Anomalies associated with canonical transformations in quantum-mechanical systems are examined in the context of the path-integral formalism, where they appear as nontrivial Jacobians. The quantum-mechanical anomaly, for the case of a transformation to cyclic coordinates, is shown to be equivalent to a term in the action, similar to a gauge field configuration, whose presence maintains self-adjointness of the Hamiltonian or corrects the phase-space measure of the path integral to reflect the bound-state spectrum of the original problem. Various nonperturbative aspects of quantum-mechanical transition amplitudes are calculated by using classical solutions to Hamilton’s equations of motion combined with the anomaly generated by the canonical transformation.

We present a different class of quantum-mechanical potentials. These are midway between the exactly solvable potentials and the quasiexactly ones. Their fundamental feature is that one can find the entire s-wave spectrum of a given potential, provided that some of its parameters are conveniently fixed.

We have measured the relative population in the two ${\mathit{m}}_{\mathit{j}}$ states of barium 6${\mathit{p}}_{1/2}$ ions produced by the autoionization of (6${\mathit{p}}_{3/2}$nd${)}_{\mathit{J}=\mathit{M}\mathit{J}}$=3 states by detecting the helicity of the emitted fluorescence. These populations can be related to the relative branching ratio into the 6${\mathit{p}}_{1/2}$ε${\mathit{d}}_{5/2}$ and 6${\mathit{p}}_{1/2}$ε${\mathit{g}}_{7/2}$ continuum channels. Rydberg states with n=16–23 have similar branching ratios, producing approximately six times as much 6${\mathit{p}}_{1/2}$ε${\mathit{d}}_{5/2}$ population as 6${\mathit{p}}_{1/2}$ε${\mathit{g}}_{7/2}$ population.

We investigate the classical scattering patterns of an electron off a ${\mathrm{He}}^{+}$ ion. The scattering functions exhibit interesting self-similar structure, which can be interpreted in terms of the indefinite number of electronic returns to the vicinity of the nucleus, encounters among the particles, and Kepler-like electronic excursions during the collisional process. Based on this mechanism a binary coding is introduced to organize the dynamics of this three-body system and yields escape rates that vary with the sectional cut in the parameter space. The physical interpretation and the symbolic dynamics introduced here are generally useful for all three-body collisional systems.

We demonstrate an experimental technique that selects the nuclear spin I=0 isotope ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$ for spectroscopic measurements from a beam of natural barium containing seven stable isotopes. A cw dye laser is used to optically pump the I=3/2 isotopes ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}$ and ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}$ into the metastable 6s5d ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ and ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_{1,2}$ levels via the 6s6p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ excited state, leaving nearly pure ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$ in the ground state. Photoionization spectra of the excited 5d6p ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_1$ even isotope state recorded with optical pumping of ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}$ and ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}$ to the metastable levels are essentially devoid of forbidden features associated with the hyperfine interaction in the odd isotopes.

Using spin-asymmetry data from electron-impact-ionization studies of H, ${\mathrm{He}}^{\mathrm{*}}$, Li, Na, K, and Cs, we determine the energies at which dynamical influences on the inside part of the final-state wave function create detectable departures from the simple Wannier power-law dependence of the cross section on escape energy for the singlet and triplet channels separately. From a comparison of these energies for the six valence-1 systems examined, we conclude that asymmetry measurements provide a window for observing the effects of screening and core polarization on the dynamics of the highly correlated Coulomb three-body breakup.

The hyperfine-quenched transition 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{0–}$1 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ has been observed in heliumlike silver (${\mathrm{Ag}}^{45+}$) in the two isotopes ${}_{}{}^{107}{}_{}{}^{}\mathrm{Ag}$ and ${}_{}{}^{109}{}_{}{}^{}\mathrm{Ag}$. The lifetime for the transition has been measured for each isotope and found to be ${\mathrm{\tau }}_0$(107)=3.98(37)×${10}^{\mathrm{-}12}$ sec and ${\mathrm{\tau }}_0$(109)=2.84(32)×${10}^{\mathrm{-}12}$ sec. From the measured lifetimes a value is inferred for the absolute value of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{0–}$2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ fine-structure splitting ‖Δ${\mathit{E}}_{0\mathrm{-}1}$‖ in ${\mathrm{Ag}}^{45+}$ with the result ‖Δ${\mathit{E}}_{0\mathrm{-}1}$‖=0.79(04) eV, where the uncertainty is the experimental uncertainty taken at the 1σ confidence level. This result is compared with calculations based on the multiconfigurational Dirac-Fock method, the unified method, and recent results from the relativistic configuration-interaction method.

The cross section for two-electron photoionization of the hydrogen molecule by high-energy photons is predicted in the nonrelativistic dipole approximation to be 2.25% of the cross section for single photoionization.

Generalizing a recent theoretical result obtained by Freyberger and Schleich [Phys. Rev. A 47, R30 (1993)], we show that the phase-measurement scheme proposed and realized by Noh, Fougères, and Mandel [Phys. Rev. Lett. 67, 1426 (1991); Phys. Rev. A 45, 424 (1992)] amounts to measuring the Q function for the light under investigation, provided the reference beam (used for homodyne detection) is a very strong coherent field so that it can be described classically. The desired phase distribution follows from the Q function by averaging over the field amplitude. Since an analysis of an earlier proposal by Bandilla and Paul [Ann. Phys. (Leipzig) 23, 323 (1969)] to measure phase distributions via amplification led to just the same result, a perfect physical equivalence of those two approaches has thus been established.

