The effects of the solid-state heterostructure environment on the properties of embedded qubits are investigated. An electric dipole emitter in the form of an $F$ center has recently been used as the qubit for quantum information processing and, possibly, quantum computing. Modeled here in terms of an isotropic three-dimensional harmonic oscillator localized in a dielectric, we show that it experiences level shifts due to its proximity to a metallic contact plane. Appropriate parameters are used to model a nitrogen $F$ center localized in diamond within nanometer distances from a metallic surface.

Due to their collective nature Casimir forces can strongly depend on the geometrical shape of the interacting objects. We study the effect of strong periodic shape deformations of two ideal metal plates on their quantum interaction. A nonperturbative approach which is based on a path-integral quantization of the electromagnetic field is presented in detail. Using this approach, we compute the force for the specific case of a flat plate and a plate with a rectangular corrugation. We obtain complementary analytical and numerical results which allow us to identify two different scaling regimes for the force as a function of the mean plate distance, corrugation amplitude, and wavelength. Qualitative distinctions between transversal electric and magnetic modes are revealed. Our results demonstrate the importance of a careful consideration of the nonadditivity of Casimir forces, especially in strongly nonplanar geometries. Nonperturbative effects due to surface edges are found. Strong deviations from the commonly used proximity force approximation emerge over a wide range of corrugation wavelengths, even though the surface is composed only of flat segments. We compare our results to that of a perturbative approach and a classical optics approximation.

We analyze the ground-state entanglement in a quantum adiabatic evolution algorithm designed to solve the $NP$-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the energy gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover’s algorithm is bounded by a constant.

The Groverian entanglement measure $G\left(\psi \right)$ is applied to characterize pure quantum states $\mid \psi ⟩$ of multiple qubits. This is an operational measure of entanglement in the sense that it quantifies the utility of the state $\mid \psi ⟩$ as an initial state for the search algorithm. A convenient parametrization is presented, which allows us to calculate the Groverian measure analytically for certain states of high symmetry. A numerical procedure is used in order to calculate it for arbitrary pure states of multiple qubits. Using the Groverian measure to evaluate the entanglement produced by quantum algorithms may provide useful insight into the role of entanglement in making quantum algorithms powerful. Here we calculate $G\left(\psi \right)$ for the intermediate states generated during the evolution of Grover’s algorithm for various initial states and for different sets of marked states. It is shown that Grover’s iterations generate highly entangled states in intermediate stages of the quantum search process, even if the initial state and the target state are product states.

Measurements of the absolute total and differential cross sections for the production of protons and hydrogen atoms in the energy range of $1–5\text{keV}$ for reactions of $\mathrm{H}{}_2{}^{+}$ molecular ions in $\text{Ar}$ and $\text{Kr}$ targets are reported. The results show that the cross section for the dissociative capture (DC) proccess is about one order of magnitude higher than that for the collision-induced dissociation. The angular distribution of the fragments in both targets and for all acceleration energies shows a monotonic decrease in the differential cross section with increasing angle. A sharp increase in the angular distribution at scattering angles $<1.6°$ is observed for hydrogen atoms resulting from DC and in particular for the $\text{Kr}$ target.

Charge transfer due to collisions of ground state ${\mathrm{O}}^{3+}\left(2s^{2}2p{}^2{P}^o\right)$ ions with molecular hydrogen are investigated using the quantum-mechanical molecular-orbital (QMO) coupled-channel method. The QMO calculations utilize $ab$ initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach for a representative range of orientation angles and diatom internuclear separations. Vibrationally resolved cross sections for nondissociative single electron capture are obtained for energies between 0.1 eV∕u and 10 keV∕u for ${\mathrm{H}}_2$ in its ground vibrational level using the infinite order sudden approximation (IOSA). Two further approximations are considered in which the electronic radial couplings are assumed to be independent of the diatom stretching. In the first case, vibrational motion is taken into account by multiplying the electronic radial couplings by Franck-Condon (FC) ionization factors while in the second, vibrational motion is completely neglected. We refer to these two approaches as the vibrational sudden approximation (VSA) and the electronic approximation (EA), respectively. In the latter, the resulting cross sections for electronic transitions are multiplied by FC factors to obtain relative vibrationally resolved cross sections which are independent of the collision energy (the centroid approximation). Comparison with existing experimental data for total and electronic state-selective cross sections shows best agreement with IOSA and VSA, but discrepancies for EA. The triplet-singlet electronic cross section ratio reveals a departure at low collision energies from the statistical value.

