We show that cyclic quantum evolution can be realized and the Aharonov-Anandan (AA) geometric phase can be determined for any spin-j system driven by periodic fields. Two methods are extended for the study of this problem: the generalized spin-coherent-state technique and the Floquet quasienergy approach. Using the former approach, we have developed a generalized Bloch-sphere model and presented a SU(2) Lie-group formulation of the AA geometric phase in the spin-coherent state. We show that the AA phase is equal to j times the solid angle enclosed by the trajectory traced out by the tip of a generalized Bloch vector. General analytic formulas are obtained for the Bloch vector trajectory and the AA geometric phase in terms of external physical parameters. In addition to these findings, we have also approached the same problem from an alternative but complementary point of view without recourse to the concept of coherent-state terminology. Here we first determine the Floquet quasienergy eigenvalues and eigenvectors for the spin-j system driven by periodic fields. This in turn allows the construction of the time-evolution propagator, the total wave function, and the AA geometric phase in a more general fashion.

A linear stability analysis of a plane-wave model of a unidirectional ring cavity, which allows the slowly varying field amplitudes to vary along the length of the atomic medium, yields a characteristic equation having singularities coincident with estimates of the atomic-dominant eigenvalues derived under the mean-field limit. This result calls into question the validity of previous estimates of these eigenvalues. Using this general characteristic equation, we estimate the cavity- and atom-dominant eigenvalues by applying a perturbation expansion in sequential powers of the uniform-field parameter η=2 ln‖scrĒ(L)/scrĒ(0)‖. The resulting eigenvalue estimates appear as asymptotic expansions with limited domains of validity. The cavity-dominant eigenvalues, which are responsible for the well-known ‘‘self-pulsing’’ instability in unidirectional ring lasers and optically bistable resonators, are shown to be consistent with estimates derived in previous studies. However, the new expressions for the atom-dominant eigenvalues exhibit a more intricate distribution in the complex plane.

Nonlinear pulse propagation at the zero group-dispersion wavelength is studied analytically. It is discovered that, after the characteristic initial frequency splitting, evolution of the pulse envelope that is shifted down to the anomalous regime is described by the nonlinear Schrödinger equation with higher-order dispersion as a perturbation. The effect of the perturbation on the pulse is to excite radiation at a frequency inversely proportional to the small parameter β. The amplitude of the radiation is exponentially small (∝exp(-1/β)] and can be calculated only by the perturbation method that goes beyond all orders.

Optical nutation in Ba ii has been studied with a rapid Doppler-shifting technique in a cw collinear fast-ion-beam–laser experiment. Time-resolved nutation curves have been recorded as a function of transition, laser irradiance, laser frequency detuning, and laser polarization. Frequency spectra recorded at different, well-specified, times of interaction between the ions and the laser field reveal several interesting effects. Among them is the pronounced influence of the postacceleration potential on the line profiles. Theoretical curves, calculated in the density-matrix formalism, reproduce all the characteristics of the experimental data. Future possibilities of this technique are discussed, e.g., the prospects of determining transition probabilities through the measurements of optical nutation.

We analyze the macroscopic quantum jumps (sudden interruptions in the fluorescence on a macroscopic time scale) that are produced when a pair of two-level atoms separated by a distance d is irradiated by a strong laser having wavelength ${\lambda }_0$, with ${\lambda }_0$≫d. Included in the analysis is the dipole-dipole coupling of the atoms, the ac Stark effect, and the role played by a term that is present in the atom-laser field interaction Hamiltonian when k⋅d≠0 (k is the wave vector of the laser field and d is the vector connecting the two atoms). Our treatment is based on frequency-resolved delay functions, an extension of a concept developed by Reynaud, Dalibard, and Cohen-Tannoudji [IEEE J. Quantum Electron. 24, 1395 (1988)], which is shown to be useful to study frequency-resolved photon statistics. As examples, we study the statistics of the fluorescence produced by the two-atom system as well as those in the components of the fluorescent triplet produced by a single two-level atom.

This paper applies many-body theory for an electron-hole plasma in semiconductors to multimode semiconductor-laser operation and sidemode generation. We derive third-order laser amplitude and frequency-determining equations and the corresponding propagation equations for multiwave mixing. The equations are similar to those found in multimode gas-laser theory. We include the effects of population pulsations in the total carrier density, but, due to the rapid carrier-carrier scattering, we explicitly suppress spectral hole burning. We also include band-gap renormalization and Coulomb enhancement contributions. The theory is evaluated numerically for the example of nondegenerate four-wave mixing in an amplifier configuration. We discuss the dependence of the sidemode intensity on the length of the active medium, the intermode beat frequency, and the pump-wave intensity.

It is shown by example that sub-Poissonian photon-counting statistics need not imply photon antibunching, but can be accompanied by photon bunching, i.e., by the tendency of two photons to be close together more frequently than further apart. Some comments on the relation between antibunching and sub-Poissonian statistics are made.

