An exact reduced-density-operator for the output quantum states in time-convolutionless form was derived by solving the quantum Liouville equation which governs the dynamics of a noisy quantum channel by using a projection operator method and both advanced and retarded propagators in time. The formalism developed in this work is general enough to model a noisy quantum channel provided specific forms of the Hamiltonians for the system, reservoir, and the mutual interaction between the system and the reservoir are given. Then we apply the formulation to model a two-bit quantum gate composed of coupled spin systems in which the Heisenberg coupling is controlled by the tunneling barrier between neighboring quantum dots. Gate characteristics, including the entropy, fidelity, and the purity, are calculated numerically for both mixed and entangled initial states.

An alternative quantum algorithm for combinatorial search, adjusting amplitudes based on number of conflicts in search states, performs well, on average, for hard random satisfiability problems near a phase transition in search difficulty. The algorithm exploits correlations among problem properties more effectively than some current heuristics, and improves on prior quantum algorithms that ignore these correlations.

We analyze the bound states of negatively charged ions that were predicted to exist because of the presence of a magnetic field by Avron et al. [Commun. Math. Phys. 79, 529 (1981)]. We confirm that the number of such states is infinite in the approximation of an infinitely heavy nucleus and provide insight into the underlying physical picture by means of a combined adiabatic and perturbation theoretical approach. We also calculate the corresponding binding energies that are qualitatively different for the states with vanishing and nonvanishing angular momentum. An outlook on the case of including center-of-mass effects is presented.

A method for the calculation of logarithmic sums that yields very high accuracy even for small basis-set dimensions is introduced. The best values achieved are accurate to 23 significant figures without extrapolation. The sums are performed directly on variational intermediate sets. The method automatically rejects any basis functions that could introduce linear dependence, therefore guaranteeing high numerical stability for a wide range of nonlinear parameters. Accurate values for the ordinary and a higher-order version of the Bethe logarithm are presented for a range of energy states and angular momenta. Given that the intermediate basis functions are increasingly confined to extremely small distances from the origin, a discussion of finite nuclear-size effects is given. The contribution to the sums from states with extremely high energies, orders of magnitude larger than the electron rest mass, is discussed.

The principles of the quantum theory of open systems are used to calculate the collisional relaxation parameters of the ground rotational transition for a dipole molecule. The conditions for a microwave-field saturation of the rotational transition are specified taking into account degeneracy of the excited state. A simple quantum model is used to illustrate the idea of rigorous substantiation of the second law of thermodynamics.

The improvements in the characterization of II-VI compound-based solar cells and the recent experimental characterization of small clusters and nanoparticles make the study of small II-VI clusters very interesting. In this work, the ground states of small ${\mathrm{Zn}}_i{\mathrm{S}}_i$ clusters are studied, $i=1\mathrm{}–9.$ Ringlike structures have been found to be the global minima in the case of the smaller studied clusters, i.e., $i=1\mathrm{}–5,$ and three-dimensional spheroid structures for larger ones, $i=6\mathrm{}–9.$ This is due to the stability of obtuse $\mathrm{S}\mathrm{—}\mathrm{Zn}\mathrm{—}\mathrm{S}$ angles in the first case, and to the stability gained from higher coordination in the second case. The three-dimensional structures may be envisioned as being built from ${\mathrm{Zn}}_2{\mathrm{S}}_2$ and ${\mathrm{Zn}}_3{\mathrm{S}}_3$ rings, the last ring being the building block of the zinc-sulfide crystal structures, both zinc blende and wurtzite. As cluster size increases, the geometry of the ${\mathrm{Zn}}_3{\mathrm{S}}_3$ rings is closer to the one of bulk. Moreover, this structural tendency produces trends to bulklike properties in other properties such as cohesive energy and atomic charges.

