Although the initial proposal for ion trap quantum computation made use of an auxiliary internal level to perform logic between ions, this resource is not necessary in principle. Instead, one may perform such operations directly using sideband laser pulses, operating with an arbitrary (sufficiently small) Lamb-Dicke parameter. We explore the potential of this technique, showing how to perform logical operations between the internal state of an ion and the collective motional state and giving explicit constructions for a controlled-NOT gate between ions.

A four-component equivalent of the Schrödinger equation, describing both the nonrelativistic electron and the nonrelativistic positron, is introduced. The difference between this equation and the Dirac equation is treated as a perturbation. The relevant perturbation equations and formulas for corrections to the energy are derived. Owing to the semibounded character of the Schrödinger Hamiltonian of the unperturbed equation the variational perturbation method is formulated. The Hylleraas functionals become then either upper or lower bounds to the respective exact corrections to the energy. In order to demonstrate the usefulness of this approach to the problem of the variational optimization of nonlinear parameters, the perturbation corrections to wave functions for the of hydrogenlike atoms have been approximated in terms of exponential basis functions. The Dirac equation in this algebraic approximation is solved iteratively starting with the solution of the Schrödinger equation.

We study binding corrections to the gyromagnetic factor $g_{\mathrm{e}}$ of an electron in hydrogenlike ions. We argue that the leading order binding effects in radiative corrections $\Delta g_{\mathrm{rad}}$ are universal to all orders in $\alpha /\pi$ and the complete result reads $\Delta g_{\mathrm{rad}}{=(g}_{\mathrm{free}}-2\left)\right[1+(Z\alpha {)}^2/6\mathrm{}]+O\left(\right(\alpha /\pi \left)\right(Z\alpha {)}^4).$ The theoretical uncertainty in the prediction for the experimentally interesting carbon ion is decreased by a factor of about 3.

Infrared NO-${\mathrm{N}}_2$ line-broadening coefficients for the fundamental 1-0 band are ab initio computed by means of the exact trajectory model extended to the case of a symmetric top active molecule. As intermolecular potential, the sum model composed of long-range dipole-quadrupole and quadrupole-quadrupole interactions as well as short-range atom-atom interactions, is taken. Line-broadening coefficients for both R and P branches of diamagnetic ${}^2{\Pi }_{1/2}$ and paramagnetic ${}^2{\Pi }_{3/2}$ sub-bands are reported for various temperatures in the range 163–296 K, thus significantly improving available theoretical results in the common temperature domain, while proposing values for temperatures that as yet have not been studied. The computed results are found to be in good agreement with a bulk of the experimental data.

Improvements in the characterization of II-VI compound-based solar cells, and a recent experimental characterization of small clusters and nanoparticles, make the study of small II-VI clusters very interesting. In a previous work the global minima of small ${\mathrm{Zn}}_i{\mathrm{S}}_i$ clusters $i=1\mathrm{}–9$ were characterized. In order to calculate the excitation energies of these clusters, basically two methods are available: on the one hand, the traditionally used configuration interaction singles (CIS) theory, and on the other hand the recently developed time dependent density-functional theory (TDDFT). Calculations of the excitation energies of small ${\mathrm{Zn}}_i{\mathrm{S}}_i$ clusters, $i=1\mathrm{}–3,$ were performed with both methods in an attempt to find the most appropriate one. The relativistic compact effective core potentials and shared-exponent basis set of Stevens, Krauss, Basch and Jasien (SKBJ) [Can J. Chem. 70, 612 (1992)], systematically enlarged with extra functions, were used in this work. These larger basis sets are labeled according to the number of added functions. Thus, as an example, if two extra $\mathrm{sp}$ functions and one d function are added, the final basis set is denoted $\mathrm{SKBJ}\mathrm{}\left(2sp1d\right).$ These basis sets were combined with both methods. In this way the most appropriate method and basis-set combination was chosen, for further excitation energy calculations on larger ${\mathrm{Zn}}_i{\mathrm{S}}_i$ clusters. It was seen in both methods that more than one polarization function was needed. Combined with the CIS method, the smallest basis yielding good results was $\mathrm{SKBJ}\mathrm{}\left(1sp2d3f\right),$ and with TDDFT $\mathrm{SKBJ}\mathrm{}\left(1sp2d2f\right).$ In the CIS case, this basis was too large even for ${\mathrm{Zn}}_3{\mathrm{S}}_3.$ In addition to this, in the literature TDDFT was seen to provide a better description of the excitations, and therefore a $\mathrm{TDDFT}-\mathrm{SKBJ}\mathrm{}\left(1sp2d2f\right)\mathrm{}$ combination was chosen for further calculations. However, due to the fact that no experimental data are available, some results confirming the TDDFT results are necessary, in this way ensuring that our choice is the correct one. Multireference configuration interaction calculations, combined with a triple-ζ double polarization (TZ2P) basis set, were carried out for ${\mathrm{Zn}}_i{\mathrm{S}}_i,\hspace{0.5em}i=1\mathrm{}$ and 2. For $i=3,$ a TZ basis without polarization was used; otherwise the limit of 255 on the basis function number was exceeded. These results were clearly in agreement with the TDDFT results, and confirm our previous choice.

