Positron annihilation on molecules is known to depend sensitively on molecular structure. For example, in the case of hydrocarbon molecules, modest changes in molecular size produce orders of magnitude changes in the observed annihilation rates. Although this process has been studied for more than three decades, many open questions remain. Experimental studies are described which are designed to test specific features of the annihilation process. Two possible mechanisms of the annihilation are considered theoretically: direct annihilation of the positron with one of the molecular electrons, including possible enhancement of this process when low-lying virtual or bound positron-molecule states are present, and resonant annihilation through positron capture into vibrationally excited states of the positron-molecule complex. The dependence of annihilation rates, $\lambda ,$ on positron temperature $T_p$ is studied for the first time for molecules, and at low values of $T_p$ the dependence follows a power law $\lambda \propto T^{-\xi },$ with $\xi \approx \mathrm{0.5.}$ These data are used to test the predictions of direct numerical calculations and theories of the virtual-level enhancement. Partially fluorinated hydrocarbons are studied in order to understand the rapid changes in annihilation rate produced in hydrocarbons as a result of fluorine substitution. These data are compared with the behavior expected due to direct annihilation when there is virtual or bound level enhancement. Measurements of positron annihilation on deuterated hydrocarbons are described which test the dependence of the annihilation on the nature of the molecular vibrations. The relationship of the presently available experimental data for annihilation in molecules to current theories of the annihilation process is discussed.

The aim of this work is to identify the mechanisms responsible for very large rates and other peculiarities observed in low-energy positron annihilation on molecules. The two mechanisms considered are the following: (i) Direct annihilation of the incoming positron with one of the molecular electrons. This mechanism dominates for atoms and small molecules. I show that its contribution to the annihilation rate can be related to the positron elastic scattering cross section. This mechanism is characterized by a strong energy dependence of $Z_{\mathrm{eff}}$ at small positron energies and high $Z_{\mathrm{eff}}$ values (up to ${10}^3)$ for room-temperature positrons, if a low-lying virtual level or a weakly bound state exists for the positron. (ii) Resonant annihilation, which takes place when the positron undergoes resonant capture into a vibrationally excited quasibound state of the positron-molecule complex. This mechanism dominates for larger molecules capable of forming bound states with the positron. For this mechanism $Z_{\mathrm{eff}}$ averaged over some energy interval, e.g., due to thermal positron energy distribution, is proportional to the level density of the positron-molecule complex, which is basically determined by the spectrum of molecular vibrational states populated in the positron capture. The resonant mechanism can produce very large annihilation rates corresponding to $Z_{\mathrm{eff}}\sim {10}^8.$ It is highly sensitive to molecular structure, and shows a characteristic ${\varepsilon }^{-1/2}$ behavior of $Z_{\mathrm{eff}}$ at small positron energies $\varepsilon .$ The theory is used to analyze calculated and measured $Z_{\mathrm{eff}}$ for a number of atoms and molecules.

We have calculated the time-dependent dynamics of two ultracold Na atoms in an atom trap where a time-dependent magnetic field $B\left(t\right)\mathrm{}$ moves a Feshbach resonance state across the energy threshold for a binary collision. Our coupled-channel scattering calculations, which reproduce the observed properties of such resonances in sodium atom collisions, can be reduced to an effective two-channel configuration-interaction model for one bound state and one continuum. The model is adapted to describe the time-dependent dynamics induced by $B\left(t\right)\mathrm{}$ for two atoms trapped either in a strongly confining single well of an optical lattice or in an optical potential in the presence of a Bose-Einstein condensate. We show that a simple Landau-Zener curve crossing model gives quantitative agreement with exact calculations of field-induced transition rates. If $B\left(t\right)\mathrm{}$ sweeps the resonance across threshold from above, two atoms in the ground state of the trap potential can be efficiently converted to translationally cold dimer molecules. If the resonance is swept from below, the atoms can be removed from the ground state and placed in hot vibrational levels of the trap. Our calculations reproduce the rapid atom loss rates observed in a Na Bose-Einstein condensate due to sweeping a Feshbach resonance state through the binary collision threshold.