In this article we report on the use of degenerate-Raman-sideband cooling for the collimation of a continuous beam of cold cesium atoms in a fountain geometry. Thanks to this powerful cooling technique we have reduced the atomic beam transverse temperature from $60\mu \mathrm{K}\text{to}1.6\mu \mathrm{K}$ in a few milliseconds. The longitudinal temperature of $80\mu \mathrm{K}$ is not modified. The flux density, measured after a parabolic flight of $0.57\mathrm{s}$, has been increased by a factor of 4 to approximately ${10}^7\mathrm{at.}{\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}$ and we have identified a Sisyphus-like precooling mechanism which should make it possible to increase this flux density by an order of magnitude.

We study the precessing motion of a vortex in a Bose-Einstein condensate of atomic gases. In addition to the former zero-temperature studies, finite-temperature systems are treated within the Popov and semiclassical approximations. Precessing vortices are discussed utilizing the rotating frame of reference. The relationship between the sign of the lowest excitation energy and the direction of precession is discussed in detail.

We have experimentally studied the transient behaviors of photon switching by quantum interference in laser-cooled ${}^{87}\mathrm{Rb}\text{atoms}$. The experimental results are consistent with theoretical predictions. We show that the rise time of the probe absorption cannot be less than $2∕\mathrm{\Gamma }$ where $\mathrm{\Gamma }$ is the spontaneous decay rate of the excited states. In the low-intensity limit, the rise time is equal to $2\mathrm{\Gamma }∕({\mathrm{\Omega }}_c^2+{\mathrm{\Omega }}_s^2)$ for the scheme used here, where ${\mathrm{\Omega }}_c$ and ${\mathrm{\Omega }}_s$ are the Rabi frequencies of the coupling and switching fields. A simple picture based on the dark and nondark states is provided to explain these transient behaviors.

A method is presented for obtaining sub-Doppler and subnatural narrowing and increased absorption of a spectral line. The ultranarrow spectral line is confined between two closely spaced electromagnetically induced transparency windows in a nearly degenerate tripod atomic system formed by an $F_g=1\to F_e=0$ transition, split by a magnetic field. The system is driven by a $\sigma$-polarized pump and probed by a tunable $\pi$-polarized laser. It can be used to measure small magnetic fields and also as a magneto-optic switch.

Following two illustrative examples, a quite general form for the functional derivative of the Dirac density matrix $\gamma ({\mathbf{r}}_1,{\mathbf{r}}_2)$ with respect to the electron density $\rho \left(\mathbf{r}\right)$ is proposed. In turn, this functional derivative is related to a further three-point object, which reduces to the linear response function ${\chi }_0({\mathbf{r}}_1,\mathbf{r})$ when ${\mathbf{r}}_2$ tends to ${\mathbf{r}}_1$. The main application is then to derive the exchange-only potential of density functional theory. To avoid heavy numerical work in molecules and clusters, an approximation is suggested, with major calculational simplifications as a probable consequence.

Exact solutions for the low-temperature helium dimer and trimer, ${}^4\mathrm{He}_2$ and ${}^4\mathrm{He}_3$, are derived, based on our $\delta$ function model for the interatomic potential. For the trimer, the Faddeev equations are shown to be separable in hyperspherical coordinates, with the $S$-wave alone giving an exact solution. The parameters ${\lambda }_0$ and $r_0$ are fitted to accurate computations on the dimer and trimer. Excited states of the trimer are shown to exhibit the Efimov effect, whereby artificially reducing the strength of the two-body potential causes an infinite number of weakly-bound levels to condense out of the continuum. All the features anticipated by Efimov are quantitatively reproduced within our model. Since short-range details of the intermolecular forces are not relevant, our results can be considered to be universally applicable.

Exact analytical expressions for scattering lengths for potentials with four-parameter long-range tails of the form $-A{r}^{-2}{(r+\rho )}^{-2}-B{r}^{-\nu }{(r+\rho )}^{\nu -4}$ are presented. Contributions due to a potential core, with the latter not specified explicitly, are taken into account through a short-range scattering length and a core radius. For $\nu \ne 2$ and $B\ne 0$ the derived expressions contain the Bessel functions; for $\nu =2$ or $B=0$ they contain elementary functions.

Quantum computation based on quantum-cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in which all qubits of a species evolve in parallel. We show that, in spite of its inherent constraints, a QCA system can be used to study complex quantum dynamics. To this aim, we demonstrate scalable operations on a QCA system that fulfill statistical criteria of randomness and explore which criteria of randomness can be fulfilled by operators from various QCA architectures. Other means of realizing random operators with only a few independent operators are also discussed.

