The coupled ion pairs were modeled by two coupled two-level systems. The resulting Bloch equations were derived by the density-matrix formalism. They were solved numerically for identical ions and for slightly detuned ions with identical wave functions as a first approximation to the problem of inhomogeneous line broadening in solids. The following results were found: (1) intrinsic optical bistability as a function of the applied laser field; (2) regions of stability, instability, and multistability for different detunings and couplings of the ions at different laser fields; (3) asymmetric shapes of the absorption lines with unstable regions; and (4) suppression of the photon echo due to the nonlinear chaotic dynamics of the coupled ions. Experimental evidence is given which supports the computer calculations. © 1996 The American Physical Society.

We further develop the theory of the superradiant laser by allowing for submaximal atomic collectivity and spontaneous emission. In the absence of spontaneous emission we obtain a set of stationary solutions for different degrees of atomic cooperativity and investigate their fluctuation properties and interrelations with respect to the underlying U(3) symmetry. We use this set of solutions to discuss the breaking of U(3) by spontaneous emission. © 1996 The American Physical Society.

A generalized Fokker-Planck equation is used to study the problem of single-atom optical bistability in the good-cavity limit. The effects of quantum fluctuations are investigated by linearizing fluctuations around the steady-state value. It is shown that in the good-cavity limit, quantum fluctuations are relatively small, and hence there exist both absorptive and dispersive single-atom bistability. By comparing our single-atom Fokker-Planck equation with the N-atom Fokker-Planck equation, we find that in the good-cavity limit, these two different Fokker-Planck equations reduce to identical equations. We therefore come to an important conclusion that the results obtained from the many-atom Fokker-Planck equation in the good-cavity limit are also valid for a single atom. © 1996 The American Physical Society.

Photon burst detection is used to count ${\mathrm{Mg}}^{+}$ ions in a 500-eV beam with high optical isotopic selectivity. Background rates of less than 1 count in 2 h have been achieved corresponding to an optical abundance sensitivity of 2×${10}^{\mathrm{-}8}$. © 1996 The American Physical Society.

Coexistence of periodic states with antiphase periodic states or with grouping states, which consist of qualitatively different motions, is predicted in the model of globally coupled modulated multimode lasers. It is shown that the injection seeding can switch the system from periodic states to antiphase periodic states or to grouping states, which are composed of a large-amplitude periodic (chaotic) antiphase spiking mode group and a small-amplitude periodic (chaotic) mode group. A switching process between different states is investigated and the inverse power-law relation for seeding assignment is demonstrated. A class of synchronized chaos, in which two modes exhibit a small-amplitude synchronized chaotic motion while other modes show a large-amplitude antiphase chaotic motion, is found in the grouping state. Characterization of grouping phenomena is provided by Lyapunov spectrum calculation, phase-space trajectories, return map, and circulation analysis. A grouping is found to occur so as to satisfy the self-organized vanishing-gain-circulation rule, which is the strong constraint which governs globally coupled multimode laser dynamics. Synchronized chaos is shown to take place being accompanied with the cooperative power flow from the antiphase chaotic mode group to the synchronized chaotic mode group. © 1996 The American Physical Society.

A fourth-order correlation function in the {r} space is developed and applied to double-slit experiments with spontaneous down-conversion light. The predicted coincidence patterns and corresponding degrees of visibility agree with the experimental results. The van Cittert–Zernike theorem is extended to coincidence experiments. © 1996 The American Physical Society.

We discuss the nonlinear response of impurity two-level atoms in a pseudophotonic band gap (PBG) to an applied laser field. It is shown that in the case when the variance of resonant dipole-dipole interaction (RDDI) is much larger than its average value and the spontaneous emission rate, a nonequilibrium second-order phase transition occurs when the applied field strength parameter exceeds the variance of RDDI. This situation arises when the atomic density is low and the resonance frequency is near the center of a wide PBG. At this threshold the system changes from glassy phase to ferroelectric phase. In the case when the average value of RDDI is larger than its variance and spontaneous emission decay rate, this phase transition becomes first order, leading to optical bistability. This situation arises when the atomic density is high or when the photon localization length within the PBG extends over many optical wavelengths. The influence of RDDI fluctuation on bistability is discussed. These results suggest that disordered, impurity-doped, PBG materials may exhibit very low threshold switching properties. © 1996 The American Physical Society.

