An all-order multiphoton resonant theory for above-threshold ionization is presented within the resolvent formalism. An analytical expression displaying all the contributions to the electron yield is discussed. The theory is applied to the calculation of photoelectron energy spectra for ionization of H by picosecond and subpicosecond pulses of linearly polarized light at 608 nm, with laser intensities in the range ${10}^{13}$–${10}^{14}$ W/${\mathrm{cm}}^2$. The role of intensity, interaction time, and transition couplings, in the resonantly enhanced electron yield coming from each (nl) intermediate state, is discussed. The modifications which affect the shape of the spectrum as the laser peak intensity increases are described in great detail. An inversion of the relative amplitudes of the resonant structures is observed. This effect is attributed to the relative dimensions of the effective interaction volumes in which the field reaches sufficient intensities to give rise to the resonances. Our results reproduce the main features of recently measured spectra [H. Rottke et al., Phys. Rev. Lett. 64, 404 (1990)].

In this paper, we present a theoretical study of the quantum-nondemolition properties of a scheme that uses a Kerr medium in a double-ended cavity with both the signal and the probe inputs being coherent fields incident from the two sides. We find that with a suitable choice of parameters this system satisfies almost perfectly the criteria for quantum-nondemolition measurements.

Based on the standard system-heat-bath model, we have formulated a theory of the non-Markovian master equation for linear and nonlinear systems for a correlation time that is short but finite. We have applied the theory to linear systems, such as harmonic oscillators and two-level atoms and calculated the band-shape functions for transient optical absorption in the pump-probe experiments. The significant interplay of nonlinearity and non-Markovian decay has been illustrated by another application of the theory to a Morse oscillator. The theory is valid for arbitrary nonlinearity and finite temperatures but within the weak-coupling limit and has been derived without ad hoc implementation of a phenomenological memory function.

We have studied the time evolution of the phase operators of the radiation field in the system containing a ssV-type three-level atom interacting with the bimodal field by means of the phase formalism given by Pegg and Barnett [J. Mod. Opt. 36, 7 (1989); Phys. Rev. A 39, 1665 (1989)]. That the atomic coherent trapping will happen in an appropriate initial state of the system has also been verified.

We have studied the quantum-statistical properties of superfluorescence (SF) and amplified spontaneous emission (ASE) for dense media (media of densities corresponding to many atoms, on the average, within a cubic resonance wavelength). We use the Langevin equations of motion, obtained from a fully quantized model that takes into account induced near dipole-dipole interactions associated with dense media, together with the coupled Maxwell equation, to formulate a stochastic calculation ensemble. Quantum Monte Carlo methods are used in conjunction with the stochastic model, to conduct a statistical analysis of phase waves for this system. Results are presented for the phase-wave density, delay time, and peak-intensity fluctuations. The transition from SF to ASE is treated using the stochastic model.

We have studied theoretically the dependence of the Raman-enhanced nondegenerate four-wave-mixing (RENFWM) spectrum on the relative time delay between two pump beams τ when a thermal effect exists in the sample. Using the chaotic model for the incident laser beams, we give the conditions that the thermal background can be eliminated completely when the relative time delay is much longer than the laser coherence time. In this limit, the theoretical RENFWM spectra show the normal asymmetry due to the interference between the Raman-resonant term and the nonresonant background originating solely from the molecular-reorientational grating. We then turn our attention to the dependence of the RENFWM signal intensity on the relative time delay when the laser frequencies are fixed. Our results indicate that RENFWM is asymmetric about τ=0 and the maximum of the RENFWM signal does not occur at τ=0. When the beating frequency between the pump beam and the probe beam is off resonant from the Raman mode, the RENFWM signal exhibits damping oscillation as the time delay increases. We also show that the temporal behavior of the RENFWM signal is drastically different if the laser sources are described by a phase-diffusion model. The different roles of the phase fluctuation and the amplitude fluctuation can be understood in the time domain.

We present a theory of the homogeneously broadened laser that is based on the simple boundary conditions that govern the connection of intracavity traveling fields and the leaking vacuum field at the cavity mirrors. The approach is uniformly valid for arbitrary output-mirror transmissions. We compute the intrinsic linewidth of the laser both below and above threshold and for arbitrary mirror outcoupling. In the limit of complete output-mirror transmission, for which any semblance of the cavity to a lasing cavity is completely untenable and the laser is severely below threshold, we show that the laser linewidth reduces to the natural linewidth of spontaneous emission by atoms in free space. Above threshold, in contrast with most previously obtained results, the fundamental linewidth exhibits a power-independent contribution that arises from gain saturation that is spatially nonuniform.

