In a classical study of the hydrogen molecular ion beyond the Born-Oppenheimer approximation (BOA), we have found that segments of trajectories resemble that of the Born-Oppenheimer approximation periodic orbits. The importance of this fact to the classical understanding of chemical bonding leads us to a systematic study of the periodic orbits of the planar hydrogen molecular ion within the BOA. Besides introducing a classification scheme for periodic orbits, we discuss the convergence properties of families of periodic orbits and their bifurcation patterns according to their types. Semiclassical calculations of the density of states based on these periodic orbits yield results in agreement with the exact quantum eigenvalues of the hydrogen molecular ion system.

It is shown that the Einstein-Podolsky-Rosen (EPR) correlations for arbitrary spin s and the Greenberger-Horne-Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum probabilities. The nonlocality of these probabilities makes the Bell inequalities void. A description that exhibits the relation between the randomness and the nonlocality of entangled correlations is introduced. Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy. The nonlocal character of the EPR correlations is tested using the information Bell inequalities. Relations between the randomness, the nonlocality, and the entropic information for the EPR and the GHZ correlations are established and discussed.

We investigate the domain of coupling constants which achieve binding for a three-body system while none of the two-body subsystems is bound. We derive some general properties of the shape of the domain and rigorous upper bounds on its size, using a Hall-Post decomposition of the Hamiltonian. Numerical illustrations are provided in the case of a Yukawa potential, using a simple variational method.

Synchronously driven optically pumped atomic oscillators have been used to measure the electric-dipole moment of ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$ as a test of time-reversal symmetry. Our result, d${(}^{199}$Hg)<8.7×${10}^{\mathrm{-}28}$e cm, is the smallest experimental limit on the size of an electric-dipole moment and sets stringent bounds on several sources of time-reversal symmetry violation in atomic systems. This article describes the details of the experimental apparatus, the measurement procedure, and the implications of the result for CP violation in elementary particle interactions.

The influence of quantum interference on the transmission of a fluxon through an ideal long circular Josephson junction (a ‘‘Josephson ring’’) is studied. In the low-temperature regime the transmission is a periodic function of a gauge charge applied along the ring with a period 2e. Around points of full period of both the gauge charge and the optical path, the transmission shows resonances as a function of the gauge charge and ‘‘antiresonances’’ as a function of the optical path. These resonances and antiresonances are associated with energy levels of the circular junction and with short dwelling time of the fluxon in the ring. In the high-temperature regime the interaction with plasmons dephases the fluxon wave function completely. The transmission probability in this regime is calculated in a stationary picture and in a dynamical picture and two different results are obtained. The discrepancy between the two pictures is explained via the ratio of the dwelling time to the time the thermal bath needs to change the plasmons’ microscopical state. A general method that retrieves the two results is presented.

We consider splittings of the energies of degenerate quasimodes in a two-dimensional channel. This system is a model for splittings of degeneracies due to multidimensional tunneling in a general quasi-integrable system. We formulate a determinant quantization condition in terms of the transfer matrix, which enables us to relate the splittings to elements of the scattering matrix. We find that the splittings can be due to either a single- or a multiple-scattering process. In the former case, the results reduce to an earlier theoretical analysis which used an assumption that the splittings are canonically invariant quantities. We demonstrate a quantitative agreement between semiclassical theory and numerical calculations of the splittings.

We present a simple scheme for a universal two-bit quantum logic gate using circular Rydberg atoms and a superconducting millimeter-wave cavity. We analyze in detail the performances of this gate, using the parameters of an experiment currently under way in our laboratory.

We consider the product of infinitely many copies of a spin-1/2 system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of ${\mathrm{\sigma }}^{\mathit{x}}$ measurements has any specified property. In many cases, product states are eigenstates of the projections, and therefore the result of measuring the property is determined. Thus we obtain a nonprobabilistic quantum analogue to the law of large numbers, the randomness property, and all other familiar almost-sure theorems of classical probability.