We describe the micromaser in the framework of an exact semiclassical model for regular injection, allowing the case of more than one atom at a time in the cavity to be considered. For high pumping and high atom fluxes we find a new kind of phase transition corresponding to a strongly nonlinear chaotic behavior. In addition to the customary period-doubling route to chaos, unexpected scenarios are exhibited, which are a consequence of the multistable competition between different attractors for time evolution.

Some quantum-mechanical results describing the ionization of initially highly excited hydrogen atoms by a strong, circularly polarized microwave field are presented. A simplified two-dimensional model of the atom is used. Discrepancies between various classical estimates for the low-frequency ionization threshold are resolved.

We report on a two-photon interference experiment proposed by Franson [Phys. Rev. Lett. 62, 2205 (1989)], in which sinusoidal fringes with visibilities greater than 70.7%, such as those predicted by quantum mechanics, violate a Bell inequality. We observe visibility of 80.4±0.6%, implying a violation of the inequality by 16 standard deviations. Here the elements of reality under consideration are energy and time rather than spin components. Any classical field models describing separate beams in a Franson interferometer are limited to visibilities less than 50%, and hence ruled out as well, without the need for any supplementary assumptions.

We report measurements of noise accompanying two-wave mixing in a Kerr medium. Experiments were conducted at visible wavelengths using an aqueous suspension of shaped microparticles as the nonlinear medium. Theoretical calculations and computer simulations using a stochastic model for light-scattering noise are shown to give excellent agreement with the experimental results.

Clear plateaus, up to the 71st harmonic in Ne and the 69th harmonic in He, were observed in a Ti:sapphire laser, while a gradual decrease to the 25th harmonic in Ne and the 23rd harmonic in He were observed in a KrF laser. High intensity, along with a shorter pulse, induced self-phase-modulation and/or beam breakup in gas media and resulted in the serious degradation or complete disappearance of higher-order harmonics. In the Ti:sapphire laser, the harmonic distribution did not depend on the pulse width of from 120 to 730 fs at a fixed peak intensity.

We consider the scattering of an atom as it passes through a classical standing wave, without neglecting the center-of-mass kinetic energy. In the large detuning limit we show that this may be modeled as a nonlinear pendulum. In the quantum description fractional revivals of the initial state occur. These revivals are manifest as nonclassical peaks in the distribution of momentum orthogonal to the direction of beam propagation. This quantum scattering could be achieved with cooled well-collimated beams.

We propose and demonstrate the use of polarization to determine the threshold of an optical microcavity when the output power versus pump power does not show a sharp threshold. A lasing threshold is observed via a sharp transition in the polarization and a simultaneous reduction in emission linewidth. We find that dipole angular diffusion in a dye gain medium has a significant effect on the polarization of the emission. A theoretical model including the diffusion process is presented. Quantitative agreement with the measurements is obtained.

A modification of the method proposed by Ott, Grebogi, and Yorke to control chaos [Phys. Rev. Lett. 64, 1196 (1990)] has allowed us to characterize unstable orbits of a Nd-doped fiber laser in their whole domain of existence. Stabilization could be achieved both on orbits embedded inside the chaotic attractor and on orbits located in other parts of the phase space. Transient regimes provide direct experimental information on the unstable Floquet multipliers.

The time evolution of driven harmonic oscillators is determined by applying the Magnus expansion in the basis set of instantaneous eigenstates of the total Hamiltonian. It is shown that the first-order approximation already provides transition probabilities close to the exact values even in the intermediate regime.

The density of states is numerically calculated for a nonintegrable Hamiltonian whose shortest-periodic-orbit family undergoes a period-doubling bifurcation in the energy interval considered. Smoothing the density using a suitable width δE, oscillations are observed due to only the family of shortest periods or also its period doubling. The period-doubling resonance results in a higher average amplitude of the corresponding spectral oscillations than for the primitive orbit. The main periodic families produce strong scars in the wave intensities. Projections of the Husimi distributions also exhibit scars that are, however, not so clear.

It is demonstrated that the conjunction of the premises of Einstein-Podolsky-Rosen paper with a supplementary assumption lead to validity of an inequality that is sometimes grossly violated by the quantum-mechanical probabilities in the case of real experiments. The supplementary assumption is as follows: For every photon in the state λ, the sum of the detection probabilities in the ordinary and in the extraordinary beams emerging from a two-way polarizer is less than or equal to the detection probability with the polarizer removed. This assumption, which always holds for an ensemble of photons, is weaker and more general than the assumption of Garuccio and Rapisarda [Nuovo Cimento A 65, 269 (1981)] and the assumption of Clauser and Horne [Phys. Rev. D 10, 526 (1974)]. Hence an experiment based on this assumption refutes a larger family of hidden-variable series than an experiment based on the assumption of Garuccio and Rapisardo or on the assumption of Clauser and Horne.