Noise that can be attributed to vacuum fluctuations, usually referred to as quantum noise, is examined. It is shown that vacuum fluctuations of a single uncoupled mode do not constitute noise, in the sense of a random process, but the superposition of the fluctuations of a large number of modes does constitute, formally, noise. The effect of vacuum fluctuations of the free-space radiation field on a harmonic oscillator, a nondegenerate parametric amplifier, and a degenerate parametric amplifier, all driven by a prescribed sinusoidal field, is compared with the effect of classical noise. It is found that the coordinates of all systems respond in a formally similar manner to both vacuum fluctuations and classical noise. However, the resonance fluorescence spectrum—the evidence of ‘‘detection’’—is completely different for the two kinds of noise. The spectrum of the harmonic oscillator does not exhibit noise in response to vacuum fluctuations, but does so in response to classical noise. The spectra of the two types of parametric amplifiers do exhibit noise in response to vacuum fluctuations, but this noise differs from that in the classical case. An explanation for the difference is offered, based on the fact that the quantum fluctuations cannot do work, but can noise-modulate power from an outside source, which, for the parametric amplifiers, is the pump. In the analysis of noise from the degenerate parametric amplifier, it is shown that squeezed noise, viewed as an oscillation of the dispersion with a sufficiently low minimum, is generated in the same manner in the case of classical noise as in the case of quantum noise, and is due to phase conjugation.

We calculate the absorption spectrum of a weak probe interacting with a Λ-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.

In this paper, we study the generation of pure states in a two-photon micromaser with finite detuning of the intermediate atomic level. This study was done via the temporal evolution of the discrete master equation. We show that it is possible to generate the ideal squeezed vacuum for a broad range of detunings in a lossless cavity and away from the trapping condition. We also consider the effect of cavity losses.

Multiphoton detachment of ${\mathrm{H}}^{\mathrm{-}}$ is considered. An accurate one-electron model, which reproduces precisely the known ${\mathrm{H}}^{\mathrm{-}}$ detachment energy and the low-energy e-H(1s) elastic-scattering phase shifts, is developed. Generalized cross sections, based on lowest-nonvanishing-order perturbation theory, are evaluated by an accurate and efficient numerical algorithm for the solution of the associated set of inhomogeneous differential equations. Two- to eight-photon detachment cross sections are determined and compared with a recent one-electron model and two-electron ab initio calculations. It appears that the present study provides consistent results with an accuracy for higher-order (n>3) photon-detachment cross sections comparable to that of lower orders (n=2,3). Average detachment rates for linearly polarized light are calculated and compared with recent experimental measurements. It is found that, for higher-order photon detachment, the rates for circular polarization are small in comparison with the rates for linear polarization.

We describe a two-electron ‘‘atom’’ in one space dimension. This one-dimensional system is treated fully quantum mechanically and with full electron correlation. Its bare eigenstates and eigenenergies are determined numerically by solving Schrödinger’s equation on a spatial grid. When the electron-electron interaction (of soft-core long-range Coulombic form) is taken equal in strength and opposite in sign to the electron-proton interactions, this atom is found to have only one bound state, and is similar in other ways to a negative ion. We give a Z-correlation diagram, showing the relation of the system’s energy spectrum to those of its isoelectronic partners, which are one-dimensional analogs of He, ${\mathrm{Li}}^{+}$, etc. We also calculate a large number of fully correlated two-electron time-dependent wave functions for the system under excitation by a laser field, and exhibit a number of results, including one-photon and multiphoton photodetachment rates, ac Stark shifted threshold closings, photoelectron spectra, and above-threshold detachment spectra, single-electron and double-electron ionization probabilities, and light-scattering spectra.

We report an application of the prepulse technique which uses a low-intensity prepulse before the main optical drive pulse to prepare the plasma prior to lasing in low-Z, Ne-like ions. Ne-like x-ray lasers are now available over a previously inaccessible range of wavelengths. As an illustration of this technique we report an observation of lasing in ${\mathrm{Cr}}^{14+}$ and ${\mathrm{Fe}}^{16+}$ on the Ne-like J=0→1, 3p→3s transitions at 285 and 255 Å as well as gain measurements for ${\mathrm{Ti}}^{12+}$.