The relativistic linked-cluster many-body perturbation theory (RLCMBPT) has been used to investigate the hyperfine properties in the excited 7${\mathrm{}}^2$${\mathit{P}}_{3/2}$ and 7${\mathrm{}}^2$${\mathit{P}}_{1/2}$ states of ${}_{}{}^{221}{}_{}{}^{}\mathrm{Ra}_{}^{+}{}_{}{}^{}$ ions. Our calculations of the hyperfine constants yield -22.4±0.3 MHz for the 7${\mathrm{}}^2$${\mathit{P}}_{3/2}$ state and -265.3±4.0 MHz for the 7${\mathrm{}}^2$${\mathit{P}}_{1/2}$ state, in excellent agreement with the experimentally obtained values of -22.4±0.9 and -266.3±1.5 MHz, respectively. The results obtained in this work are compared with those by other theoretical methods and an attempt is made to understand the relationship between the different methods, particularly that between the RLCMBPT procedure adopted in this work and the many-body multiconfigurational Dirac-Fock procedures.

Resonantly excited x-ray fluorescence spectra of the benzene molecule are presented and analyzed in terms of symmetry-selective resonant scattering processes. The sharp frequency dependency that is observed can be understood from strict parity and symmetry-selection rules operating in the full ${\mathit{D}}_{6\mathit{h}}$ point group symmetry. The experimental results prove that the electronic symmetry is not broken for the lowest unoccupied level involved in the resonant x-ray emission process.

We report direct measurements of two-electron contributions to the ground-state energy of high-Z heliumlike ions. The difference in radiative-recombination x-ray energy (i.e., ionization potential of the recombined ion) was measured for bare and hydrogenlike target ions trapped in an electron-beam ion trap for six elements ranging from Z=32 to Z=83. The achieved uncertainties (as small as 1.6 eV) test the second-order many-body contributions to the energy and approach the size of the two-electron (screened) Lamb shift. We also report a measurement of the ground-state ionization potential of heliumlike bismuth relative to heliumlike xenon. All results are in agreement with available theories.

The effect of quantum-mechanical symmetry on the geometric structures and internal motions of the intrashell states of three-valence-electron atoms is investigated with a model where the core and all the radial degrees of freedom of the valence electrons are frozen. A number of correlative densities have been defined and calculations have been carried out for the eight N=2 intrashell states of boron as examples. For each state, the most probable shape, the preference of orientation, and the favorable modes of internal motion have been found.

A general equation is constructed for magneto-optical spectra. The incident laser beam has an arbitrary polarization and its direction is arbitrary relative to the magnetic field. The analyzer has an arbitrary extinction ratio function. The Faraday and Voigt formulas are deduced as special solutions. From the generalized Faraday formula, the absorption spectra of ${\mathrm{\sigma }}^{+}$ and ${\mathrm{\sigma }}^{\mathrm{-}}$ light are measured without influence of the birefringence. The circular dichroism is estimated. The measured spectra clearly show the frequency shifts of ${\mathrm{\sigma }}^{+}$ and ${\mathrm{\sigma }}^{\mathrm{-}}$ light. The magnitude of the shift for a magnetic field of 0.015 T is twice as large as the Doppler width for the Cs ${\mathit{D}}_2$ line. These shifts are induced by the Larmor precession defined by the fine-structure g factor. The Larmor precession does not induce a real shift of Zeeman levels, but induces a phase shift of optical coherence through the Rabi frequency.

A time-dependent functional approach is developed for calculating the dynamical optical response and ground-state properties of nonrelativistic fermion systems. The functional (effective action) uses the particle-hole components of the reduced single-electron density matrix as variables and is constructed using the natural orbitals as a reference. It is defined on pairs of trajectories that constitute a Liouville space path in the phase space of the classical analog of the quantum system. A perturbative ‘‘semiclassical’’ calculation of the effective Liouville-space action is used to incorporate correlation effects in the linear optical response.

Using our relativistic-configuration-interaction methodology, we report multireference calculations of energy differences and magnetic-dipole and electric-quadrupole hyperfine structure constants of all five levels in the (5d+6s${)}^2$ J=2 manifold of singly ionized ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$. The errors in the splittings of the bottom four levels are no more than 0.02 eV, while the separation of the two highest levels has an error of 0.11 eV due to an incomplete description of the correlation in the levels belonging to higher manifolds. The hyperfine-structure constants show strong sensitivity to many-body effects, resulting in striking improvements over the multiconfiguration Dirac-Fock values. Seven of the ten hyperfine constants are accurate within 2–12 %. For the rest of the constants we have identified the primary cause of the errors as an incorrect description of many-body effects in the high-lying levels and have discussed possible remedies.

