Recent work on the dynamics of open systems has shown how the density operator may be unraveled into component state-vector trajectories using quantum-state diffusion or the quantum-jump model. In traditional dissipative environments the coherent evolution is stochastically perturbed by the action of the reservoir or environment, so that superposition states are dephased. We examine a system in which both coherent driving and dissipative damping involve the simultaneous creation and annihilation of pairs of photons. This has unusual consequences for the creation and decay of coherences. We analyze this problem using the two recently proposed simulation methods and compare the results of the simulation methods with each other and with density-matrix calculations. We also demonstrate the formation of Schrödinger ‘‘cat’’ states of the field through the action of dissipation and depict them using the Wigner and Husimi quasiprobability functions.

We show that a simple nonperturbative two-level model of an atom driven by a very strong periodic field results in a rich picture of very high harmonic generation and related phenomena. It reproduces the experimentally observed plateau, yields simple analytic formulas for the plateau cutoff frequency, critical driving intensity, and saturation, and predicts intensity-induced multiresonances.

The properties of one-dimensional straight-line superposition states obtained as a continuous generalization of the even and odd coherent states are studied. Superposition states with Hermite-polynomial–Gaussian distribution functions are introduced. These states form a complete orthonormal basis set in the Hilbert space of quantum oscillators. This basis makes it possible to obtain the straight-line coherent-state distribution function for a given state. As an example, the distribution functions for squeezed coherent states are derived.

We study the effect of non-coherent-state pumps on the behavior of the degenerate parametric amplifier. This is done both by developing some exact results and by extending the parametric approximation. Relations are found between the number fluctuations in the pump and those in the signal. The effect of initial phase uncertainty in the pump on the squeezing in the signal is also determined. In addition, we find that rotational symmetry in phase space of the signal-mode state is twice that of the pump-mode state. This implies, for example, that a pump in the squeezed vacuum state will produce a signal-mode state with a four-pronged structure. The effect of a squeezed pump with nonzero amplitude is studied by using a more general form of the parametric approximation. It is shown that in the time interval during which the parametric approximation is valid the effect of this pump is the same as one which is an incoherent superposition of coherent states. We find that while the squeezing of the pump degrades the squeezing of the signal it enhances its amplitude-squared squeezing.

Measurements on an optically pumped ${\mathrm{NH}}_3$ single-mode laser show three different types of chaotic dynamics, Lorentz-type spiral chaos, period-doubling chaos, and type-III intermittency. Analysis of the measurements shows that the peak-intensity return maps of these three types of dynamics have the same shape, indicating that a unique attractor exists for the laser whose topological structure is independent of laser parameters.

We consider the equations for N coupled class-B lasers in a ring geometry. We investigate the first bifurcation to time-periodic solutions in the limit of (i) small damping, (ii) small coupling, and (iii) large N. We identify the relevant scaling between these three quantities from the linear stability analysis and derive a nonlinear partial differential equation for the slow time and slow space evolution of the time-periodic traveling-wave modes. The equation is similar but not identical to the Ginzburg-Landau equation derived in the areas of fluid or chemical instabilities. It contains an additional term and the boundary conditions are different if N is even or odd. We next determine solutions of this equation. If N is even, the first bifurcation corresponds to a time-periodic standing wave and its amplitude is identical to the amplitude previously obtained for N even but arbitrary [Li and Erneux, Phys. Rev. A 46, 4252 (1992)]. If N is odd, the bifurcation diagram is quite different. We find two primary bifurcations to traveling-wave solutions and one secondary bifurcation to a standing-wave solution. Our analytical results are in agreement with a detailed numerical study of the original laser equations.