A three-level cascade atomic system is considered where atomic coherence can be achieved either by applying an intense pump field or initially preparing the atoms in a coherent superposition of the states. It is predicted that the system, under certain conditions, exhibits almost perfect squeezing outside the cavity. By using the steady-state Q solution it is also shown that certain higher-order squeezing can also be achieved inside the cavity, under a suitable choice of different parameters.

Marginal properties of arbitrary s-ordered quasiprobability distribution fucntions are investigated. The positivity of marginal distributions for all quasiprobabilities, interpolating between the Wigner function and the Q representation of the density operator (s≤0), is proven. We also show that, on the contrary, marginal distributions of the remaining quasiprobabilities, interpolating between the Wigner function and the P representation (s>0), can take on negative values. General formulas for the marginal distributions are given, and their relations to the actual quantum-mechanical probability distributions for position and momentum are established. Our results provide an interesting generalization of some recent results concerning marginal properties of the P representation [G. S. Agarwal, Opt. Commun. 95, 109 (1993)].

We introduce a unitary operator representing the exponential of the phase difference between two modes of the electromagnetic field. The eigenvalue spectrum has a discrete character that is fully analyzed. We relate this operator with a suitable polar decomposition of the Stokes parameters of the field, obtaining a natural classical limit. The cases of weakly and highly excited states are considered, discussing to what extent it is possible to talk about the phase for a single-mode field. This operator is applied to some interesting two-mode fields.

We present experimental studies of high-order harmonic generation in the rare gases performed with a short-pulse titanium sapphire laser operating at 794 nm in the ${10}^{14–}$${10}^{15}$-W/${\mathrm{cm}}^2$ range. The harmonic yields generated in neon and in argon are studied for all orders as a function of the laser intensity. They vary first rather steeply, in the cutoff region, then much more slowly in the plateau region, and, finally, they saturate when the medium gets ionized. The dependence of the high-order harmonic cutoff with the laser intensity in neon and argon is found to be lower than that predicted in single-atom theories. We observe high-order harmonics in argon and xenon (up to the 65th and 45th, respectively) at ${10}^{15}$ W/${\mathrm{cm}}^2$, which we attribute to harmonic generation from ions. We also show how the harmonic and fundamental spectra get blueshifted when the medium becomes ionized.

A systematic theoretical and experimental study of focusing femtosecond light pulses by single lenses is presented. By evaluation of the diffraction integral the interplay of spherical and chromatic aberration is shown to determine the temporal as well as the spatial intensity distribution in the focal region of a lens. Conditions are derived under which the effect of spherical aberration dominates. Here a temporally unbroadened, in-focus pulse occurs while the spatial distribution is that expected from an annular lens aperture. If chromatic aberration is the major aberration, the in-focus pulses are considerably broadened. Both effects could clearly be measured with 100-fs pulses using a modified Michelson interferometer. In an intermediate parameter range both chromatic and spherical aberration contribute to the pulse broadening and to the spatial intensity pattern in a given plane in the focal region. From Fresnel diffraction we expect a weak-intensity distribution to precede the in-focus pulse on the axis. Another weak intensity peak is produced by the pulse traveling on axis. By measuring its separation from the main pulse in the marginal focal plane one can estiamte the aberration parameters.

In experiments on induced coherence without induced emission performed under conditions of minor losses and good alignment, the measured visibility has been well below the predicted value of 1. The quantitative understanding of this visibility is crucial in the interpretation of this phenomenon that has no classical counterpart. An explanation for the reduced visibility is proposed here that involves the ratio of the coherence area of light emitted from a crystal 1 to the source area on a crystal 2, together with the fraction of spatially distinguishable light occurring immediately after a crystal 2.

