We investigate the use of concatenated coding to protect against dephasing in the absence of other types of error in order to carry out large quantum computations. This analysis is based on a well-known three-bit quantum code. Fault tolerant methods for carrying out gate operations, ancilla preparation, and syndrome identification are discussed and the maximum (or threshold) error rate which can be tolerated (if quantum coherence is to be maintained for arbitrarily long computations) is estimated. The methods for performing fault tolerant gate operations are compared to the methods appropriate for the seven-bit code and it is concluded that the three-bit code is not likely to be useful for large-scale quantum computation.

Quantum teleportation of an unknown broadband electromagnetic field is investigated. The continuous-variable teleportation protocol by Braunstein and Kimble [Phys. Rev. Lett. 80, 869 (1998)] for teleporting the quantum state of a single mode of the electromagnetic field is generalized for the case of a multimode field with finite bandwith. We discuss criteria for continuous-variable teleportation with various sets of input states and apply them to the teleportation of broadband fields. We first consider as a set of input fields (from which an independent state preparer draws the inputs to be teleported) arbitrary pure Gaussian states with unknown coherent amplitude (squeezed or coherent states). This set of input states, further restricted to an alphabet of coherent states, was used in the experiment by Furusawa et al. [Science 282, 706 (1998)]. It requires unit-gain teleportation for optimizing the teleportation fidelity. In our broadband scheme, the excess noise added through unit-gain teleportation due to the finite degree of the squeezed-state entanglement is just twice the (entanglement) source’s squeezing spectrum for its “quiet quadrature.” The teleportation of one half of an entangled state (two-mode squeezed vacuum state), i.e., “entanglement swapping,” and its verification are optimized under a certain nonunit gain condition. We will also give a broadband description of this continuous-variable entanglement swapping based on the single-mode scheme by van Loock and Braunstein [Phys. Rev. A 61, 10 302 (2000)].

We propose mixed states in two qubits that have a property that the amount of entanglement of these states cannot be increased by any unitary transformation. The property is proven when the rank of the states is less than 4, and confirmed numerically in the other general cases. The corresponding entanglement of formation specified by its eigenvalues gives an upper bound of that for density matrices with the same eigenvalues. Further, as a simple application of the upper bound of the entanglement of formation, we analyze the entanglement of formation of the state generated by a decohered controlled-NOT gate in the spin-boson model.

With bichromatic fields, it is possible to deterministically produce entangled states of trapped ions. In this paper we present a unified analysis of this process for both weak and strong fields, for slow and fast gates. Simple expressions for the fidelity of creating maximally entangled states of two or an arbitrary number of ions under nonideal conditions are derived and discussed.

Rates of an intercombination transition and several electric-dipole forbidden transitions between the levels of the ground complex in C-like ions of O and F and in N-like ions of S have been measured optically at a heavy-ion storage ring. The lifetime results, 1.250(13) ms for the ${2s2p}^3$ ${}^5{S}_2^o$ level in ${\mathrm{O}}^{2+},$ 530(25) and 304(5) ms for the ${2s}^2$ ${2p}^2$ ${}^1{S}_o$ level in ${\mathrm{O}}^{2+}$ and ${\mathrm{F}}^{3+},$ respectively, and 5.20(15) and 2.10(6) ms for the ${2s}^2{2p}^3$ ${}^2{P}_{1/2,3/2}^o$ levels of $S^{9+},$ agree with only some of the theoretical predictions, while they have a lower estimated uncertainty than all of them.

Four-component (spinor) solutions of the Dirac equation may be approximated by L-spinor expansions. We discuss their orthogonality and completeness and relate L-spinor properties to those of the Coulomb Sturmians. The mathematics of Rayleigh-Ritz approximations for one-electron Schrödinger and Dirac operators provides a rigorous setting for applying finite L-spinor matrix approximations to the relativistic hydrogenic atom. Convergence of eigenvalues and eigenvectors with respect to the size of the L-spinor set, of expectation values of quantum-mechanical operators, sum rules, and perturbation expansions is examined. The contribution to perturbation sums over states from solutions with eigenvalues in the continuum range ${(mc}^2,\infty )$ (electronic scattering states) and $(-\infty ,-{\mathrm{mc}}^2)$ (positronic scattering states) is shown to be essential to get accurate results.