We study the structure of the hydrogen atom when placed in a high-frequency, superintense laser field, within the framework of a nonperturbative theory recently developed for this purpose. The theory predicts that in the high-frequency limit the atom is stable against decay by multiphoton ionization, and that its structure is determined by a time-independent Schrödinger equation containing a ‘‘dressed’’ Coulomb potential. The laser frequency ω and the intensity I enter only combined in the parameter ${\alpha }_0$=$I^{1/2}$${\omega }^{\mathrm{-}2}$ a.u. We first analyze the symmetry of the eigenvalue problem for the case of linear polarization under consideration and adopt an appropriate classification scheme for the levels. The small-${\alpha }_0$ limit of the levels is obtained analytically. In the large-${\alpha }_0$ limit scaling laws are derived for the ${\alpha }_0$ dependence of the eigenvalues and eigenfunctions. At finite ${\alpha }_0$ we have carried out a very accurate numerical computation over an extended range of ${\alpha }_0$ values (0≤${\alpha }_0$≤200 a.u.) for a number of symmetry manifolds, by diagonalization of the Hamiltonian in a Gaussian basis. The correlation diagrams relating the small- and large-${\alpha }_0$ limits exhibit several avoided crossings. The binding energies show an overall decrease with ${\alpha }_0$, in some cases preceded by an increase through a maximum. For the ground state this decrease is quite steep. The extreme distortion of the atomic structure accompanying it is studied. It is shown that, with increasing ${\alpha }_0$, the (oscillating) electronic cloud undergoes radiative stretching, which eventually culminates at large ${\alpha }_0$ in its splitting into two parts (dichotomy). The consequences of our findings for the experimental energy spectrum of the ejected electrons are considered.

We analyze a type of spurious resonance recently identified [see, for example, B. Apagyi, P. Lévay, and K. Ladányi, Phys. Rev. A 37, 4577 (1988)] in the Schwinger variational method. It is found that this type of anomaly is associated with ill conditioning of the potential matrix V, and that this fact allows the identification and removal of any such resonances by straightforward numerical procedures. We therefore anticipate that such anomalies will have little relevance to practical applications of the Schwinger method.

A new alternative local method to solve the Schrödinger equation is established, in which powers of the Hamiltonian are used to set up algebraic equations. The computation is integration-free and easy to carry out. The method is applied to the quartic anharmonic-oscillator problem.

A formulation according to which the positions and widths of metastable quasienergy states can be obtained for any time-periodic field within the framework of the finite-basis-set (real or complex) approximation is presented. A numerical example is given to illustrate the potential use of the proposal method in the study of the dynamics of laser-driven systems and of the dynamics of time-periodic classical chaotic Hamiltonians.

The magnetic-field perturbed decay rate of m=0 triplet positronium is computed in the mass matrix Hamiltonian approximation. The rate differs only by at most ≊8 ppm from the conventional result leading to a negligible correction to the singlet-state annihilation rate measured by Gidley et al. [Phys. Rev. Lett. 49, 525 (1982)].

The method of complex-coordinate rotation is used to calculate the lowest-lying ${}_{}{}^1{}_{}{}^{}\mathrm{D}_{}^{\mathrm{e}}{}_{}{}^{}$ resonances below the n=2 and 3 hydrogen thresholds. Hylleraas functions with up to N=1230 terms are used. Resonance parameters for the n=2 resonance are determined as E=-0.255 873 7±1×${10}^{\mathrm{-}6}$ Ry and Γ=0.000 633 4±2×${10}^{\mathrm{-}6}$ Ry. The resonance parameters for the n=3 resonance are determined as E=-0.131 906 6±1×${10}^{\mathrm{-}6}$ Ry and Γ=0.003 316±2×${10}^{\mathrm{-}6}$ Ry.

Electron transfer and excitation in 0.05- to 20-keV/amu ${\mathrm{He}}^{+}$+Na(3s) collisions is studied theoretically within the close-coupling method with two-electron molecular- and atomic-orbital expansion basis sets. Results agree with the trend of other information on this system. Remaining discrepancies that are larger than those in similar contemporary studies of one-electron systems are discussed with reference to the convergence of this two-electron study. Results for the integral alignment parameter $A_{20}$ are also presented as a guideline for future experimental study.

Using laser-induced fluorescence, the lifetime of the 3$p_8$ level of argon was measured. Variation of the pressure in the observation chamber by three orders of magnitude allowed a precise extrapolation to the collision-free lifetime.

Oscillations in the photon distribution of squeezed states are explained based on the interpretation of the generating function in terms of the generalized superposition of coherent fields and quantum noise.

The Glauber-Sudarshan P representation of negative binomial states is presented and its properties are discussed. It is shown that for the limiting cases the states approach the random-phase coherent state and the thermal noise state. Thus these states may allow a unified description of coherent and thermal states of the field. The two-dimensional representation of the P function is plotted on the complex-α plane. The probability density function of waiting-time intervals between the arrivals of successive photons on a photodetector irradiated by a beam of the negative binomial light is also investigated.

New scattering orders in degenerate four-wave mixing with a bulk semiconductor have been observed due to spatial subharmonic bifurcation of the laser-induced grating. For the observation, wave mixing in the Raman-Nath regime was performed in a thin platelet of CdS that exhibited increasing absorption optical bistability. A qualitative theoretical model is presented that explains the appearance of new scattering orders.

We construct new sum rules for the nonlinear susceptibility modulus of Raman processes using the complex analysis proposed in a previous paper [K.-E. Peiponen, Phys. Rev. B 37, 6463 (1988)]. The validity of the sum rules is confirmed by the Lorentzian line-shape approximation for the Raman susceptibility.

The incoming interaction picture is introduced in accordance with the adiabatic hypothesis. A generalized Wick’s theorem and, accordingly, a real-time formalism of perturbation theory at finite temperatures are constructed for the closed-time-path Green’s functions. This new approach is illustrated in terms of the simple case of an electron-phonon system.