A model describing three boson fields with the decay of Rayleigh mode into the Stokes and vibration (phonon) modes is examined. The problem of exact eigenvalues and eigenstates is reduced to the calculation of zeros of new orthogonal polynomials defined in terms of difference and differential equations. The instability of the spectrum of eigenvalues is established. The quantum-statistical properties are investigated for various initial conditions. The possibility of using the correlation Raman spectroscopy to measure the quantum-statistical properties of the vibration mode is discussed.

We have made direct observations of microwave multiphoton Rabi oscillations between two Rydberg states in potassium in the strong-radiation-field regime, where a perturbative treatment of the atom-field interaction becomes invalid. The results of measurements of the Rabi oscillation frequency are presented and compared with results calculated using Floquet theory, which predicts a very different field dependence for the Rabi frequency than is typical in the perturbation-theory limit.

The light-beam scattering at a symmetric dielectrical waveguide formed by two interfaces between three nonlinear focusing media is considered analytically and numerically. The problem of beam transmission and reflection is effectively analyzed in the framework of the so-called equivalent-particle theory. It is shown also that the beam scattering may be accompanied by a strong emission of radiation which is not taken into account by the equivalent-particle approximation. Radiative losses of the scattering beam are calculated, and the applicability limits of the equivalent-particle approach are discussed by making a comparison between numerical and analytical results. In particular, it is shown that the incident beam may be captured by the thin-film waveguide to form a surface wave, due to radiation-induced losses.

Using a hybrid approach, based on the recursion relations for shape-invariant potentials developed by Das and Huang [Phys. Rev. D 41, 3241 (1990)] and a time-dependent transformation of variables, we derive the propagator for a radial oscillator. Although this is not a new result, we explicitly show that time-dependent transformations are very beneficial even within the context of time-independent Hamiltonians in quantum mechanics.

The retarded van der Waals forces between neutral molecules in their ground states is obtained by a conceptually simple route. Vacuum fluctuations of the electromagnetic field induce a dipole moment in each molecule and these induced moments interact via the retarded potential that is appropriate for resonant coupling. The dispersion potential is the sum over the field modes of the product of this potential and the second-order spatial correlation function of the electromagnetic field. This gives the familiar Casimir-Polder potential an an integral over imaginary frequencies. An extension to obtain the interaction energy between one molecule in its ground state and another in an excited state is outlined.

A recently derived Laplace-transform method [R. A. Swainson and G. W. F. Drake, J. Phys. A 24, 79 (1991)] is adapted for the N-dimensional Schrödinger equation. Specific results are presented for the recurrence relations of the radial wave functions for (i) an isotropic harmonic oscillator and (ii) the hydrogen atom. The dimensionality of the problem is seen to enter into these relations in such a way that one can immediately verify the corresponding three-dimensional results.

Starting from the known unimodal character of the momentum density γ(p) of numerous ground-state atoms, two general inequalities relating the location of the maximum ${\mathit{p}}_{\max }$, the value at the origin γ(0), and the momentum expectation values 〈${\mathit{p}}^{\mathrm{\alpha }}$〉, α>-3, are found. As a limiting case, an upper bound to ${\mathit{p}}_{\max }$ is given in terms of the number of electrons N and the mean logarithmic momentum 〈lnp〉. Finally, the quality of these bounds is numerically analyzed.

Lifetimes of rovibronic levels of d ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$ states in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ have been measured by using the electron-impact-excitation and delayed-coincidence method. Observed differences between the lifetimes of ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{\mathrm{e}}{}_{}{}^{}$(v,N) and ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{\mathrm{f}}{}_{}{}^{}$(v,N) sublevels in ${\mathrm{H}}_2$ were the direct result of perturbations arising from interactions between d ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{\mathrm{f}}{}_{}{}^{}$(v,N) and ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$(v’,N) levels. Different lifetime variation with N of the d ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{\mathrm{f}}{}_{}{}^{}$(v,N) states in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ implied that several e ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ levels were predissociated in ${\mathrm{H}}_2$ but not in ${\mathrm{D}}_2$.