Rate coefficients and absolute cross sections for center-of-mass energies between 0.0001 and 1 eV are reported for both resonant ion-pair formation and dissociative recombination in electron collisions with ${\mathrm{HF}}^{+}$ ions. The heavy-ion storage ring CRYRING in Stockholm was used for these measurements. Notable is the fact that the dissociative recombination cross section is substantially smaller than that for most diatomic molecular ions. The recombination seems to have an underlying $E^{-1}$ energy dependence characteristic of the direct process in dissociative recombination, but both cross sections show structure, which may be attributed to contributions from different indirect processes. The cross sections have no observable energy thresholds. The ratio of the cross section for resonant ion-pair formation to that for dissociative recombination is about 0.25 at ${10}^{-3}$ eV, with the ratio depending on the interaction energy, so the competition of the ion-pair process is much stronger than for other ions so far studied. The ${\mathrm{HF}}^{+}$ ion is unique in the fact that the electron affinity of F, the binding energy of ${\mathrm{HF}}^{+},$ and energy of the atom pair $\left[\mathrm{H}\mathrm{}\right(n=2\mathrm{})+\mathrm{F}{(}^2{P}_{3/2})]$ are the same within the rotational-energy spread of the ${\mathrm{HF}}^{+}$ target. The resonant ion-pair formation process, $e+{\mathrm{HF}}^{+}\to {\mathrm{H}}^{+}+{\mathrm{F}}^{-},$ has some similarities to the photon process, $h\nu +\mathrm{HF}\to {\mathrm{H}}^{+}+{\mathrm{F}}^{-},$ and we discuss comparisons. We deduce thermal rate coefficients from our measurements and discuss them in the context of rate coefficients for other diatomic ions available in the literature.

The rotational eigenvalues of isotopically substituted hydrogen molecules adsorbed into single-walled carbon nanotubes are calculated using a semiclassical method and using a model potential. The resulting eigenvalues are used to calculate the separation factors due to rotational confinement between different isotopic species as a function of temperature and nanotube size. The results show that even for small shifts in the eigenvalues, significant fractionations should occur, suggesting possible application as an isotope-separation technique.

The effective integral collision cross section of small water cluster molecules, $[{\mathrm{H}}_2\mathrm{O}{]}_N,$ with N from 4 to 8, has been measured. A controlled mixture of water vapor and argon, expanding into vacuum, produces neutral water clusters in a supersonic molecular beam. The clusters undergo collisions in a scattering cell with target gases Ar, He, or ${\mathrm{N}}_2,$ and are detected by a quadrupole mass spectrometer after electron-impact ionization. The detected cluster ions are in the form of proton hydrates ${\mathrm{H}}^{+}[{\mathrm{H}}_2\mathrm{O}{]}_K.$ The apparent cross sections determined from attenuation measurements are approximately of $3\times {10}^{-18}{\mathrm{m}}^2$ for Ar and ${\mathrm{N}}_2$ target gases, and ${10}^{-18}{\mathrm{m}}^2$ for He. Additional data, with a beam having a smaller proportion of heavy clusters gives the same cross section for attenuation of the $K=3\mathrm{}$ cluster, which suggests that there one dominant channel for the generation of ions from clusters.

