The van der Waals coefficients, $C_6,C_8,$ and $C_{10}$ for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient, $D_8$ and the three-body coefficient, $C_9$ are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.

We investigate elastic scattering of positrons by hydrogen atoms and helium ions using a time-dependent coupled-channel (TDCC) method. Phase shifts are calculated with the time-energy Fourier transform of a wave packet. Numerical accuracy of the TDCC method is demonstrated for S-, P-, and D-wave scatterings by hydrogen atoms. For helium ions, we examine the low-lying S-wave resonances with a broad width recently predicted in variational eigenenergy calculations. However, resonancelike behaviors are not discernible in the S-wave phase shift for the ground-state target.

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton’s equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.

Pairing gaps for fermionic atoms in harmonic-oscillator traps are calculated for a wide range of interaction strengths and particle numbers, and compared to pairing in nuclei. Especially systems where the pairing gap exceeds the single-level spacing but is smaller than the shell splitting $ħ\omega$ are studied, which applies to most trapped Fermi atomic systems as well as to finite nuclei. When solving the gap equation for a large trap with such multilevel pairing, one finds that the matrix elements between nearby harmonic-oscillator levels and the quasi particle energies lead to a double logarithm of the gap, and a pronounced shell structure at magic numbers. It is argued that neutron and proton pairing in nuclei belongs to the class of multilevel pairing, that their shell structure follows naturally, and that the gaps scale as $\sim A^{-1/3}$—all in qualitative agreement with odd-even staggering of nuclear binding energies. Pairing in large systems is related to that in the bulk limit. For large nuclei the neutron and proton superfluid gaps approach the asymptotic value in infinite nuclear matter: $\Delta \simeq 1.1\mathrm{MeV}.$

Solutions of the Schrödinger equation and propagators for the general quadratic and the linear Hamiltonian system of canonical variables whose coefficients are arbitrary and time dependent are obtained when the corresponding classical solution is oscillatory, linear, or monotonic. All of them are given by the coefficients of the Hamiltonian and the classical solution of the system under the conditions for which the classical solution exists.

From experiments on doped alkali-metal halide crystals there is reason to believe that localized, stationary lattice solitons, often called breathers, form and inhibit the crystal’s relaxation. We quantize these excitations using the Einstein-Brillouin-Keller method (which is also generalized). Topologically independent loops on the Kolmogorov-Arnold-Moser torus are found stroboscopically, using easily calculated periods, and the classical action evaluated. Wave functions can also be evaluated using a path-integral-motivated semiclassical wave-function calculation.

We theoretically demonstrate a method for producing the maximally path-entangled state $(1/\sqrt{2})(|N,0\mathrm{}〉+\exp [\mathrm{iN}\phi ]|0,N〉)$ using intensity-symmetric multiport beam splitters, single photon inputs, and either photon-counting postselection or conditional measurement. The use of postselection enables successful implementation with non-unit efficiency detectors. We also demonstrate how to make the same state more conveniently by replacing one of the single photon inputs by a coherent state.

A programmable gate array is a circuit whose action is controlled by input data. In this paper we describe a special-purpose quantum circuit that can be programmed to evaluate the expectation value of any operator O acting on a space of states of N dimensions. The circuit has a program register whose state $|\Psi \mathrm{}\left(O\right)\mathrm{}{〉}_P$ encodes the operator O whose expectation value is to be evaluated. The method requires knowledge of the expansion of O in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.

We present the absolute photoionization cross section of doubly ionized silicon as a function of photon energy. These were obtained by merging a ${\mathrm{Si}}^{2+}$ ion beam generated in an electron cyclotron resonance source with monochromatized synchrotron radiation from an undulator. The photoion yield measurements were carried out in the photon energy range between 95 eV and 170 eV, i.e., the region corresponding to the excitation followed by the ionization (threshold $\sim 133.8\mathrm{eV})$ of an inner-subshell $2p$ electron. Resonance structure due to $2p$ excitation in the ${2p}^{6}3s3p{}^{3}P$ metastable state was also observed with its contribution to the total cross section not exceeding 3%. Calculation of the $2p$ photoionization continuum cross section as a function of photon energy was carried out using the relativistic random-phase approximation (RRPA) and agreed very well with the corresponding measurements. The resonance structure in the $3s$ cross section below the $2p$ threshold was found to be in good agreement with the multiconfiguration atomic structure calculations of Sayyad et al. [J. Phys. B 28, 1715 (1995)], while the corresponding RRPA-RMQDT (relativistic multi-channel quantum-defect theory) calculations proved less successful.