The density of electrons on a distance scale 1/Z near the nucleus of a large atom with nuclear charge Ze is given (asymptotically as Z→∞) by the sum of the squares of all the hydrogenic bound-state functions (with nuclear charge Ze). This density function, which is an important limiting function in quantum chemistry, is investigated here in detail. Several analytic results are found: In particular, the asymptotic expansion for large r is derived and it is shown that the function falls off as ${\mathit{r}}^{\mathrm{-}3/2}$ for large r; this behavior coincides with the Thomas-Fermi density for small r. ‘‘Shell structure’’ is visible, but barely so.

Magnesium and copper plasmas produced by 2-ns pulses of a Nd-glass laser were used to investigate satellite spectra of Li-like Mg x and Na-like Cu xix and to verify a near resonance between Mg xi and Cu xx transitions, which is the basis of a proposed resonantly photopumped x-ray laser scheme. The emission was measured with a spherical crystal spectrograph that provided high spectral resolution (λ/Δλ≊8000) and spatial resolution in one dimension. The high resolution allowed improved wavelength measurements for a number of n=2→1 Mg x transitions that are satellites to the He-like resonance line, including transitions with n=3,4 spectator electrons. Using composite targets, the spatial resolution of the spectrograph enabled highly accurate measurements of 2p-4d Na-like copper transitions. Collisional-radiative models were used to assist the identification of the Mg x and Cu xix transitions. Finally, the wavelength difference between the 2${\mathit{p}}^6$-(2${\mathit{p}}^5$${)}_{3/2}$4${\mathit{d}}_{5/2}$(J=1) Cu xx transition and the 1${\mathit{s}}^2$${\mathrm{}}^1$${\mathit{S}}_0$–1s2${\mathit{p}}^3$${\mathit{P}}_1$ Mg xi intercombination line was measured to be 2.5±0.8 mÅ, with the copper line having a longer wavelength.

We apply a recently developed electron-beam ion trap technique to measure the lifetime of the 1s2s${\mathrm{}}^3$${\mathit{S}}_1$ level in heliumlike magnesium. The technique employs a fast-switching electron beam to produce and excite electrostatically trapped ions. The radiative lifetime is determined by observing the fluorescent decay of the 1s2s${\mathrm{}}^3$${\mathit{S}}_1$ level after the beam energy is switched below the threshold for electron-impact excitation. A value of 13.61±0.49 μs has been measured for the 1s2s${\mathrm{}}^3$${\mathit{S}}_1$ level in heliumlike magnesium, in good agreement with theoretical predictions.

This work presents expressions for the excited population resulting from a Ramsey pump-probe interferometric experiment in the short-weak-pulse limit. It describes time-resolved measurements, which have no direct frequency-resolved analogy, in terms of the eigenenergies, amplitudes, and lifetimes of the excited wave packet. An interferometric phase cross correlation is shown to affect wave packet dynamics by shifting the dispersion of a Rydberg-like wave packet with respect to zero delay. This work phenomenologically introduces eigenstate lifetimes into the expression for the excited population in the Ramsey pump-probe interferometric measurement. An interferometric intensity cross correlation is shown to produce an excited population that, as a function of the delay between pump and probe pulses, is asymmetric about zero delay when the excited eigenstate decays.

Subshell-resolved M and L level widths and fluorescence yields are derived from high-resolution K${\mathrm{\alpha }}_{1,2}$ and K${\mathrm{\beta }}_{1,3}$ x-ray emission spectra of copper. As the contribution of spectator hole satellites was removed from the spectra by computer fits based on an ab initio calculated transition array, the widths and yields obtained pertain to pure one-hole states and single-electron diagram transitions. A considerable improvement in the agreement with theoretical widths and yields is observed for all levels studied. A significant contribution of Coster-Kronig transitions to the ${\mathit{L}}_2$ level width is confirmed. Individual ${\mathit{M}}_2$ and ${\mathit{M}}_3$ widths and yields are derived from x-ray spectra. They are in good agreement with recent theoretical Dirac-Hartree-Slater calculations, but the widths are consistently larger than those measured for the same subshells by photoelectron spectroscopy. 3d spectator holes are found to broaden the widths of the corresponding x-ray emission lines by up to a few tenths of an eV.