Our recent analysis [J. Phys. B 33, R141 (2000)] of the problem of ${\mathrm{H}}^{-}$ in both laser and strong static electric fields, which treated effects that are linear in the laser intensity I (e.g., the dynamic polarizability and the single-photon detachment cross section), is extended here to treat effects of higher order $\left(\sim I^2\right)$ in the laser intensity (e.g., the dynamic hyperpolarizability, the two-photon detachment cross section, the linear in I corrections to the single-photon detachment rate, etc). We introduce the concept of the dynamic hyperpolarizability of an atom in the presence of a strong electric field based on the complex quasienergy approach with properly normalized, quasistationary quasienergy wave functions. Our analysis of the general structure of the dynamic hyperpolarizability tensor of an atom in a nondegenerate $(S$-) state is performed for arbitrary field geometries and laser polarizations. The connection of the hyperpolarizability $\gamma (\mathcal{F};\omega )$ to the complex quasienergy and to atomic ionization rates is established. Analytic results (in terms of Airy functions) are obtained for five irreducible components of a hyperpolarizability tensor (that are independent of the laser polarization and the field geometry) for the case of a weakly bound electron in a three-dimensional, zero-range potential. These results are used for the analysis of the frequency, field geometry, and laser polarization dependence of the two-photon detachment rate as well as of the linear in laser intensity corrections to the single-photon detachment rate. It is shown that the oscillatory behavior of the frequency dependence of both the real and the imaginary parts of $\gamma (\mathcal{F};\omega )$ exists for both the coplanar and orthogonal field geometries, and that this behavior is qualitatively different for frequencies below and above the single-photon detachment threshold. The threshold behavior of the two-photon detachment rate is analyzed in detail and the static electric-field-induced modification of Wigner’s threshold law for a short-range potential is discussed.

We study the process of four-wave mixing (FWM) in ultracold degenerate atomic gases. In particular, we address the problem of FWM in boson-fermion mixtures. We develop an approximate description of such processes using asymptotic analysis of high-order perturbation theory taking into account quantum statistics. We perform also numerical simulations of FWM in boson-fermion mixtures and obtain an analytic and numerical estimate of the efficiency of the process.

Superfluid suppression of the elastic scattering loss in atomic Bose condensed systems can be significant when the ratio of the relative velocity of the wave packets to the critical velocity is $\sim 1.$ We show how to incorporate the effect of such losses and their suppression into the time-dependent dynamics of two colliding condensate wave packets. We illustrate the magnitude of the effect through three-dimensional simulations of the collision dynamics of an $|F=2,M_F=2\mathrm{}〉$ with an $|F=2,M_F=1\mathrm{}〉{}^{87}\mathrm{Rb}$ condensate in a harmonic trap, as studied in a recent experiment [Maddaloni et al., Phys. Rev. Lett. 85, 2413 (2000)]. These calculations show that the effect of elastic scattering and its suppression should be seen in the oscillatory center-of-mass amplitude of the $M_F=1\mathrm{}$ wave packet for suitable experimental conditions.

Phase-sensitive amplification in a three-level atomic system exhibits interesting features. For example, in the zero-detuning limit and for sufficiently strong driving field, this system becomes an ideal parametric amplifier, whereas, for a weak driving field it is a phase-insensitive amplifier [Ansari et al., Phys. Rev. A 41, 5179 (1990)]. In this paper, we show that this system could be used to measure the quantum state of the radiation field inside a cavity. To reconstruct the quantum state, we amplify it through a three-level atomic system and in the parametric limit, when noise in both the quadratures approaches to zero measure the amplified field quadrature. The complete quadrature distribution is obtained by measuring the quadratures for different values of the driving field phases. The inverse Radon transformation is then employed to reconstruct the original quantum state. Our scheme is insensitive to the problems associated with nonunit detector efficiency in homodyne detection measurement.

Stimulated rotational and vibrational Raman scattering is investigated with a XeCl excimer laser by varying either the ellipticity degree of the pump radiation polarization and the pump beam quality factor ${(M}^2)$ and divergence (θ). It is shown that the dependence of stimulated rotational Raman scattering upon pump radiation polarization is substantially influenced by the optical properties ${(M}^2$ and θ) of the pump beam. Gain suppression effects on stimulated vibrational Raman scattering and their dependence on pump beam optical properties have been evaluated to support experimental results. Introducing the effective vibrational Raman gain provides a good understanding of the experimental results.

