A model is presented to describe spontaneous type-II parametric down-conversion pumped by a broadband source. This process differs from the familiar cw-pumped down-conversion in that a broader range of pump energies is available for down-conversion. The properties of the nonlinear crystal determine how these energies are distributed into the down-converted photons. Because the two photons are polarized along different crystal axes, they have different spectral characteristics and are no longer exactly anticorrelated. As the pump bandwidth is increased, this effect becomes more pronounced. A fourth-order interference experiment is proposed, illustrating some of the features of broadband pumped down-conversion.

A high-precision experiment to measure parity-nonconservation in atomic Yb has been proposed recently [D. De Mille, Phys. Rev. Lett. 74, 4165 (1995)]. We use a relativistic configuration-interaction approach to highlight the importance of correlation effects in the ${6s}^2{(}^1{S}_0)\to {6s5d(}^3{D}_1)$ parity-nonconserving electric transition amplitude for Yb. Our result shows that this transition amplitude is dramatically altered by the strong mixing between some of the configurations that make up the odd-parity ${6s6p(}^1{P}_1)$ atomic state.

An approach to the measurement induced geometric phase based on the de Broglie–Bohm hidden-variable model is developed. The analysis involves an evolving geometric phase connecting the initial and final states of an individual experimental run. As an illustration the geometric phase produced by a cyclic sequence of spin-$\frac{1}{2}$ filtering experiments is considered. It is argued, in this case, that the evolving geometric phase can be made close to the Samuel-Bhandari phase.

The variational self-consistent field molecular-orbital method is used to compute both atomic and molecular full configuration interaction (FCI) energies of the hydrogen anion and the hydrogen molecule, for the Yukawa potential. The spin orbitals have been expanded as linear combinations of Gaussian basis functions, for which complete analytical formulas for all the required basic integrals are available. Both the ionization potential of the hydrogen anion and the behavior of the molecular properties of the hydrogen molecule have been analyzed in detail with extensive basis sets at the FCI level of theory. Finally, the growing importance of the electron correlation energy as the screening parameter increases has been demonstrated clearly by our calculations.

Five theorems and one lemma, regarding the limits of density functionals as one or several of the coordinate-scaling parameters go to zero or infinity, are proved. A unified description of the coordinate-scaling method and the adiabatic-connection formulation is also introduced.

The resonant structures corresponding to selected He $sp,$ ${2n}^{\pm }$ and $2pnd{}^{1,3}{P}^o$ autoionization series below the ${\mathrm{He}}^{+}$ $N=2\mathrm{}$ threshold, following photoionization from $1s2s{}^{1,3}S$ metastable states, are examined in detail. Theoretical photoionization cross sections, calculated using a $B$-spline-based configuration-interaction approach with a length-velocity agreement better than 1%, are presented. A sign change in Fano profile parameters $q$ in $1s2s{}^{1}S\to {sp,2n}^{+}{}^{1}P$ transitions along the ${2n}^{+}$ autoionization series is identified and analyzed.

Single-ionization cross sections for ${\mathrm{W}}^{4+},$ ${\mathrm{W}}^{5+},$ and ${\mathrm{W}}^{6+}$ are calculated in the configuration-average distorted-wave approximation. Contributions from excitation autoionization are found to be strong for each ion. When comparing theory with the recent crossed-beams measurements of Stenke et al. [J. Phys. B 28, 2711 (1995)], ionization from the ground configuration dominates for ${\mathrm{W}}^{4+}$ and ${\mathrm{W}}^{5+},$ while ionization from metastables of excited configurations dominates for ${\mathrm{W}}^{6+}.$

We investigate specific maximum-entropy states of a single harmonic-oscillator mode that arise when only number states (Fock states) differing by a multiple of a certain integer $k$ $(k>~1)$ are allowed to be occupied. For $k=2\mathrm{}$ the number-probability distribution of the even-number maximum-entropy state has a close resemblance to that of a squeezed-vacuum state. These maximum-entropy states can be obtained as the stationary solutions of a master equation which takes into account $k$-quantum absorption as well as $k$-quantum emission processes only. The steady-state solution of this master equation depends on the initial conditions. For the vibrational motion of a trapped ion such nonclassical maximum-entropy states could be produced with the help of the recently proposed method of laser-assisted quantum reservoir engineering.

The recent single-atom microlaser experiment [K. An et al., Phys. Rev. Lett. 73, 3375 (1994)], in which a stream of inverted two-level atoms is injected into an ultrahigh $Q$ cavity, can be understood in the context of a semiclassical four-level laser model. Transit time broadening due to short atom-cavity interaction time effectively introduces nonradiative decay of the two levels in the model. The steady-state solution of semiclassical photon and atom rate equations for the intracavity mean photon number versus the intracavity atom number provides a good fit to the experimental data.