A computational method to study three-body rearrangement processes for nonzero total angular momentum is presented. The method is applied to muon exchange between muonic hydrogen and a heavier nucleus $X^{Z+}:p\mu +X^{Z+}\to p+{\left(\mu X\right)}^{(Z-1)+}$. Muon-transfer rates are calculated for oxygen and neon including partial waves up to $J=4$ for collision energies in the range ${10}^{-3}–10\text{eV}$. An excellent agreement is obtained with available experimental results.

We analyze the ground-state properties of an artificial atom made out of repulsive bosons attracted to a center for the case that all the interactions are short ranged. Such bosonic atoms could be created by optically trapping ultracold particles of alkali-metal vapors; we present the theory describing how their properties depend on experimentally adjustable strength of “nuclear” attraction and interparticle repulsion. The binding ability of the short-range potential increases with space dimensionality, only a limited number of particles can be bound in one dimension, while in two and three dimensions the number of bound bosons can be chosen at will. Particularly in three dimensions we find an unusual effect of enhanced resonant binding: for not very strong interparticle repulsion the equilibrium number of bosons bound to a nuclear potential having a sufficiently shallow single-particle state increases without bound as the nuclear potential becomes less attractive. As a consequence of the competing nuclear attraction enhanced by the Bose statistics and interparticle repulsions, the dependence of the ground-state energy of the atom on the number of particles has a minimum whose position is experimentally tunable. This implies a staircase dependence of the equilibrium number of bound bosons on external parameters which may be used to create a single-atom pipette—an arrangement which allows the transport of atoms into and out of a reservoir, one at a time.

It should be possible to separate experimentally the contributions to dielectronic recombination (DR) of energetically unresolved intermediate autoionizing Rydberg $nl$ states using electric fields. This notion is based on two essential ideas. First, electric fields enhance the DR rate by Stark-mixing low-$l$ states with high autoionization rates with high-$l$ states with low autoionization rates. Second, the field at which an $l$ state becomes Stark mixed is determined by its quantum defect, a known function of $l$. Consequently, the electric-field dependence of the DR rate should reflect the $l$ dependence of the autoionization rates and thus the contributions of the zero-field $nl$ states to the DR rate. This notion cannot be tested experimentally by examining true DR. However, it can be tested by studying DR from a continuum of finite bandwidth (CFB), for in this case the intermediate Rydberg $nl$ states are restricted to a single value of $l$. Specifically, we have examined the electric-field dependence of DR from two CFB’s, the $\mathrm{Ba}6p_{3∕2}11d$ and $6p_{3∕2}8g$ states. In these two cases the intermediate autoionizing Rydberg states are restricted to the $\mathrm{Ba}6p_{1∕2}nd$ and $6p_{1∕2}ng$ states $(l=2\text{and}4)$, which have quantum defects of 0.25 and 0.02, respectively. For the same $n$ they are Stark mixed at fields differing by an order of magnitude. We show experimentally that enhancement of the DR rate occurs at fields differing by a factor of 10 for $nd$ and $ng$ states of the same $n$, as expected, confirming that the field dependence of DR can be used to extract information about the contributions of energetically unresolved $l$ states to the zero-field DR rate.

We obtain a necessary and sufficient condition for a finite set of states of a finite-dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition is valid for states which may be mixed, entangled, or both. When the support of the set of states is the entire multiparticle Hilbert space, this condition is found to have an intriguing connection with the theory of entanglement witnesses.

He and N atoms are scattered with keV energies under a grazing angle of incidence from clean and flat Ag(111) and Al(111) surfaces. For incidence along low index crystallographic directions in the surface plane, atomic projectiles are steered by rows of atoms (“axial surface channeling”) giving rise to characteristic rainbows in their angular distribution. From the analysis of this effect we derive effective scattering potentials which reveal pronounced dynamical effects. We attribute our observation to the embedding energy for penetration of atoms in the electron gas of a metal.

High-resolution doubly differential cross-section measurements and calculations for quasifree electrons elastically scattered through 180° from ground-state He- and H-like boron ions are presented. The measurements, covering the entire $1s2ln{l^{\prime }}^{}$(for ${\mathrm{B}}^{3+}$) and $2ln{l^{\prime }}^{}$(for ${\mathrm{B}}^{4+}$) Rydberg series populated by resonant excitation, were performed by zero-degree Auger projectile electron spectroscopy of $3.91\mathrm{MeV}{\mathrm{B}}^{4+}$ and $3.08–7.48\mathrm{MeV}{\mathrm{B}}^{3+}$ ions in collisions with ${\mathrm{H}}_2$ targets. The projectile energy dependence study is used to further investigate other background contributions such as direct electron capture, direct excitation, and nonresonant transfer excitation. $R$-matrix calculations, particularly sensitive at this large scattering angle to electron correlation, exchange, and interference effects, are found to be in excellent overall agreement within the electron scattering model.