We show that in resonant ultrafast spectroscopic experiments, such as in fluorescence interferometry, polarizability effects may be relevant. That is, due to the shortness of the light pulses in the molecular vibrational time scales, Raman scattering processes are always present and therefore they should be included in the analysis of the corresponding experimental situations. We present our arguments using an effective two-electronic-level Hamiltonian for a diatomic molecule that explicitly includes molecular polarizability terms. We calculate fluorescence interferograms due to pairs of phase-locked ultrashort light pulses in resonance with an electronic transition, and compare cases with and without polarizability terms. We also suggest how this analysis could be used to measure electronic polarizabilities. © 1996 The American Physical Society.

The problem of noise from external feedback control is addressed for homodyne detection of optical phase shifts. Two different schemes are analyzed: the conventional single-homodyne detection, and a two-quadrature scheme, which involves couples of independent measurements of two conjugated quadratures. The effectiveness of the feedback mechanism in both schemes is studied versus the feedback coupling parameter and high-sensitive detection regimes are discussed. The effect of nonunit quantum efficiency of photodetectors is also considered. It is shown that nonunit quantum efficiency affects phase sensitivity in the single-quadrature scheme to a larger extent than in the double-quadrature one. © 1996 The American Physical Society.

We study the phase sensitivity of SU(2) and SU(1,1) interferometers fed by two-mode field states which are intelligent states for Hermitian generators of the SU(2) and SU(1,1) groups, respectively. Intelligent states minimize uncertainty relations and this makes possible an essential reduction of the quantum noise in interferometers. Exact closed expressions for the minimum detectable phase shift are obtained in terms of the Jacobi polynomials. These expressions are compared with results for some conventional input states, and some known results for the squeezed input states are reviewed. It is shown that the phase sensitivity for an interferometer that employs squeezing-producing active devices (such as four-wave mixers) should be analyzed in two regimes: (i) fixed input state and variable interferometer, and (ii) fixed interferometer and variable input state. The behavior of the phase sensitivity is essentially different in these two regimes. The use of the SU(2) intelligent states allows us to achieve a phase sensitivity of order 1/N¯ (where N¯ is the total number of photons passing through the phase shifters of the interferometer) without adding four-wave mixers. This avoids the duality in the behavior of the phase sensitivity that occurs for the squeezed input. On the other hand, the SU(1,1) intelligent states have the property of achieving the phase sensitivity of order 1/N¯ in both regimes. © 1996 The American Physical Society.

The linear stochastic Schrödinger equation of a cavity mode subject to a homodyne measurement and to a phase-sensitive feedback loop realized with part of the output homodyne photocurrent is derived. We show that quantum feedback has stabilizing effects which manifest themselves in a significant retardation of the decoherence of a Schrödinger-cat state. © 1996 The American Physical Society.

This paper examines the effect of index guiding on Raman gain. The slowly varying Maxwell wave equation including both the real and imaginary parts of the Raman susceptibility for a seeded Raman amplifier is explored. Using a Gauss-Laguerre mode expansion for the Stokes field, the output Stokes energy is numerically studied as a function of gain and detuning from the Raman resonance. The calculations indicate that the real part of the Raman susceptibility causes the Raman medium to act as a lens when the Stokes seed is detuned from the Raman resonance. This focusing effect leads to higher peak Stokes energy when the Stokes seed is tuned to the blue side of the Raman resonance. Specifically for Raman scattering in ${\mathrm{H}}_2$ with a pump laser at 532 nm and an input seed near 683 nm, the peak Stokes energy can shift by as much as 300 MHz from the Raman resonance. An experiment which confirms these predictions is also presented. © 1996 The American Physical Society.

In this paper, we present a simple purely algebraic method to solve a coupled-channel cavity QED model with three nondegenerate quantized field modes proposed by Wang, Puri, and Eberly [Phys. Rev. A 46, 7192 (1992)]. By transforming it into one describing a spin-1/2 particle in a magnetic field and utilizing the relations between field variables and an orbital angular momentum, we can easily obtain energy eigenvalues without the need to know concrete expressions for eigenstates in terms of the usual Fock states, and analytical expressions of evolution and atomic inversion operators. The eigenstates of energy and orbital angular momentum are also explicitly expressed in terms of Fock states. © 1996 The American Physical Society.