We discuss the dynamics of a quantum vacuum in a one-dimensional cavity formed by two ideal mirrors: one fixed, the other moving. A nonrelativistic equation of motion is found for the wall that self-consistently determines the wall position and the evolution of the quantum field. This equation is applied to a system with an external potential chosen so that the mirror oscillates at a resonant frequency of the cavity. It is found that this system has an evolutionary cycle during which energy is transferred back and forth between the cavity field and the wall. During the first and third phases of the cycle, energy is transferred from the wall to the cavity; wave packets form in the field as the wall motion decays. During the second and fourth phases, energy is transferred from the field to the wall. The wave packets disperse, providing an impetus for the waxing wall motion.

Relaxation of $\mathrm{O}{(}^3{P}_{j=0\mathrm{}})$ by collisions with He at ultracold temperatures is investigated, and it is illustrated that cross sections and rate constants for the $j=\overrightarrow{0}j=2\mathrm{}$ and $j=\overrightarrow{0}j=1\mathrm{}$ transitions exhibit qualitatively different threshold behaviors stemming from the different mechanisms of these nonadiabatic transitions. The results allow us to make the conclusion that, in general, rate constants for the nonadiabatic transitions governed by electrostatic couplings should obey Wigner’s threshold law for s-wave scattering approaching a finite value at $\overrightarrow{T}0\mathrm{K},$ while cross sections and rate constants for the transitions determined by Coriolis couplings should vanish in the zero-temperature limit.

We analyze the problem of quantum data compression of commuting density operators in the visible case. We show that the lower bound for the compression factor given by the Levitin-Holevo function is reached by providing an explicit protocol.

We discuss the estimation of channel parameters for a noisy quantum channel—the so-called Pauli channel—using finite resources. It turns out that prior entanglement considerably enhances the fidelity of the estimation when we compare it to an estimation scheme based on separable quantum states.

We present a nonlocal construction of universal gates by means of holonomic (geometric) quantum teleportation. The effect of the errors from imperfect control of the classical parameters, the looping variation of which builds up holonomic gates, is investigated. Additionally, the influence of quantum decoherence on holonomic teleportation used as a computational primitive is studied. Advantages of the holonomic implementation with respect to control errors and dissipation are presented.

Using two-dimensional photoelectron spectroscopy, relative partial photoionization cross sections of all accessible Auger decay channels have been measured in the vicinity of the $\mathrm{Ar}\hspace{0.5em}{2p}^{-1}3d$ resonances. Significant asymmetric resonance profiles are observed, which mirror each other in their asymmetric features, giving symmetric Lorentzian profiles for the total photoionization cross section. This indicates that interference between direct photoionization and resonant photoexcitation autoionization needs to be taken into account in order to accurately describe partial photoionization cross sections, despite the absence of asymmetric features in the total cross section.

Using recoil-ion momentum spectroscopy, combined with a multihit detector system, the full momentum vectors of both fragment ions produced by fragmentation of ${\mathrm{D}}_2$ by fast 50-kV protons and slow (9.56–0.191 keV/u) ${\mathrm{Xe}}^{26+}$ ions have been measured. The data are kinematically complete, and make it possible to separate the laboratory momentum of the center of mass of the molecule from the momentum of each fragment in the center-of-mass system of the molecule. Using this separation, we find that, for higher collision velocities, the overall reaction can be described as double-electron capture, followed in a second and separate step by a Coulomb explosion of the doubly charged ${\mathrm{D}}_2$ molecule. For the lowest collision velocities, however, the projectile remains in the vicinity of the molecule during the fragmentation, and this clean separation of steps is lost. The projectile is found to extract internal energy from the molecule, thus leading to less energetic fragments in the center-of-mass system of the molecule. This effect causes a distortion in the spherical momentum images, as shown by the two-dimensional momentum distributions in the collision plane. The experimental results are found to be in good agreement with five-body classical trajectory Monte Carlo calculations.