The frequency dependence of the dipole polarizability $\alpha \left(\omega \right)$ of ${\mathrm{P}}_4$ is obtained from refractive index measurements on gaseous phosphorus by means of asymmetric white-light interferometry. The experimental results obtained in the range between 10 000 and 30 300 ${\mathrm{cm}}^{\mathrm{-}1}$ yield an extrapolated static value of $\alpha {=91.71\mathrm{}\left(92\right)e}^2{a}_0^2{E}_H^{-1}.$ An extensive theoretical study, based on finite-field many-body perturbation theory and coupled cluster methods, leads to a theoretical estimate at zero frequency of $\alpha \approx 93.2\left(0.9\right)\mathrm{}\hspace{0.5em}{e}^2{a}_0^2{E}_H^{-1}$ at the experimental bond length $R_0=2.1958\mathrm{}$ Å. For the symmetric stretch of the molecule the dipole polarizability of ${\mathrm{P}}_4$ varies around $R_0$ as $\left[\alpha \mathrm{}\right(R\left)\mathrm{}-\alpha {(R}_0\right)]{/e}^2{a}_0^2{E}_H^{-1}=34.02\mathrm{}\Delta R+3.68\mathrm{}\Delta R^2-0.29\Delta R^3$ showing an essentially linear dependence on the change of the P–P bond distance $\Delta R\equiv (R-R_0{)/a}_0.$ The dipole polarizability per atom is significantly smaller than that of the phosphorous atom 25.22 $e^2{a}_0^2{E}_H^{-1}.$ This differs from the corresponding change of $\alpha$ in the homologous ${\mathrm{As}}_4$ cluster, where the single atom value is very close to the polarizability per atom of the cluster.

We have constructed a magneto-optical trap for chromium atoms. Using trapping light at 425 nm and two repumping lasers tuned to intercombination transitions, over ${10}^6$ atoms were trapped and average densities of over ${10}^{16}{\mathrm{m}}^{\mathrm{-}3}$ were obtained. Nonexponential loss of atoms is observed at high densities indicating inelastic collisions between trapped atoms. Over a range of trapping conditions, the density-dependent trap loss rate constant β is extracted from fluorescence decay curves and found to have values in the range of ${10}^{-15}{\mathrm{m}}^3{\mathrm{}\mathrm{s}}^{\mathrm{-}1},$ much larger than is observed in alkali-metal traps.

We have studied the expansion of a bright rubidium three-dimensional optical molasses realized with an intense laser light. In this regime, in addition to the laser friction force, the atoms strongly repel each other due to the radiation trapping force, which is analogous to the Coulomb force. The experimental observations show that the cloud volume increases linearly in time and that, simultaneously, the cloud temperature decreases following the law $(1+t/\tau {)}^{-4/3}.$ These time evolutions are explained using a physical picture of Coulomb explosion in a viscous medium.

High-order harmonic generation from the interaction of high-intensity femtosecond laser pulses with the organic molecules benzene and cyclohexane has been observed using laser pulses of 240 and 70 fs duration at wavelengths around 800 nm. Harmonic intensities were measured as a function of laser intensity in the range $4\times {10}^{13}–5\times {10}^{15}{\mathrm{W}\mathrm{}\mathrm{cm}}^{\mathrm{-}2},$ of laser polarization, and of the density of the medium. Harmonics from the 7th to the 13th order were found to have comparable intensities with those produced by xenon at the same density. The 7th harmonic from cyclohexane was measured to be four times more intense than that from xenon. No saturation of this harmonic was observed in cyclohexane up to a peak intensity of $2\times {10}^{15}{\mathrm{W}\mathrm{}\mathrm{cm}}^{\mathrm{-}2},$ in contrast with xenon, where saturation was seen above $8\times {10}^{14}{\mathrm{W}\mathrm{}\mathrm{cm}}^{\mathrm{-}2}.$ These results are related to previous studies of ionization and fragmentation of these molecules in the same intensity range. The role of resonances between harmonics and high-lying molecular states is discussed.

