The positive P representation is a very successful tool in quantum optics. However, the usual assumption of negligible boundary terms in the time-evolution equations is not always valid. We explore the range of validity of the time-evolution equations both analytically and by numerical investigation of a number of specific examples. We present practical ways of verifying the validity of the use of the positive P representation and find that the standard time-evolution equation can become invalid when nonlinear terms (at unit photon number) are large relative to the damping rate. This is very much larger than is normally the case in nonlinear optics, except possibly near resonances. We are able to show that when the positive P representation is invalid, the boundary terms, normally neglected in an integration by parts, become non-negligible. When numerical simulations are carried out using the positive P representation, specific checks given in this paper should be carried out to verify the compactness of the distribution. In conclusion, we find that (apart from special cases) this technique of quantum time evolution is typically asymptotically valid in the limit of small nonlinearity, rather than exact.

In a microlaser experiment performed by An et al. with collaborators [Phys. Rev. Lett. 73, 3375 (1994)] an atomic beam interacts with a microcavity field under such conditions that the average number of atoms in the cavity is less than unity. However, due to the random statistics of atoms in the beam, the probability of two atoms being in the cavity simultaneously in time is not negligible. This must lead to collective two-atom effects that are not included in the standard microlaser model. We have developed a theory that incorporates such collective effects. This theory allows a better understanding of the observed experimental results and predicts some different features of the microlaser.

It is shown that because of the radiation pressure a Schrödinger cat state can be generated in a resonator with an oscillating wall. The optomechanical control of quantum macroscopic coherence and its detection is taken into account by introducing new cat states. The effects due to the environmental couplings with this nonlinear system are considered by developing an operator perturbation procedure to solve the master equation for the field mode density operator.

We examine the generalized squeezed states defined as eigenstates of a linear combination of the lowering and raising operators ${\mathrm{a}}^2$ and (${\mathrm{a}}^{\mathrm{†}}$${)}^2$, respectively. This approach is entirely equivalent to the minimum-uncertainty method applied to the amplitude-squared operators. We solve the eigenvalue equation in Glauber's coherent-state representation and find two independent solutions. Their Fock-state expansions, one containing only even and the other only odd number states, reveal a strong nonclassical character. We show that the calculation of the mean photon number is sufficient to obtain the expectation values of interest. Consequently, photon statistics is investigated in both cases by using the generating function of the photon-number distribution. We find the conditions under which the second-order squeezed states display photon antibunching and quadrature squeezing. Also discussed is the preservation of their amplitude-squared squeezing by linear amplification at gains exceeding 2. Analytically, our results are simple formulas in terms of Kummer and Gauss hypergeometric functions that allow straightforward numerical calculations.

We analyze the influence of system-size effects on the quantum properties of a degenerate parametric oscillator below, at, and above the classical threshold using a Green's-function approach. The many-body technique permits a systematic analysis of finite-size corrections to standard linearization results. In particular we study a ``semiquantum'' limit, where even above threshold only few photons are in the subharmonic mode while the pump mode is highly populated and behaves quasiclassically. Substantial deviations from classical and linearization predictions are found. We show that the depletion of the pump mode is rather strong and the threshold of parametric oscillation is shifted to higher pump strength, when the subharmonic system is small.

The rate-equation approximation is one of the most fundamental and universally employed simplifications in laser analyses. The accuracy and regions of applicability of this approximation are explored in comparisons with more rigorous semiclassical models. Higher-order rate-equation approximations are also developed, and these improved models can yield much better accuracy than conventional rate equations with little added complexity. The modified adiabatic elimination methods reported here would also be useful in reducing the mathematical models governing other physical systems.

The object of this study is to quantitatively elucidate the laser-power dependence in transient degenerate four-wave mixing (DFWM) with an emphasis on the high laser-pump intensity region. We discuss our investigation on the power dependence of transient DFWM by taking gas-phase iodine (${\mathrm{I}}_2$) molecules as a testing example. The distinct physical feature is that in the high-power laser pump, where both laser-pulse duration and the inverse of pump rate are much shorter than the molecular population relaxation time, the steady-state DFWM theory of Abrams and Lind [Optical Phase Conjugation, edited by R. A. Fisher (Academic, New York, 1983), Chap. 8, pp. 211–284; Opt. Lett. 2, 94 (1978); 3, 205 (1978)] is not appropriate. The prediction by the steady-state theory has shown the DFWM to decrease with increasing laser-pump intensity as a function of 1/${\mathrm{I}}_{\mathrm{laser}}$, which disagrees with the saturation behavior observed in the experiment. To elucidate the dependence of DFWM on the laser pump intensity, a non-steady-state extension of the nonperturbative theory of Abrams and Lind is required. The non-steady-state theoretical result will be shown to be in good agreement with the experimental power dependence at resonance transient DFWM especially in the high-power pump region.

A two-dimensional model for the self-pumped phase conjugation in photorefractive crystals is presented. Numerical simulations of the beam path for beam fanning and the self-pumped phase conjugation within the crystals show good agreement with the experimental observations. We numerically study the dependence of the self-pumped phase conjugation reflectivity and spatial fidelity on the incident angle, the position of the incident beam upon the input face, and the input wavelength, which are in good agreement with the published and our experimental results.

A generalization of the stochastic wave-function method to open quantum systems under the influence of strong laser fields is derived. To this end, quantum-statistical ensembles of reduced state vectors are represented in terms of probability distributions on the projective Hilbert space of the open system. By employing the Floquet expansion of the quantum time evolution, this representation is shown to lead in the Markov approximation to a piecewise deterministic stochastic process for the reduced wave function. The realizations of the stochastic process consist of smooth deterministic parts that are interrupted by sudden jumps. The jump operators are the eigenoperators of the Floquet Hamiltonian and describe instantaneous transitions between Floquet states. Two examples are given that serve to illustrate the method and the stochastic simulation technique of the process.