We present a nonempirical potential model for studying threshold vibrational excitation of polar molecules by electron impact. This work builds on the zero-range potential virtual state model of Gauyacq and Herzenberg [J. P. Gauyacq and A. Herzenberg, Phys. Rev. A 25, 2959 (1982)], using known analytic properties of the S matrix for a dipole potential to predict the analytic continuation of the negative ion potential curve into the continuum. We derive an equation that determines the nuclear dynamics which can be solved without the need for an expansion in target vibrational states. The model is applied to $e^{-}$-HCl and is found to capture the essential features of the observed excitation cross sections, including both the threshold peaks as well as oscillatory structures at energies above threshold.

Bose-Einstein condensates (BEC’s) have recently been the subject of considerable study as possible analog models of general relativity. In particular it was shown that the propagation of phase perturbations in a BEC can, under certain conditions, closely mimic the dynamics of scalar quantum fields in curved space-times. In two previous papers [Int. J. Mod. Phys. A 18, 3735 (2003); Int. J. Mod. Phys. D (to be published), e-print gr-qc/0305061] we noted that a varying scattering length in the BEC corresponds to a varying speed of light in the “effective metric.” Recent experiments have indeed achieved a controlled tuning of the scattering length in ${}^{85}\mathrm{Rb}.$ In this paper we shall discuss the prospects for the use of this particular experimental effect to test some of the predictions of semiclassical quantum gravity, for instance, particle production in an expanding universe. We stress that these effects are generally much larger than the Hawking radiation expected from causal horizons, and so there are much better chances for their detection in the near future.

The system of two coupled Bose-Einstein condensates is mapped onto a uniaxial spin with an applied magnetic field. The mean-field interaction, the coupling, and the asymmetry or the detuning correspond to the anisotropy, the transverse field, and the longitudinal field, respectively. A generalized Bloch equation is derived. In the low barrier limit for the quasispin model, the tunneling rate is analyzed with an imaginary-time path-integral method. The dependence of the tunneling rate on the system parameters is obtained. The crossover temperature $T_c$ from the thermal regime to the quantum regime is estimated. Below $T_c$ quantum tunneling prevails, otherwise thermal activation dominates.

Fractional decay of population inversion and spectral shift of superfluorescence in photonic crystals due to anomalous Rabi splitting and localization of macroscopic polarization field are demonstrated by means of the coupled-mode analysis for the pencil-like excitation of embedded atoms. Noninteger exponents of atomic density dependence are predicted for the temporal profile of emitted light pulses.

Grover’s algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover’s search algorithm to a random phase error in the oracle and analyzes the complexity of the search process as a function of the scaling of the oracle error with database or library size. Both the discrete- and continuous-time implementations of the search algorithm are investigated. It is shown that unless the oracle phase error scales as ${O(N}^{-1/4}),$ neither the discrete- nor the continuous-time implementation of Grover’s algorithm is scalably robust to this error in the absence of error correction.

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\phi \mathrm{}\left(t\right)\mathrm{}$ at the same time that it is inverted. For polynomial twist, $\phi \mathrm{}\left(t\right)\mathrm{}\sim {\mathrm{Bt}}^n.$ We show that for $n>~3,$ multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength B, which can be used to control the time separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wave function. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum controlled-NOT and NOT gates is discussed.

The lowest-order interelectron interaction and electron self-energy radiative corrections to the hyperfine structure intervals for the ${2p}_{3/2}$ state of Li-like, B-like, and N-like ${}_{83}^{209}\mathrm{Bi}$ ions are calculated. The contributions of the magnetic dipole, electric quadrupole, and magnetic octupole moments are included. The “dynamical” model of the hyperfine interaction is employed, where the electron is assumed to interact with the valence proton in ${}_{83}^{209}\mathrm{Bi}$ nucleus via the exchange of a virtual photon. Within this model the magnetic and the electric moment distributions inside the nucleus are simultaneously taken into account.