A theory of two-mode phase-sensitive amplification by a three-level atomic system in the cascade configuration is presented, within the framework of the theory of multiwave mixing. Two photons of a strong external pump field induce coherence between the top and bottom levels. It is shown that both quadratures of the field modes acquire unequal gain and added noise. For large values of the dimensionless pump intensity, with a particular choice of its phase, and zero side-mode detuning, the system behaves as a nondegenerate parametric amplifier.

We introduce the inverse of the harmonic-oscillator creation and annihilation operators by their actions on the number states. We then show that three of the two-photon annihilation operators, a^ ${}_{}{}^{\mathrm{°}\mathrm{-}1}{}_{}{}^{}$a^, a^a^ ${}_{}{}^{\mathrm{°}\mathrm{-}1}{}_{}{}^{}$, and a^ ${}_{}{}^2{}_{}{}^{}$, possess eigenstates that are analogous to the often-used coherent and squeezed states. A family of the eigenstates of the operator a^ ${}_{}{}^{\mathrm{°}\mathrm{-}1}{}_{}{}^{}$a^ is the customary squeezed vacuum S(σ)‖0〉 while another family of the eigenstates of a^a^ ${}_{}{}^{\mathrm{°}\mathrm{-}1}{}_{}{}^{}$ is the state S(σ)‖n=1〉. We find some interesting properties related to squeezing, bunching, and antibunching exhibited by these states. An alternative method of summing some series by using these states is also considered. It is hoped that these states will find applications in quantum optics and quantum mechanics in general.

The generalized nonlinear Schrödinger equation governs wave propagation in nonlinear dispersive media by including the effects of group-velocity dispersion, self-phase-modulation, stimulated Raman scattering, and self-steepening. This equation is shown to have solitary-wave solutions that correspond to an optical shock front moving at the group velocity. The properties of such kink-type solitary waves are discussed.

We present a scheme for experimentally observing the quantum Zeno effect using the quantum-nondemolition measurement recently proposed by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)]. The Zeno effect refers to the freezing of the (unitary) free dynamics of a system by rapid measurements. We generalize the Zeno effect to be any change in the survival probability of an initial state induced by very rapid measurements, when such measurements are the dominant source of fluctuations in the system. We derive a master equation for the evolution of a cavity mode when the photon number is monitored by this method. This equation describes a phase-diffusion process. We propose that this measurement scheme be used to monitor the exchange of a single photon between the cavity and a single Rydberg atom. We show that for very rapid monitoring the free oscillation of the atomic inversion is disrupted and the atom can be trapped close to the initial excited state. This is the quantum Zeno effect.

An investigation is carried out of higher-order squeezing in a class of three- and four-wave mixing processes that can be modeled by a master equation. In (2N)th-order squeezing, as defined by Hong and Mandel, the Nth-power of the variance of a field quadrature falls below the value it would have for a coherent state. Higher-order squeezing is of interest because (i) it occurs in many processes in which ordinary (or second-order) squeezing occurs, and (ii) it allows a much larger fractional noise reduction to be achieved than ordinary squeezing. The master equation we use models a degenerate three- or four-wave process and takes into account the losses in the signal mode. We convert the master equation into a Fokker-Planck equation for the Wigner distribution function and solve it for a wide range of initial signal states (including thermal, coherent, Fock states, and mixtures of these). Results are presented for the enhancement of fourth- and sixth-order squeezing over second-order squeezing. Differences in the character of higher-order squeezing for different input states are pointed out. The role of losses in limiting the amount of achievable squeezing in all orders is especially investigated.

The dynamics of a nonlinear resonant tapered coupler is analyzed by using coupled-mode equations. The constituent waveguides are made of a linear host material doped with resonant impurities. Such a system allows a mechanism for all-optical switching. It is shown that nonlinear exchange between coupled waveguides originates from the group-velocity dependence on the propagating pulse power and/or area. The transmitted signal is always a multiple of the self-induced-transparency fundamental soliton. The dynamics of the pulse tuned or detuned from the resonance and with the inclusion of the material relaxation terms is discussed. In the last section the problem of soliton collision in the coupling region is considered; in this case an initial interpulse phase difference may determine a power-dependent outport switching.

