionization among neighboring trajectories.

A semiconductor laser in an external high-quality cavity is analyzed using a composite-resonator-eigenmode description of two coupled resonators. Laser threshold and lasing frequency are studied for various cavity lengths and coupling-mirror transmissions controlling the amount of light feedback into the laser. The results are valid for all values of coupling. Pronounced mode hopping is predicted, which leads to dramatic laser-frequency shifts for small variations of the external cavity length.

There has been a great deal of interest in periodic dielectric materials that exhibit photonic band structures. One of the more interesting features of such a substance is its ability to alter the emission rate of probe atoms embedded in the periodic lattice. Large enhancements and complete inhibition of emission rates can be obtained. It has been known for some time that the influence of a cavity on atomic emission is essentially a classical effect. Hence, we develop a general classical treatment of radiation rates in an inhomogenous medium. Our results agree with those of a fully quantum calculation, and are applied to a simple scalar model of a dipole in a one-dimensional periodic lattice of the Kronig-Penney type.

The basic mechanisms of the polarization switching in vectorial bistable lasers are studied both theoretically and experimentally versus internal parameters. In particular, by scanning the frequency of a gas laser with two linearly polarized eigenstates, two quite different flipping processes with hysteresis occur according to the linear-phase-anisotropy value of the cavity. Indeed, when the anisotropy increases, rotation and inhibition mechanisms appear successively. The variations of the hysteresis loop for different anisotropy and excitation values are theoretically found to be opposed in the two processes. Additional evolutions of the polarization, such as multiple switchings in the inhibition mechanism and ‘‘hybrid’’ hysteresis loops, are predicted. The experiments, essentially performed on a monomode 3.39-μm ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^{20}{}_{}{}^{}$Ne laser containing an adjustable linear phase anisotropy, confirm the existence of the two processes and their corresponding properties. These processes may also occur in other quasi-isotropic lasers versus other internal parameters, such as, for instance, the injection current in semiconductor lasers. In this case the TE and TM modes flip only in the inhibition mechanism when the bistability conditions are satisfied. The knowledge of the basic flipping mechanisms in the laser itself enables us to understand and realize the external optical-polarization control by an anisotropic feedback (one-frequency systems). Induced-rotation and induced-inhibition mechanisms are then theoretically predicted and experimentally verified. Sensitive optical gates are realized by varying the feedback phase in both processes.

We characterize the evolution operator of a quantum system with generic spectral properties (in agreement with random-matrix theory), with a time-dependent Hamiltonian. The results are applied to the independent-electron model for the dissipation of energy: an example of a physical application would be the absorption of low-frequency electromagnetic radiation by small metallic particles. We discuss the statistical properties of the various regimes of the model, which depend on whether the perturbation is large enough to mix levels, and on whether the frequency is low enough for the quantum adiabatic theorem to apply. We also show that the eigenstates of the evolution operator are Anderson localized in the adiabatic basis, and present results concerning the localization length. This localization causes a saturation of the energy absorption if the Hamiltonian is periodic in time. The addition of a small amount of noise to the Hamiltonian destroys this nonclassical saturation effect.