The results of the investigation of Stokes energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump are presented. The pulse-energy distributions and their standard deviations were measured. The comparison of the experimental data with known ones for coherent pump shows the strong difference in the distribution shape and the standard deviation value. This difference is explained as a manifestation of the non-Gaussian (super-Gaussian) statistics in stimulated scattering with a broad-band pump. The results of numerical calculations for statistics of Stokes intensity are in a qualitative agreement with the experimental findings.

The problem of deriving analytic formulas for transition probabilities in two-level systems is studied. The two-level systems are described by a pair of first-order differential equations coupled by a time-dependent potential. One such model is given by ${\mathrm{da}}_m/dt=-i\beta {f\left(t\right)a}_n{e}^{(-{1)}^{n}i\alpha t}$ $(m,n=1,2\mathrm{}$; $m\ne /n)$, which describes certain types of ion-atom collisions and some quantum-optics two-level problems. It will be shown that the correct approach in solving the coupled equations is to adopt a Zwaan-Stueckelberg phase-integral analysis of the four-transition-point problem based on the parabolic noncrossing model of Crothers [J. Phys. B 9, 635 (1976)]. Alternatively, one may obtain an approximation by employing adiabatic perturbation theory, but such an approach can at best provide only weak-coupling solutions and can never guarantee unitarity in the probability amplitudes. The advantage of the phase-integral method is that it produces a strong-coupling approximation by embracing the appropriate asymptotic expansions for cylinder functions of large order and argument [D. S. F. Crothers, J. Phys. A 5, 1680 (1972)] and it also ensures analyticity, unitarity, and symmetry.

When neon is introduced as a buffer gas the interaction time of cesium atoms in a vapor cell with resonant laser beams is drastically increased. Using a pair of phase-locked lasers we have observed linewidths as narrow as $42\hspace{0.5em}$Hz for coherent dark resonances in a cesium vapor cell. We study the influence of power and pressure broadening and systematic shifts of the resonance frequency. Our experiments demonstrate that coherent dark resonances could rival direct radio-frequency precision measurements, which have a wide range of applications in physics.

On the basis of recently measured ${\mathrm{Rb}}_2$ bound-state energies and continuum properties, we predict magnetically induced Feshbach resonances in collisions of ultracold rubidium atoms. The resonances make it possible to control the sign and magnitude of the effective particle-particle interaction in a Rb Bose-Einstein condensate by tuning a bias magnetic field. For the case of ${}^{85}\mathrm{Rb}$ they occur at field values in the range where these atoms can be magnetostatically trapped. For ${}^{87}\mathrm{Rb}$ they are predicted to occur at negative field values.

We have measured, using electron spectroscopy, the lowest-energy doubly hollow lithium triply excited ${(3l3l}^{\prime }{3l}^{″})$ ${}^{2}P$ state. Energies, widths, and partial cross sections have been measured and calculated using the saddle-point technique and the $R$-matrix approximation. Our results show good agreement between experimental and theoretical data for the energy and the width of the doubly hollow state.

A laser probing technique has been applied to a stored ion beam of ${\mathrm{Xe}}^{+}$ to study collisional destruction of metastable states as well as collisional excitation by the residual gas in the storage ring. The results are of great importance for the evaluation of lifetime measurements of metastable states in storage rings. For the states studied in ${\mathrm{Xe}}^{+},$ it was found that neither of the two processes caused systematic errors in the lifetime determination. It is also shown that the method can yield partial cross sections for collisional excitation.

Calculations based on the theory of radiationless resonant Raman scattering are employed in the interpretation of new $\mathrm{Xe}{L}_3{-M}_{4,5}{M}_{4,5}$ Auger spectra recorded using synchrotron radiation tuned to energies across the $L_3$ edge. Fits of theoretical line shapes to the spectra are employed in separating intensities due to $\mathrm{nd}$ spectator (resonant) and diagram Auger processes. Near-threshold Auger intensity, previously attributed to diagram decay, is found to be due to the large$-n$ spectator lines that result from postcollision-interaction–induced “recapture” of threshold photoelectrons to $\mathrm{nd}$ orbitals.

We propose an experiment that exploits the quantum interference between two noninteracting ensembles of spatially degenerate Bose-Einstein atoms to measure phase shifts of atomic coherences at the Heisenberg limit.

We calculate the spectrum of a beam of atoms output from a single-mode atomic cavity. The output coupling uses an internal-state change to an untrapped state. We present an analytical solution for the output energy spectrum from a broadband coupler of this type. An example of such an output coupler, which we discuss in detail, uses a Raman transition to produce a nontrapped state.

A theory of ground-state Ramsey fringes is developed. The fringes are produced when two pulses, time delayed with respect to one another and each consisting of a pair of traveling waves, interact with an ensemble of atoms. Advantages of this technique for meaurements of inertial effects and atomic recoil are discussed.