Our Dirac R-matrix calculations suggest that none of the heavy alkali-metal negative ions, Rb, Cs, and Fr, has an excited bound state. Their lowest excited state appears to be a multiplet of ${}^3{P}_J^o$-shape resonances, the $J=1\mathrm{}$ component of which was recently observed in photodetachment experiments on ${\mathrm{Cs}}^{-}.$ We analyze these ${}^3{P}_J^o$ and the ${}^3{S}^e$ excited negative ion states in partial and converged total scattering cross sections for slow electrons with incident kinetic energies below 120 meV. Our results are in excellent agreement with available experimental data. We also propose a new value for the electron affinity of Fr, provide the scattering length for electronic collisions with Rb, Cs, and Fr, and discuss the nuclear charge dependence of relativistic effects in the resonance profiles.

Ratios of total cross sections for electron-impact ionization and photoionization in Ar, Kr, and Xe in the energy range from 140 to 4000 eV for electrons and from 16 to 1012 eV for photons were measured. Comparatively low relative standard uncertainties of 1.3–1.9 % were achieved using an apparatus combining two recent instrumental developments. The first is associated with a highly accurate device for the determination of soft-x-ray and vacuum-UV photon flux, a cryogenic electrical substitution radiometer. The second is an upgraded ionization chamber for the precise comparison of total-ion yields for electron and photon impact. On the basis of our measured cross-section ratios and well-known total photoionization cross-section data, we deduced absolute total electron-impact ionization cross sections of the rare gases with relative standard uncertainties as low as 2%.

We used channeling through a thin crystal to get an estimate of the cross section of the resonant trielectronic capture by ${\mathrm{Kr}}^{34+}$ ions. K x-ray–$K$ x-ray coincidence measurements were performed with a selection on the charge state and energy loss of transmitted ions. An upper limit of $1.9\times {10}^{-27}\hspace{0.5em}{\mathrm{cm}}^2$ at the resonance is obtained, and this represents an improvement by two orders of magnitude with respect to previous ion-gas experiments. The possibility to reach the theoretical predictions experimentally is discussed.

We describe a theoretical treatment of the exchange contributions in Bethe’s theory of the stopping of electrons. Starting with the first Born approximation, we obtain an expansion in powers of the ratio of the electronic energy of the target atom to the incident electron’s kinetic energy. The binding of the electron within the atom is systematically taken into account, and the leading contribution recovers Bethe’s results. The approach involves the use of sum rules that are generalizations of the Bethe sum rule, specifically dealing with the contributions from electron exchange. Though we restrict our discussion to the stopping power here, the method is quite general and may also be used to find the exchange contributions to other quantities related to cross sections of electron-atom scattering. Our results indicate that there may be significant corrections when one accounts for the binding energy.

The calculated upper limit ${\mathcal{K}}_i^{\mathrm{pol}}<~{10}^{-14}{\mathrm{cm}}^3/\mathrm{s}$ of the rate constant for suppressed ionization in a gas of metastable $\mathrm{Ne}{(}^3{\mathrm{P}}_2)$ atoms in the fully aligned $|{J=2,m}_J=2\mathrm{}〉$ state is used as input to investigate the prospects for achieving Bose-Einstein condensation (BEC). The heating rate of the trap population by secondary collisions of the hot products of the process of ionization—i.e., ground-state atoms, ions, and dimer-ions—with cold trapped metastable atoms is discussed in terms of a semiclassical model. An important step lies in limiting the depth of the magnetic trap to a value of a few millikelvin, to limit the range of small-angle scattering that contributes to heating. Also, a tight radial confinement reduces the probability for secondary collisions. At a trap depth of 10 mK, a radial dimension of $3\mu \mathrm{m},$ and a density of $2\times {10}^{13}{\mathrm{cm}}^{-3}$ the heating rate is $1.4\mu \mathrm{K}/\mathrm{s},$ which should be compared to the transition temperature to BEC of $0.6\mu \mathrm{K}.$ The collisional heating is dominated by ion—metastable-atom collisions, due to their long-range charge-induced dipole interaction. Keeping the evaporative cooling switched on at ${T=T}_C$ reduces the heating a hundredfold. Using a bright beam of laser cooled neon atoms, an initial population of $>~{10}^{10}$ atoms can be loaded into a magneto-optical trap in one second. Tight magnetic traps are easy to achieve for metastable neon atoms, due to their magnetic moment of $3{\mu }_B.$ We conclude that achieving BEC is feasible for metastable neon. This also holds for triplet metastable helium, once the loading rate of traps has been improved. Finally, the semiclassical model used for calculating the heating rate is applicable to a wide range of inelastic collisions in trapped alkali gases and/or collisions with background gas.