A refined three-dimensional version of the time-dependent Thomas-Fermi model is used to qualitatively study the explosion of rare-gas atomic clusters in an intense laser field. Clusters as large as 55 atoms are exposed to a strong subpicosecond laser pulse. A stepwise character of the explosion is observed in which atomic shells are expelled sequentially. The role of “hot” electron dynamics in the explosion process is also investigated via initial temperature effects. Contrary to previous opinions it seems that the so-called hydrodynamic explosion scenario is important for most energetic ions coming from the outermost shells only.

Many investigators have been exploring the intensity domain where, in laser interactions with atoms, the $v/c$ effects of magnetic fields are important, but it is not necessary to treat the ${\mathrm{}(v/c)\mathrm{}}^2$ effects of a full-fledged relativistic treatment. We delineate the intensity regimes as a function of frequency where one must consider magnetic fields, but not relativistic effects per se. Since it is known that inconsistencies can arise when retardation terms are incorporated into the nonrelativistic Schrödinger equation, a Schrödinger equation is exhibited that is free of retardation terms, but that nevertheless contains both electric and magnetic fields in dipole approximation, and configured as in a plane wave electromagnetic field.

We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced center-of-mass temperature.

We study an effective interaction potential between a neutral atom and a nanometric probe tip in optical near-field systems. The wave-number dependence of the coupling coefficients of exciton polaritons is described with the effective-mass approximation, where massive virtual photons are exchanged between the atom and the probe tip. The near-field optical potential is shown as the sum of the Yukawa functions with several kinds of effective masses or interaction ranges, and is characterized in terms of detuning for the resonance energies of the atom and the probe tip. Consequently, we find that a potential minimum is produced for a blue detuning case. This result indicates that an atom can be trapped in the near-field optical potential well. Furthermore, we numerically investigate deflection and trapping of a single atom by means of optical near fields generated from a nanometric probe tip. The dependence on the probe-tip size, the kinetic energy of the cold atom, and the excitation energies of both probe tip and atom is clarified.

We report numerical and theoretical investigations of the formation and transition of domain patterns in a two-dimensional optical system with cosine-type nonlinearity and a feedback loop. Labyrinthine stripe domain patterns of the electric field are observed in the system, intiated from the Turing instability. The labyrinths are found to undergo a transition to domain patterns of coexisting stripes and hexagons and disordered hexagon domains on variation of the incident field intensity, a control parameter of the system. The parameter regions for these domain structures are explained through the existence and competition of stripes and hexagons in terms of their amplitude equations. Moreover, the transition from straight stripes to labyrinths is investigated by varying the feedback coupling coefficient of the system. The transition is shown to be the consequence of coexistence of and interaction between stripes and domain walls.

We describe an experiment in which we have used a cold damping feedback mechanism to reduce the thermal noise of a mirror around its mechanical resonance frequency. The monitoring of the Brownian motion of the mirror allows one to apply an additional viscous force without any extra thermal fluctuations. This scheme has been experimentally implemented with the radiation pressure of an intensity-modulated laser beam. Large noise reductions, up to 30 dB, have been obtained. We have also checked the mechanical response of the cold damped mirror, and monitored its transient evolution between the cooled regime and the room-temperature equilibrium. A simple theoretical model allows us to fully explain the experimental results. A possible application to the active cooling of the violin modes in a gravitational-wave interferometer is discussed.

Electron impact dissociation and dissociative attachment (DA) via the ${}^2{\Sigma }_u^{+}$ shape resonance in $e-{\mathrm{H}}_2$ collisions is treated by the quasiclassical version of the nonlocal resonance theory. Optical theorem is applied to analyze all the energetically accessible channels. Collisionally induced dissociation and dissociative attachment cross sections for vibrationally or rotationally excited ${\mathrm{H}}_2$ molecule are presented in the electron energy range up to 5 eV. It is shown that the DA cross sections we published recently [Phys. Rev. A 61, 052705 (2000)] in fact represent the sum of the cross sections for the DA and dissociation processes in the energy range above the dissociation threshold.

In Moyal’s formulation of quantum mechanics, a quantum spin s is described in terms of continuous symbols, i.e., by smooth functions on a two-dimensional sphere. Such prescriptions to associate operators with Wigner functions, P or Q symbols, are conveniently expressed in terms of operator kernels satisfying the Stratonovich-Weyl postulates. In analogy to this approach, a discrete Moyal formalism is defined on the basis of a modified set of postulates. It is shown that appropriately modified postulates single out a well-defined set of kernels that give rise to discrete symbols. Now operators are represented by functions taking values on ${\mathrm{}(2s+1)\mathrm{}}^2$ points of the sphere. The discrete symbols contain no redundant information, contrary to the continuous ones. The properties of the resulting discrete Moyal formalism for a quantum spin are worked out in detail and compared to the continuous formalism.