We have performed semiempirical as well as ab initio density-functional theory (DFT) calculations at $T=0\mathrm{}$ to analyze the equilibrium configurations and electronic properties of spheroidal ${\mathrm{C}}_{60}$ as well as of cylindrical armchair (5,5) and (8,8) fullerenes passivated with ${\mathrm{SCH}}_3$ and $\mathrm{S}({\mathrm{CH}}_2{)}_2{\mathrm{CH}}_3$ thiols. Our structural results reveal that the lowest-energy configurations of the adsorbates strongly depend on their chain length and on the structure of the underlying substrate. In the low-coverage regime, both ${\mathrm{SCH}}_3$ and $\mathrm{S}({\mathrm{CH}}_2{)}_2{\mathrm{CH}}_3$ molecules prefer to organize into a molecular cluster on one side of the ${\mathrm{C}}_{60}$ surface, providing thus a less protective organic coating for the carbon structure. However, with increasing the number of adsorbed thiols, a transition to a more uniform distribution is obtained, which actually takes place for six and eight adsorbed molecules when using $\mathrm{S}({\mathrm{CH}}_2{)}_2{\mathrm{CH}}_3$ and ${\mathrm{SCH}}_3$ chains, respectively. In contrast, for the tubelike arrangements at the low-coverage regime, a quasi-one-dimensional zigzag organization of the adsorbates along the tubes is always preferred. The sulfur-fullerene bond is considerably strong and is at the origin of outward and lateral displacements of the carbon atoms, leading to the stabilization of three-membered rings on the surface (spheroidal structures) as well as to sizable nonuniform radial deformations (cylindrical configurations). The electronic spectrum of our thiol-passivated fullerenes shows strong variations in the energy difference between the highest occupied and lowest unoccupied molecular orbitals as a function of the number and distribution of adsorbed thiols, opening thus the possibility to manipulate the transport properties of these compounds by means of selective adsorption mechanisms.

The ${\mathrm{He}}_2-{\mathrm{SF}}_6$ trimers, in their different He isotopic combinations, are studied in the framework of both the correlated Jastrow approach and the correlated hyperspherical harmonics (CHH) expansion method. The energetics and structure of the ${\mathrm{H}\mathrm{e}-\mathrm{S}\mathrm{F}}_6$ dimers are analyzed, and the existence of a characteristic rotational band in the excitation spectrum is discussed, as well as the isotopic differences. The binding energies and the spatial properties of the trimers, in their ground and lowest lying excited states, obtained by the Jastrow ansatz are in excellent agreement with the results of the converged CHH expansion. The introduction of the He-He correlation makes all trimers bound by largely suppressing the short range He-He repulsion. The structural properties of the trimers are qualitatively explained in terms of the shape of the interactions, Pauli principle, and masses of the constituents.

The coherence properties of phase fluctuating Bose-Einstein condensates are studied both theoretically and experimentally. We derive a general expression for the N-particle correlation function of a condensed Bose gas in a highly elongated trapping potential. The second-order correlation function is analyzed in detail, and an interferometric method to directly measure it is discussed and experimentally implemented. Using a Bragg diffraction interferometer, we measure intensity correlations in the interference pattern generated by two spatially displaced copies of a parent condensate. Our experiment demonstrates how to characterize the second-order correlation function of a highly elongated condensate and to measure its phase coherence length.

The preparation of mesoscopic states of radiation and matter fields through atom-field interactions has been achieved in recent years and employed for a range of striking applications in quantum optics. Here we present a technique for the preparation and control of a cavity mode which, in addition to interacting with a two-level atom, is simultaneously submitted to linear and parametric amplification processes. The role of the amplification-controlling fields in the achievement of real mesoscopic states is to produce highly squeezed field states and, consequently, to increase both (i) the distance in phase space between the components of the prepared superpositions and (ii) the mean photon number of such superpositions. When the squeezed superposition states are submitted to the action of similarly squeezed reservoirs, we demonstrate that under specific conditions the decoherence time of the states becomes independent of both the distance in phase space between their components and their mean photon number. An explanation is presented to support this remarkable result, together with a discussion of the experimental implementation of our proposal. We also show how to produce number states with fidelities higher than those derived as circular states.