Measurements of stimulated Raman gain in rubidium vapor are made and compared with a detailed model. Amplification of a weak probe laser is observed in a Λ-type three-level system that is driven by a strong cw coupling laser. The intensity of the coupling laser is sufficiently strong that it both optically pumps the atomic levels, causing a population inversion in the ground-state hyperfine levels, and drives the stimulated Raman process producing gain. A theory that models all aspects of the gain mechanism is presented. The model includes all interactions between the external fields and the atomic transitions, including those processes that involve multiple fields interacting with the same transition. Numerical calculations are compared with gain measurements made at several coupling laser intensities and detunings from the $D1\mathrm{}$ line in ${}^{85}\mathrm{Rb}.$

We study spontaneous emission in an atomic ladder system, with both transitions coupled near resonantly to the edge of a photonic band gap continuum. The problem is solved through a recently developed technique and leads to the formation of a two-photon $+$ atom bound state with fractional population trapping in both upper states. In the long-time limit, the atom can be found excited in a superposition of the upper states and a direct two-photon process coexists with the stepwise one. The sensitivity of the effect to the particular form of the density of states is also explored.

We investigate the transient response of a $\Lambda$-type system with one transition decaying to a modified radiation reservoir with an inverse square-root singular density of modes at threshold, under conditions of transparency. We calculate the time evolution of the linear susceptibility for the probe laser field and show that, depending on the strength of the coupling to the modified vacuum and the background decay, the probe transmission can exhibit behavior ranging from underdamped to overdamped oscillations. Transient gain without population inversion is also possible depending on the system’s parameters.

We measure the suppression of Penning ionization in an ultracold $\mathrm{He}\left(2\mathrm{}{}^3{\mathrm{S}}_1\right)$ atomic cloud after spin-polarizing the atoms by optical pumping in a small magnetic field. An upper limit of $6\times {10}^{-12}\hspace{0.5em}{\mathrm{cm}}^3/\mathrm{s}$ for the ionization rate constant is deduced, at least a factor 20 lower than measured in an unpolarized gas.

The Airy gas model is used to derive an expression for the local kinetic energy in the linear potential approximation. The expression contains an explicit Laplacian term $\frac{2}{5}({ħ}^2/2m){\nabla }_{\mu }^2\left(\mathbf{r}\right)$ that, according to jellium surface calculations, must be a universal feature of any accurate local description. Applied to the noble gases the expression reduces the errors by a factor of $50$ over previous results obtained by the linear potential approximation.

The $K\alpha$ x-ray emission spectra of Ca, Ti, Cr, and Fe targets bombarded by 2–19-MeV/amu C, O, and Ne ions were measured by means of high-resolution crystal diffractometry. The ${\mathrm{KL}}^N$ x-ray satellite lines appearing in these spectra as a result of the radiative decay of atomic states with one hole in the K shell and N in the L subshells could be resolved, and their relative intensities determined. The latter were corrected to account for the intra-atomic rearrangement processes preceding the K x-ray emission. From the values obtained the heavy ion induced L-shell vacancy distribution was then deduced for each collision. Significant deviations from the binomial distribution were observed. The discrepancies could be slightly diminished by assuming that the L-shell vacancy production is due to two uncorrelated processes: direct Coulomb ionization and target L-shell electron capture into the projectile K shell. A new ${\mathrm{KL}}^N$ vacancy yield distribution model based on statistical considerations was built, which takes into account both mechanisms of vacancy production. The average direct L-shell ionization probabilities per electron related to the investigated collisions were determined by fitting this distribution to the corrected experimental L vacancy yields, employing results of three-body classical trajectory Monte Carlo (CTMC) calculations for the electron capture probabilities. The so-obtained direct ionization probabilities were found to be somewhat smaller than the ones deduced from the standard binomial distribution, especially in low-energy collisions for which electron capture is more important. It was furthermore observed that CTMC calculations significantly overestimate the direct ionization probabilities found in the present experiment. To a smaller extent, the same holds for the geometrical model predictions, whereas theoretical results from the semiclassical approximation model were found to reproduce the experimental data better.