We discuss a balanced homodyne detection scheme with imperfect detectors in the framework of the operational approach to quantum measurement. We show that a realistic homodyne measurement is described by a family of operational observables that depends on the experimental setup, rather than a single field quadrature operator. We find an explicit form of this family, which fully characterizes the experimental device and is independent of a specific state of the measured system. We also derive operational homodyne observables for the setup with a random phase, which has been recently applied in an ultrafast measurement of the photon statistics of a pulsed diode laser. The operational formulation directly gives the relation between the detected noise and the intrinsic quantum fluctuations of the measured field. We demonstrate this with two examples: the operational uncertainty relation for the field quadratures, and the homodyne detection of suppressed fluctuations in photon statistics.

Coupled-cavity mode-locked lasers, useful as they may be, can have a tendency to display dynamic instabilities; the mechanisms for this phenomenon are poorly understood. We show here by analytic means, supplemented with numerics, how these instabilities arise from the coupling of nonlinear resonators and how the thresholds for instability depend strongly on the topology of the laser. Four different topologies are considered, the Michelson, the Fabry-Pérot, and two further configurations. The results of this comprehensive theory identify the most stable and the most unstable configuration and explain empirical findings of several authors.

An analytical solution of the photoconductive material equations for dynamic holographic gratings of arbitrary contrast has been obtained. A method of measuring high-contrast correlation functions has been suggested and tested experimentally. Good agreement with the analytical expression for the current at high contrast and experiment is found. An interesting effect of the holographic transversal photocurrent is predicted and a number of high-contrast-related topics are discussed.

We report the experimental investigation of spectral hole burning and four-wave mixing at the interface of glass and a dense cesium vapor using two tunable diode lasers in a pump-probe experiment. Narrow spectral features were observed in the center of the strongly self-broadened ${\mathrm{D}}_2$ line at Cs number density from 9×${10}^{15}$ to 2.8×${10}^{16}$${\mathrm{ncm}}^{\mathrm{-}3}$. The origin of the resonances is associated with the coherent scattering of laser beams at a self-induced population grating, and their spectral widths reflect the relaxation rate of the population difference. A simple asymptotic expression is used to fit the spectral line shapes and to infer a population relaxation time of 3.7(2) ns, which is almost an order of magnitude shorter than natural lifetime of the excited state.

We investigate the interference of Fock state photons in terms of the quantum trajectory theory. We performed a fast simulation of the experiment with a million photons initially prepared. We show that the physics of the phenomenon is transparently understood through an analytic approach within the quantum trajectory formalism without actually going into the numerical study. We find that the visibility of the interference pattern is essentially given by ${\mathrm{V}}_{\mathrm{k}}$=k/(k+1) at the kth photodetection. We review the phenomenon in connection with the historical discussions about interference between independent light sources.

A quantum theory of nearly degenerate backward four-wave mixing in a two-level atomic system is developed. The theory is used to calculate the quantum noise produced by a phase-conjugate mirror based on this system. The results indicate that in the case of pure radiative broadening the ideal quantum-noise limit is reached for relatively small pump-wave strengths and for relatively large probe-pump and pump-resonance detunings, so that the phase-conjugate reflectivity is far from its maximum value. Conversely, in the collisionally broadened case, operation closest to the quantum-noise limit occurs near the point of maximum reflectivity.

The quantum state of a one-dimensional molecular vibration can be reconstructed via molecular emission tomography [T. J. Dunn, I. A. Walmsley, and S. Mukamel, Phys. Rev. Lett. 74, 884 (1995)] even in the case of anharmonic potentials. We assume a Morse-oscillator model for the vibration and calculate analytically the irregular wave functions. These mathematical objects serve as ingredients of the reconstruction procedure [U. Leonhardt and M. G. Raymer, Phys. Rev. Lett. 76, 1989 (1996)]. Additionally, we show why the observation time until the revival of order is sufficient for an accurate state determination.

Pattern selection in wide aperture lasers is provided by active sources of traveling waves. Finite absorbing transverse boundaries select near-field lasing patterns from a one-parameter continuous family of allowed modes. The selected pattern on the boundary invades the interior consuming any spiral waves that are formed in this region. As a result, only simple stationary patterns are established in nonstiff lasers.

We show that the coherence time and the pulse envelope of ultrashort fluorescence can be measured with two-photon interference. We have performed these measurements in a solution of Nile Blue in N,N-dimethylaniline in the femtosecond regime. The coherence time and the envelope contribute two components to a dip in the coincidence count rate. We have verified that these components can be measured separately at will. This technique provides the means to measure the pulse envelope of ultrashort pulses over a wide range of wavelengths and intensities.

A scheme for generating Schrödinger-cat-like states of a single-mode optical field by means of conditional measurement is proposed. Feeding a squeezed vacuum into a beam splitter and counting the photons in one of the output channels, the conditional states in the other output channel exhibit a number of properties that are very similar to those of superpositions of two coherent states with opposite phases. We present analytical and numerical results for the photon-number and quadrature-component distributions of the conditional states and their Wigner and Husimi functions. Further, we discuss the effect of realistic photocounting on the states.

We conjecture that optical coherences, i.e., quantum-mechanical coherences between states separated by Bohr frequencies in the optical regime, do not exist in optics experiments. We claim the exact vanishing of optical field amplitudes and atomic dipole expectation values, and we discuss the seemingly contradictory success of assigning finite values to such quantities in theoretical calculations. We show that our conjecture is not at variance with the observed interference between different light sources. The connection to the concept of spontaneous symmetry breaking and the identification of entangled states as pointer basis states is discussed.