We give a complete characterization of the stochastic wave formalism when color Gaussian fluctuations are assumed. It is shown that in this case there is only one possible generalization of the stochastic wave dynamics, which is given by the “non-Markovian quantum state diffusion model” [Phys. Rev. A 58, 1699 (1998)]. Using functional techniques, we found an equivalent evolution in terms of the stochastic propagator. From this equation any controlled approximation can be constructed. The mean density-matrix evolution is given in a closed form. A relation with quantum master equations is established. An interaction parameter expansion and a small correlation time expansion are developed.

We calculate the optical properties of a vacuum when a static magnetic field $B_0$ and electric field $E_0$ are applied perpendicular to the direction of light propagation. Apart from the known Cotton-Mouton and Kerr effects, with crossed fields we find magnetoelectric linear birefringence with optical axes parallel to the external fields. With parallel fields we find magnetoelectric Jones birefringence with optical axes under 45° with the external fields. Both birefringences are linear in $E_0{B}_0,$ and have the same magnitude.

We propose a practical solid-state system capable of demonstrating quantum teleportation. The setup exploits recent advances in the optical control of excitons in coupled quantum dots, in order to produce maximally entangled Bell and Greenberger-Horne-Zeilinger states. Only two unitary transformations are then required: a quantum controlled-$\mathrm{NOT}$ gate and a Hadamard gate. The laser pulses necessary to generate the maximally entangled states, and the corresponding unitary transformations, are given explicitly.

Evidence of circular dichroism has been observed in the spectral properties of a gas of left-right symmetric molecules. This dichroism comes about as the result of collisions of the symmetric molecules with left-right asymmetric molecules introduced as a buffer gas. In this sense, the dichroism can be said to have been transferred from the chiral buffer molecules to the symmetric, nonchiral molecules of the background vapor. This transferred dichroism appears as a broadening in the gain line of the symmetric molecule that is asymmetric with respect to the right or left handedness of a circularly polarized probe. The broadening of the 119-μm line of the methanol molecule was observed using infrared–far-infrared double-resonance spectroscopy.

We present experimental absolute and total electron-capture cross sections for ${\mathrm{Ar}}^{q+}-{\mathrm{C}}_{60}$ $(q=4,$ 6, and 8–18) collisions at $3.3q\hspace{0.5em}\mathrm{keV}.$ The absolute scale is based on the ${\mathrm{C}}_{60}$ vapor pressure by Abrefah et al. [Appl. Phys. Lett. 60, 1313 (1992)], which together with the results of Mathews et al. [J. Phys. Chem. 96, 3566, (1992)] are the only possible choices among the many, widely dispersed, vapor pressures reported in the literature. In order to support this statement, we calculate total electron-capture cross sections modeling ${\mathrm{C}}_{60}$ as a pointlike object and as an infinitely conducting sphere (ICS). These model results are shown to differ little, since polarization and finite-size effects are relatively unimportant for the distant collisions at which the outermost (first) electrons are transferred. We are thus able to use the semiempirical formula for absolute ion-atom cross sections by Selberg et al. [Phys. Rev. A 54, 4127 (1996)], treating ${\mathrm{C}}_{60}$ as a hypothetical atom with ionization potential $I_1=7.6\mathrm{}\hspace{0.5em}\mathrm{eV},$ and the ICS model to define lower and upper bounds for the absolute cross-section scale. We find significant oscillations in the total electron-capture cross sections as functions of q.

Regarding an experimental measurement of proton kinetic energy spectra of ${\mathrm{H}}_2^{+}$ with a chirped pulse [L. J. Frasinski, J. H. Posthumus, J. Plumridge, and K. Colding, Phys. Rev. Lett. 83, 3625 (1999)], we present a nonperturbative, time-dependent calculation for the photodissociation of ${\mathrm{H}}_2^{+}$ in intense laser fields by combining three numerical techniques. The results show a finer kinetic-energy distribution structure of a proton due to the intrapulse pump-dump mechanism between two electronic states as the pulse duration and intensity change. Higher-energy peaks are also suppressed by frequency chirping of the laser field. The dissociation probabilities show that a positively chirped pulse is always more efficient for population inversion than no chirping or negatively chirped pulses, and a slight coordinate shift of the initial state could result in a significant increase of dissociation probability.

The simplest model of three coupled Bose-Einstein condensates is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean-field approximation. This semiclassical analysis, using system symmetries, shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points, and our analysis shows that the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, and undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays a dynamical transition. The quantum case has collapse and revival sequences superimposed on the semiclassical dynamics, reflecting the underlying discreteness of the spectrum. Nonzero circular current states are also demonstrated as one of the higher-dimensional effects displayed in this system.