This work is a response to a problem which was most clearly formulated by Wolf [Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, New York, 1973), p. 339] in this way: ‘‘Attempts to generalize [the extinction theorem] within the framework of molecular optics encounters formidable difficulties.’’ Here the method of integral equations is applied to an arbitrary nonlinear and anisotropic medium, taking into account quadrupole and magnetic-dipole radiation. Using the fundamental equations of molecular optics, we prove the extinction theorem in a general case, and its physical interpretation is elucidated. The question about structure of a surface layer that produces the reflected wave is clarified. A connection between the microscopic and macroscopic characteristics of nonlinear media is obtained. This advance was achieved by the implementation of the straightforward idea of variable substitution in the original integral equation. This substitution turns out to yield insight into the transition from a local to a Maxwellian field.

The formalism of Maker, Terhune, and Savage [Phys. Rev. Lett. 12, 507 (1964)] for third-order nonlinear susceptibilities is extended to account for nonlocal response. In the case of counterpropagating beams, we show that five constants instead of two are required in general to describe the nonlinearity. In the particular case of optical pumping nonlinearities, which we study extensively, we show that four constants, which describe the magnetization and electric-quadrupole moment of the medium induced by the forward and backward beams, are sufficient. We evaluate these constants for various values of the angular momenta of the atomic levels connected by the incident field. We finally show how this formalism can be applied to several problems such as induced focusing, four-wave-mixing generation, optical instability, and polarization properties of phase-conjugate and phase-contrast mirrors.

Because of radiation pressure, an optical cavity with harmonically bound mirrors has an intensity-dependent length and behaves as an effective Kerr medium. We determine the quantum fluctuations of the field reflected by such a cavity, taking into account the input field fluctuations and the mirror Brownian motion. In the regions of parameter space close to bistability turning points, we obtain a significant quantum-noise reduction effect.

Stability analysis allows the understanding of experimental steady and pulsed regimes observed in cw-pumped Brillouin fiber-ring lasers. The instantaneous acoustic response model proves to be singular, while the coherent stimulated-Brillouin-scattering (SBS) three-wave model yields a well-behaved Hopf bifurcation for a critical value of the feedback (several percent in intensity). The computed nonlinear dynamics shows self-organization of asymptotically stable Brillouin pulses, not depending on the initial noise. Further experiments support the bifurcation.

We present the quantum theory of optical cavity feedback mediated by homodyne detection, with an arbitrary time delay. We apply this theory to a system with nonclassical dynamics, a sub-Poissonian pumped laser. By using the feedback to phase lock the laser it is possible to produce output light which exhibits perfect quadrature squeezing on resonance, rather than just sub-Poissonian intensity statistics. However, we also show that feedback mediated by homodyne detection (or any other extracavity measurement) cannot produce nonclassical light unless the cavity dynamics can do so without feedback. Furthermore, in systems which already exhibit squeezing, such feedback can only degrade the squeezing in the output. With feedback mediated by an intracavity measurement, these theorems do not apply. We show that an (admittedly unrealistic) intracavity quantum nondemolition quadrature measurement allows arbitrary squeezing to be produced by controlling the amplitude of a coherent driving field.

We present the quantum theory of the two-mode micromaser operating on Λ-type three-level atoms. The explicit expression of the detailed-balance steady-state photon distribution is derived. The photon statistics and the correlation between the modes are studied. It is shown that due to the strong anticorrelation between the modes the fluctuations in the total number of photons may be sub-Poissonian even when the fluctuations in the number of photons in each mode are super-Poissonian.

Using a first-order approximation in time-dependent perturbation theory, we evaluate the probability per unit time of spontaneous emission by a two-level system coupled to a Hermitian massless scalar field in the presence of either one or two infinite perfectly reflecting plates (mirrors). We consider the effects of a finite interaction time between the system and the quantized field. Furthermore, using the image method in imaginary time, we study radiative processes at finite temperature. We show that vacuum and thermal fluctuations give independent contributions to the total transition rate and that both are modified by the presence of the mirrors. In the two-parallel-plate geometry, we find that the position average of the spontaneous emission rate is equal to the free-space rate for resonant cavities, but is suppressed in nonresonant cavities.