We propose a dipole-force linear waveguide which confines neutral atoms up to $\lambda /2\mathrm{}$ above a microfabricated single-mode dielectric optical guide. The optical guide carries far blue-detuned light in the horizontally-polarized TE mode and far red-detuned light in the vertically-polarized TM mode, with both modes close to optical cut-off. A trapping minimum in the transverse plane is formed above the optical guide due to the differing evanescent decay lengths of the two modes. This design allows manufacture of mechanically stable atom-optical elements on a substrate. We calculate the full vector bound modes for an arbitrary guide shape using two-dimensional non-uniform finite elements in the frequency-domain, allowing us to optimize atom waveguide properties. We find that a rectangular optical guide of $0.8\mu \mathrm{m}$ by $0.2\mu \mathrm{m}$ carrying 6 mW of total laser power (detuning $\pm 15\mathrm{nm}$ about the $D2\mathrm{}$ line) gives a trap depth of $200\mu \mathrm{K}$ for cesium atoms ${(m}_F=0),$ transverse oscillation frequencies of $f_x=40\mathrm{}\mathrm{kHz}$ and $f_y=160\mathrm{}\mathrm{kHz},$ collection area $\sim 1\mu {\mathrm{m}}^2$ and coherence time of 9 ms. We discuss the effects of non-zero $m_F,$ the $D1\mathrm{}$ line, surface interactions, heating rate, the substrate refractive index, and the limits on waveguide bending radius.

The process of laser-assisted resonance-energy transfer (LARET) is described and analyzed within the framework of molecular quantum electrodynamics. LARET is a higher-order perturbative contribution to the familiar spontaneous dipole-dipole mechanism for resonance-energy transfer, in which an auxiliary laser field is applied specifically to stimulate the energy transfer. The frequency of the auxiliary beam is chosen to be off-resonant with any molecular transition frequencies in order to eliminate direct photoabsorption by the interacting molecules. Here consideration is given to the general case where the energy exchange takes place between two uncorrelated molecular species, as for example in a molecular fluid, or a system in which the molecules are randomly oriented. In the ensuing calculations it is necessary to implement phase-weighted averaging in tandem with standard isotropic averaging procedures. Results are discussed in terms of a laser intensity-dependent mechanism for energy transfer. Identifying the applied field regime where LARET should prove experimentally significant, transfer rate increases of up to 30% are predicted on reasonable estimates of the molecular parameters. Possible detection techniques are discussed and analyzed with reference to illustrative models.

We propose simple experiments in cavity quantum electrodynamics leading to the generation and detection of highly squeezed states of the electromagnetic field, even in the presence of experimental constraints like dissipation, atomic velocity spread, and detection inefficiency. Our proposal gives an operational meaning to the rotational and translational widths of a squeezed state.

Calculations of the photoionization cross section for the atomic iodine atom and its ions ${\mathrm{I}}^{\mathrm{-}}$ and ${\mathrm{I}}^{2+}$ using the random-phase approximation with exchange are performed in a broad photon energy range from 40 to 136 eV. A significant (factor of 3) difference between recent experimental data and our theoretical results is found in the region dominated by the giant resonance from the $4d$ subshells. Sum-rule analysis suggests that the experimental situation requires reexamination.