Contrary to well-established recent theoretical results based on second-order Moller-Plesset perturbation theory, it is illustrated here that the distorted octahedron of $D_{4h}$ symmetry cannot be the ground state of the “magic” ${\mathrm{Si}}_6$ cluster, but a transition state, connecting two almost isoenergetic structures of lower symmetry, which can coexist. This conclusion, the consequences of which could be far reaching for other magic clusters, is based on higher-order perturbation theory, accurate coupled-cluster CCSD(T) calculations and density-functional theory at the hybrid B3LYP level. The discrepancy is due to the poor convergence of the perturbation expansion, related to the flatness of the energy hypersurface near the minimum. As a result, the structural and electronic properties of ${\mathrm{Si}}_6$ are still not well understood, although several suggestions are put forward here.

We present a proposal for implementing quantum phase gates using selective interactions. We analyze selectivity and the possibility to implement these gates in two particular systems, namely, trapped ions and cavity QED.

We study the Aharonov-Casher effect and its electromagnetic-dual effect, introduced by He, McKellar, and Wilkens, in $2+1$ dimensions. In this restricted space these effects are the result of the interaction of the electromagnetic field tensor with the dual of a current. Transferring the dual operation from the current to the field tensor shows that this interaction may be reinterpreted as due to the interaction of an effective vector potential and a current, and the topological effects follow immediately. The restriction to $2+1$ dimensions, with this interpretation, provides a unified way of treating these topological effects for an arbitrary spin, and a general proof for this case is provided. Perhaps more interestingly the treatment shows that a spin-0 particle can show these effects, although it has no magnetic or electric dipole moment in the usual sense.

In a standard Grover’s algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this paper we present a modified version of Grover’s algorithm that searches a marked state with full successful rate. The modification is done by replacing the phase inversion by phase rotation through angle $\phi .$ The rotation angle is given analytically to be $\phi =2\mathrm{}\arcsin \left(\sin \right[\pi /(4J+6)\mathrm{}]/\sin \beta ),$ where $\sin \beta =1/\sqrt{N},$ N is the number of items in the database, and J is any integer equal to or greater than the integer part of $\left[\right(\pi /2\left)-\beta \right]/\left(2\mathrm{}\beta \right).\mathrm{}$ Upon measurement at the $\mathrm{}(J+1\mathrm{})\mathrm{}\mathrm{th}$ iteration, the marked state is obtained with certainty.

The C $1s$ and O $1s$ excitation of formaldehyde $\left({\mathrm{H}}_2\mathrm{CO}\right)$ has been studied within an ab initio framework. The second-order algebraic-diagrammatic construction [ADC(2)] polarization propagator method has been used to calculate energies and oscillator strengths of the electronic transitions. For selected C $1s$ excited states also multireference configuration-interaction (MRCI) calculations were performed. The vibrational excitations accompanying the electronic transitions have been studied using a linear vibronic coupling model. The theoretical C $1s$ and O $1s$ spectra are in excellent qualitative agreement with high-resolution K-shell photoabsorption measurements. The present results support the previous assignments of the C $1s$ spectrum, while they revise the interpretation of the O $1s$ spectrum above 537 eV. In contrast to the C $1s$ case, the main photoabsorption intensity in the O $1s$ spectrum is due to nd rather than to np Rydberg excitations. For the two lowest singlet excited states, that is, the ${}^1{B}_1\left(\mathrm{C}1\overrightarrow{s}{\pi }^{*}\right)$ single excitation and the ${}^1{B}_2(\mathrm{C}1s,\overrightarrow{n}{\pi }^{*2})$ double excitation, we find vibronic interaction with the ${}^1{A}_1\left(\mathrm{C}1\overrightarrow{s}3s\right)$ and ${}^1{A}_2\left(\mathrm{C}1\overrightarrow{s}3d\right)$ Rydberg states via the ${\nu }_4$ out-of-plane bending mode. In addition, the ${}^1{B}_2(\mathrm{C}1s,\overrightarrow{n}{\pi }^{*2})$ and the ${}^1{A}_1\left(\mathrm{C}1\overrightarrow{s}3s\right)$ states interact via the ${\nu }_5$ mode. The vibronic coupling leads to a complex spectral pattern in the low-energy part of the C $1s$ excitation spectrum, allowing one to interpret the finer details of the experiment.