The phase-space properties of quantum states of light are investigated. A phase-space description of the quantum phase is derived using the operational approach to homodyne detection with noise. Using the P representation for the quantum states of light, quantum phase-space quadratures are derived that satisfy the trigonometric unity rule. A generating function involving all moments of the operational sine and cosine functions is derived and the statistical properties of these phase-space quadratures are discussed.

Pancharatnam’s geometric phase is introduced for such nonlinear dissipative systems as lasers and liquid flows. Two types of geometric phases are shown to arise in these systems: the phase induced by the inner dynamics of the system and the one caused by the cyclic and adiabatic variation of the system parameters. A possible generalization of the geometric-effects theory in other dissipative systems is discussed.

We treat quantum fluctuations and squeezing of the field generated by a degenerate optical parametric oscillator operating below threshold. The analysis reported here extends our previous calculations for single-sided cavities to double-sided cavities with arbitrary transmission coefficients for the two bounding mirrors.

Quantum fluctuations and squeezing of the signal field generated by a degenerate optical parametric oscillator are sensitive to the phase and amplitude fluctuations of the second-harmonic pump. The analysis reported here extends our previous calculations for a perfectly monochromatic noise-free pump to allow for finite pump amplitude and phase fluctuations. We treat the typically intense pump field with its fluctuations as a classical Gaussian stochastic process in two limits: first, when the pump has amplitude fluctuations but its phase is fixed and second, when its phase diffuses but its amplitude is fixed. Since pump amplitude noise affects the evolution of the signal field multiplicatively, it has a lesser impact on the quantum fluctuations of the signal than pump phase diffusion which compromises such fluctuations via the extreme phase sensitivity of the parametric amplification process. For the latter limit, our calculations extend the work of Gea-Banacloche and Zubairy [Phys. Rev. A 42, 1742 (1990)] to cavities with arbitrary transmission coefficients for the bounding mirrors.

We consider a cylindrically symmetrical laser with spherical mirrors and describe the dynamics in terms of the competition among different Gauss-Laguerre modes of the cavity. In this paper we focus on the case in which the mode competition leads the laser to a dynamical state that, according to the values of the control parameters, can be periodic or quasiperiodic. The linear stability analysis of the single-mode stationary solutions, in which the laser oscillates with the fundamental ${\mathrm{TEM}}_{00}$ or the ${\mathrm{TEM}}_{01}^{\mathrm{*}}$ mode, provides an initial guideline in our search for the various spatiotemporal patterns which emerge. We consider cases in which the gain line activates one, two, or three frequency-degenerate families of modes. The motion of optical vortices, from the simple rotation to creation and annihilation in pairs is analyzed, together with the correlated movement of the peaks of the intensity distribution in the traverse plane. We study also the patterns which appear when the cylindrical symmetry of the system is broken. The parameters of our calculations correspond closely to those which characterize ${\mathrm{Na}}_2$ lasers, ${\mathrm{CO}}_2$ lasers, and Nd-doped yttrium aluminum garnet lasers.

We analyze the simplest dynamical transverse patterns which appear in ${\mathrm{Na}}_2$ and ${\mathrm{CO}}_2$ lasers. The experimental values of the control parameters correspond closely to those considered in the theoretical study reported in the companion paper [Brambilla et al., preceding paper, Phys. Rev. A 49, 1427 (1994)]. We perform a systematic comparsion between theoretical predictions and experimental observations.

Electric charges carried by positive and negative muons in units of an electric charge, ${\mathit{e}}_{\mathrm{\mu }}^{+}$/e=1±1×${10}^{\mathrm{-}7}$ and ${\mathit{e}}_{\mathrm{\mu }}^{\mathrm{-}}$/e=-1±2×${10}^{\mathrm{-}5}$, are derived from the theoretical and experimental values of the ground-state hyperfine-structure intervals Δν in muonium and muonic helium atoms as tests of electric-charge quantization for muons. These results also provide a test of CPT symmetry for positive and negative muon charges, with an accuracy of 2 parts in ${10}^5$. Further improvements can be made from more precise theoretical and experimental values for Δν in muonium and muonic helium atoms with the approach described in this paper.