We report the observation of high-gain lasing in laser-heated exploding-foil Ag targets at pump irradiances ≥6×${10}^{14}$ W/${\mathrm{cm}}^2$. The measured gain coefficients on the dominant Ne-like J=2→1 transitions are determined to be 9.4±1.5 ${\mathrm{cm}}^{\mathrm{-}1}$ for (2${\mathit{p}}_{3/2}$)3${\mathit{p}}_{3/2}$→(2${\mathit{p}}_{3/2}$)3s at 9.9365 nm and 6.$4_{\mathrm{-}1.5}^{+2.0\mathrm{}}$ ${\mathrm{cm}}^{\mathrm{-}1}$ for (2${\mathit{p}}_{1/2}$)3${\mathit{p}}_{3/2}$→(2${\mathit{p}}_{1/2}$)3s at 10.0377 nm. These are the highest gain coefficients yet observed to our knowledge for any short-wavelength laser. Gain is observed on three other Ne-like lines including a J=0→1 transition at 8.1563 nm, the shortest wavelength yet observed to our knowledge for a Ne-like x-ray laser.

Experimental investigations of double-pass amplification of an x-ray laser in Ne-like germanium were carried out at the Shengguang laser facility (of the High Power Laser and Physics Laboratory, Shanghai, China). In these experiments a molybdenum-silicon multilayer mirror was used at normal incidence, and a flat-field grating spectrograph was used to measure the intensities of the laser lines. We observed double-pass emission intensity in Ne-like Ge at 23.2 and 23.6 nm that was five times larger than that of the single-pass amplified spontaneous emission. The damage of the multilayer mirror irradiated by laser plasma was measured simultaneously, the lifetime of Mo-Si multilayer mirror was about 440–700 ps. In addition, we measured the beam divergence of the lasing beam; the results showed that the beam divergence in the vertical direction was about 22 mrad and in the horizontal direction about 12 mrad. Also, the beam optics of the double-pass signal was observed.

Within the context of the Maxwell Garnett model, we calculate the nonlinear susceptibility of a composite optical material comprised of spherical inclusion particles contained within a host material. We allow both constituents to respond nonlinearly and to exhibit linear absorption. Our treatment takes complete account of the tensor nature of the nonlinear interaction, under the assumption that each constituent is isotropic and that the composite is macroscopically isotropic. The theory predicts that there are circumstances under which the composite material can possess a nonlinear susceptibility that is larger than that of either of its constituents. It also predicts that, for the case in which the host material responds nonlinearly, the tensor properties of the nonlinear susceptibility of the composite can be very different from those of the host material.

The application to micromasers of a recently proposed generalized master equation, which takes into account the statistics of the pumping mechanism, may lead to incorrect results for non-Poissonian pumping, due to the violation of hypotheses regarding coarse graining and the independent action of gain and dissipation.

We study the classical theory of the response of atoms to ultrastrong laser pulses. We argue that the stabilization of atoms in a strong laser field through bound states in a Kramers-Henneberger potential has a classical interpretation. We present results of numerical simulations based on a phase-space-averaging method for a one-dimensional smoothed potential, which agree very well with the results of quantum theory. In a three-dimensional Coulomb potential, classical simulations hardly allow for stabilization, in contrast to recently obtained quantum-mechanical results. We identify physical reasons for this discrepancy with the effect of smoothing the potential singularity. We stress the relevance of our studies in the context of the correspondence principle.

An analytic expression for the inversion and intensity of the Jaynes-Cummings model with cavity damping is derived in the rotating-wave approximation for vanishing thermal photon numbers. Using the s-parametrized quasiprobability distributions of Cahill and Glauber [Phys. Rev. 177, 1882 (1969)], the equation of motion for the density operator is transformed into c-number equations for the quasiprobability functions. By a suitable expansion into a Fourier series and into Laguerre functions, we obtain ordinary tridiagonal coupled differential equations for the expansion coefficients. By an appropriate choice of a scaling parameter and by a proper elimination procedure, it is shown that the coefficients that determine the inversion and the mean intensity are only coupled to coefficients with the same index and to coefficients with the next upper index. Because of this coupling the Laplace transform can be given analytically. Furthermore, it is shown that the eigenvalues and eigenvectors can also be calculated, thus leading to an analytic solution for the inversion of the Jaynes-Cummings model.

The eigenvalue moment method (EMM) is a precise technique for generating converging lower and upper bounds to the low-lying eigenenergies of singular quantum Hamiltonians. We apply it to the quartic anharmonic double-well oscillator problem, ${\mathit{P}}^2$-${\mathit{Z}}^2$${\mathit{x}}^2$+${\mathit{x}}^4$, recently studied by Saavedra and Buendia [Phys. Rev. A 42, 5073 (1990)]. In addition, we introduce important algorithmic modifications to the conventional EMM formulation, leading to more efficient applications.