Electron-impact ionization cross sections for ${\mathrm{Li}}^{+}$ are calculated using the $R$ matrix with pseudostates method and time-dependent close-coupling theory. The largest $R$-matrix calculation includes 11 spectroscopic states from the configurations ${1s}^2,$ $1s2l,$ and $1s3l;$ an additional 56 pseudostates from the configurations $1s\mathrm{n̄}l$ with $\mathrm{n̄}=4\mathrm{}–10$ and $l=0\mathrm{}–3;$ and enough continuum orbitals to adequately describe incident energies up to 175 eV. The largest time-dependent close-coupling calculations involved 16 partial differential equations on a $300\times 300$ point radial lattice. The nonperturbative $R$ matrix with pseudostate and time-dependent close-coupling calculations, as well as perturbative distorted-wave calculations, are in good agreement with the crossed-beams experimental measurements of Lineberger et al. [Phys. Rev. 141, 151 (1966)], but are slightly above the Peart and Dolder [J. Phys. B 2, 872 (1968)] and Müller et al. [Phys. Rev. Lett. 63, 758 (1989)] measurements.

We have applied the methods of quantum reactive scattering to the key resonant reaction in the muon catalyzed fusion (MCF) cycle that leads to the formation of a $\mathrm{dt}\mu$ muonic molecular ion, in which fusion takes place very rapidly. We have calculated reaction probabilities for the resonances that occur in $t\mu +{\mathrm{D}}_2$ scattering for incident kinetic energies less than 0.6 eV and total angular momentum $J_{\mathrm{tot}}=0.\mathrm{}$ To reduce the six-body problem to a three-body problem, the motions of the electrons were treated in the Born-Oppenheimer (BO) approximation while those of the muon were treated with a sophisticated adiabatic approximation. The resulting three-body potential energy surface (PES) was represented by a pairwise additive approximation. The $\mathrm{dt}\mu$ part of the PES was scaled to allow it to exhibit the correct binding energy of the crucial $\mathrm{}(J,v)=(1,1)\mathrm{}$ state. Scattering calculations were carried out using a hyperspherical formulation, and the positions of the resonances were found to occur at energies of a few meV greater than if $\mathrm{dt}\mu$ is assumed to be a point particle. A comparison of the resonances with the Breit-Wigner formula allowed us to calculate partial widths for back decay, ${\Gamma }_e^{J_{\mathrm{tot}}}.$ Once these are known for all significant $J_{\mathrm{tot}},$ the rate of formation of $\mathrm{dt}\mu$ can be determined. This rate, next to the sticking fraction, is the most important parameter in determining the rate of the entire MCF cycle. We have also carried out a calculation whereby the muon was treated in a BO formalism and have found significant differences in the final results, demonstrating the importance of treating the muon as accurately as possible. This work represents a successful ab initio calculation of this reaction.

Elastic photon scattering from the ground state and various excited states of carbon atoms and ions has been investigated, using the S-matrix formalism, for incident photon energies ranging from 100 eV to 10 keV, contrasting the results obtained for different configurations. The excited states considered include hollow-atom states, where one or more inner shells are completely vacated. Ionic cases are considered as a limit of excitation. Results demonstrate how cross sections for different excited states group together according to shared properties of the configurations, such as the number of K electrons. Cross sections may exhibit deep dips below the K edge, depending on the occupation of the subshells corresponding to the strongest transitions. Scattering from excited states can have significantly larger cross sections than scattering from the ground state, particularly just below the K resonance region, and therefore it needs to be considered in situations where there is a large population of these excited states. Results are interpreted in terms of form-factor arguments and the qualitative behavior of individual subshell amplitudes. The angular dependence of cross sections can be understood in terms of angle-dependent form factors and anomalous scattering factors, taken to be angle independent. Cases are identified for which excited-state total integrated cross sections are much larger than the corresponding cross sections for scattering from the ground state. Our main results use an averaging over magnetic substates at the level of the amplitude, exact only for fully filled subshells, but generally appropriate for the carbon case considered, which simplifies the discussion and explains most of the general features. We also present results for a hollow lithium atom with and without this approximation to illustrate the differences that can arise in certain circumstances.

We calculate the phase diagram for dilute mixtures of bosons and fermions at zero temperature. The linear stability conditions are derived and related to the effective boson-induced interaction between the fermions. We show that in equilibrium there are three possibilities: (a) a single uniform phase, (b) a purely fermionic phase coexisting with a purely bosonic one, and (c) a purely fermionic phase coexisting with a mixed phase.