Resolutions of the identity in terms of line integrals that involve SU(2) coherent states and their complementary states are presented. They are used for the expansion of various states in terms of SU(2) coherent states on a line. The properties of the complementary states are also studied. © 1996 The American Physical Society.

In this paper it is shown that the Lyman-α transition of a single hydrogenlike system driven by a laser exhibits macroscopic dark periods, provided there exists an additional constant electric field. We describe the photon-counting process under the condition that the polarization of the laser coincides with the direction of the constant electric field. The theoretical results are given for the example of ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$. We show that the emission behavior depends sensitively on the Lamb shift [W. E. Lamb and R. C. Retherford, Phys. Rev. 72, 241 (1947)] between the 2${\mathit{s}}_{1/2}$ and 2${\mathit{p}}_{1/2}$ energy levels. A possibly realizable measurement of the mean duration of the dark periods should give quantitative information about the above energy difference by using the proposed photon-counting process. © 1996 The American Physical Society.

We consider a class of nonlinear coherent states, which are right-hand eigenstates of the product of the boson annihilation operator and a nonlinear function of the number operator. Such states may appear as stationary states of the center-of-mass motion of a trapped and bichromatically laser-driven ion far from the Lamb-Dicke regime. Besides coherence properties, they exhibit nonclassical features such as amplitude squeezing and self-splitting, which is accompanied by pronounced quantum interference effects. © 1996 The American Physical Society.

The problem of a correct quantum description of the phase difference is examined from the perspective of parameter estimation theory. It is shown that an optimum phase-shift measurement defines a phase difference operator which coincides with other approaches to the same problem. We also study the fundamental limit to the accuracy of a phase difference shift detection. We show that this limit can be reached by a measurement having countable outcomes despite the fact that a phase shift can take any value. We show that this is the case of the phase difference operator defined by an optimum phase-shift measurement. © 1996 The American Physical Society.

The diffusion quantum Monte Carlo (QMC) method is applied to the calculations of the binding energies of the positronium hydride, ${}_{}{}^{1,2}{}_{}{}^{}$S[${\mathit{e}}^{+}$-${\mathrm{H}}^{\mathrm{-}}$], and the positron lithium, ${}_{}{}^{2,1}{}_{}{}^{}$S[${\mathit{e}}^{+}$-Li]. The QMC binding energy of the positronium hydride system is found to be in excellent agreement with the recent experimental value. The result of the energy of the positron-lithium system suggests that it is stable with respect to positron dissociation, but is probably unstable compared to separated Ps and ${\mathrm{Li}}^{+}$. © 1996 The American Physical Society.

The charge-transfer cross sections between a gadolinium atom and its singly charged positive ion in metastable states have been measured with a crossed-beam apparatus. The primary ions are produced by photo- ionization with a tunable dye laser. The populations of primary ions in excited states have been measured by the laser-induced fluorescence method. By measuring the populations, the charge-transfer cross sections of ${\mathrm{Gd}}^{+}$(0 ${\mathrm{cm}}^{\mathrm{-}1}$)+Gd, ${\mathrm{Gd}}^{+}$(262 ${\mathrm{cm}}^{\mathrm{-}1}$)+Gd, and ${\mathrm{Gd}}^{+}$(633 ${\mathrm{cm}}^{\mathrm{-}1}$)+Gd were obtained successfully in the energy range from 30 to 1000 eV. It has been found that the cross sections of these reactions at 1000 eV are equal to each other and are two times larger than that given by Sakabe’s formula based on all the past experimental data for resonant charge transfer [Phys. Rev. A 45, 2086 (1992)], and that the higher the state in which the primary ion is populated, the larger the cross section tends to be. The impact-energy dependences are explained qualitatively by assuming the process to include both resonant and nonresonant charge transfer. © 1996 The American Physical Society.

We have calculated total and differential cross sections for the ${\mathrm{Na}}_2$ scattering complex in the triplet ground state, using the state-of-the-art triplet Coulomb potential. Resonances in the cross section appear in the projectile velocity range 0–50 m/s for the even partial waves l=2,6,8,12,16. The most significant resonance occurs at 10.48 m/s due to l=6 with a total cross section of 7145 A${\mathrm{̊}}^2$. Pronounced structures in the differential cross sections can be resolved for projectile velocity widths of about 1 m/s which are typical for laser Doppler cooling. In order to check and improve the currently used triplet potential curve we have evaluated the feasibility of a scattering experiment. © 1996 The American Physical Society.