We have observed sustained self-pulsing in a continuously pumped, triply resonant, optical parametric oscillator. From the analysis of our experimental data, we conclude that the instability mechanism is different from the Hopf bifurcation predicted by the classical model of parametric interaction. Self-pulsing results from the interplay of a slow variable (temperature) and the optical bistability cycle, leading to a singularly perturbed system. From simple arguments, we propose a minimal dynamical model that reproduces well the observed behaviors.

Positive-operator-valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a $\mathrm{SU}\mathrm{}(2J+1)\mathrm{}$ covariant constraint. This representation allows for a simple description of the equations to be fulfilled by optimal measurements. We explicitly find the minimal positive-operator-valued measurement for the $N=2\mathrm{}$ case, a rigorous bound for $N=3,$ and set up the analysis for arbitrary N.

The Bell theorem for a pair of two-state systems in a singlet state is formulated for the entire range of measurement settings.

An approximate perturbative method is developed to calculate the corrections to the Casimir force between an isolated atom and a cavity wall due to surface roughness. The results are obtained up to the fourth order in the relative roughness amplitude. All possible types of surface roughness are considered: large scale, short scale, and intermediate, defined by the ratio of the characteristic lateral length scale of roughness to the atom-wall distance. A continuous transition between the corrections due to different types of roughness is carried out. It is shown that the large-scale roughness can lead to corrections of the order of 70% of the net Casimir force. In the cases of large-scale and intermediate-type roughness the lateral Casimir force comes into play, which leads to moving the atom to the nearest extreme point of the vertical force with subsequent dying out oscillations in its vicinity. Possible role wall roughness can play in some phenomena of cavity electrodynamics is discussed.

We propose a protocol where one can exploit dual quantum and classical channels to achieve perfect “cloning” and “orthogonal-complementing” of an unknown state with minimal assistance from a state preparer (without revealing what the input state is). The first stage of the protocol requires usual teleportation, and in the second stage the preparer disentangles the leftover entangled states by a single-particle measurement process and communicates a number of classical bits (1-cbit per copy) to different parties so that perfect copies and complement copies are produced. Our protocol produces clones and complement clones of unknown qubit each with a probability $\frac{1}{2}$ and clones of real qubit with unit probability.

A quantum key distribution scheme based on the use of squeezed states is presented. The states are squeezed in one of two field quadrature components, and the value of the squeezed component is used to encode a character from an alphabet. The uncertainty relation between quadrature components prevents an eavesdropper from determining both with enough precision to determine the character being sent. Losses degrade the performance of this scheme, but it is possible to use phase sensitive amplifiers to boost the signal and partially compensate for their effect.

We formulate the semiclassical close-coupling method for a theoretical description of ion-pair formation in Rydberg-atom–ground-state-atom collisions at thermal energies and apply it to the process $\mathrm{Ca}{(4s}^2)+{\mathrm{Ne}}^{*}\mathrm{}(n)\mathrm{}\to {\mathrm{Ca}}^{-}{(4s}^{2}4p)+{\mathrm{Ne}}^{+}.$ Our results for the formation of an isolated negative-ion state are very close to those obtained previously using the decay model, although the results for S states are somewhat higher, since the decay model underestimates the survival probability for the ion pair. After the inclusion in our close-coupling calculations of the two fine-structure components of ${\mathrm{Ca}}^{-},$ we find that the cross section increases substantially (by about a factor of 2) because of correlation between probabilities for population of two fine-structure sublevels.

We have experimentally observed the time dependence of the population oscillation between a doubly excited state and singly excited Rydberg states subsequent to excitation by a short laser pulse. Specifically, we have examined the case in which the configuration interaction between a doubly excited state and a singly excited Rydberg series is weak. The data are quantitatively reproduced using a quantum defect theory calculation, and we contrast simple classical pictures of the population oscillation for weak and strong configuration interaction. We also observe significant, and unexpected, Raman redistribution by the final laser pulse, and we are able to demonstrate that it occurs primarily by Raman transitions via a lower state, not via the continuum.