We perform dynamical calculations of direct muon-transfer rates from thermalized muonic hydrogen isotopes to bare nuclei ${\mathrm{C}}^{6+}$ and ${\mathrm{O}}^{8+}.$ For these three-body charge-transfer reactions with Coulomb interaction in the final state we use two-component integrodifferential Faddeev-Hahn-type equations in configuration space using close-coupling approximation. To take into account the high polarizability of the muonic hydrogen due to the large charge of the incident nuclei, a polarization potential is included in the elastic channel. The large final-state Coulomb interaction is explicitly included in the transfer channel. The transfer rates so calculated are in good agreement with recent experiments.

Using a variational method we study a sequence of the one-electron atomic and molecular-type systems H, ${\mathrm{H}}_2^{+},$ ${\mathrm{H}}_3^{2+},$ and ${\mathrm{H}}_4^{3+}$ in the presence of a homogeneous magnetic field in the range $B=0\mathrm{}–4.414\times {10}^{13}\hspace{0.5em}\mathrm{G}.$ These systems are taken as a linear configuration aligned with the magnetic lines. For ${\mathrm{H}}_3^{2+}$ the potential energy surface has a minimum for $B\sim {10}^{11}\hspace{0.5em}\mathrm{G}$ which deepens with growth of the magnetic field strength (A. Turbiner, J. C. López, and U. Solís, Pis’ma Zh. Éksp. Teor. Fiz. 69, 800 (1999) [JETP Lett. 69, 844 (1999)]); for $B\gtrsim {10}^{12}\hspace{0.5em}\mathrm{G}$ the minimum of the potential energy surface becomes sufficiently deep to have longitudinal vibrational state. We demonstrate that for the $\mathrm{}\left(\mathrm{ppppe}\right)\mathrm{}$ system the potential energy surface at $B\gtrsim 4.414\times {10}^{13}\hspace{0.5em}\mathrm{G}$ develops a minimum, indicating the possible existence of exotic molecular ion ${\mathrm{H}}_4^{3+}.$ We find that for almost all accessible magnetic fields ${\mathrm{H}}_2^{+}$ is the most bound one-electron linear system while for magnetic fields $B\gtrsim {10}^{13}\hspace{0.5em}\mathrm{G}$ the molecular ion ${\mathrm{H}}_3^{2+}$ becomes the most bound.

We study the scattering properties of an open quantum system, in terms of the complex poles of the analytically continued energy Green’s function. We use a model for which many dynamical properties can be expressed analytically. We first study particle wave scattering and compute the Wigner delay times. Then, using perturbation theory, we compute the photodetachment rate due to a weak time-periodic electric field. In addition, we show that the model we use qualitatively reproduces several features of the experimentally obtained photodetachment cross section of ${\mathrm{H}}^{-}$ ions and gives interesting insight into the mechanism underlying the photodetachment of ${\mathrm{H}}^{-}$ ions.

Electron capture by 50-keV fluorinated fullerene anions $({\mathrm{C}}_{60}{\mathrm{F}}_n^{-}$ $18<n<\mathrm{}48)$ produced in either a plasma or an electrospray ion source has been studied in collisions with Xe atoms. The relative importance of nondissociative vs dissociative electron capture was found to depend strongly on the ion production method and on the number of attached F atoms. The absolute size of the cross section $\sim {10}^{-16}{\mathrm{cm}}^2$ has been modeled within the over-the-barrier model.

In this paper we report a direct observation of the oscillation between bound-state configurations in a rapidly autoionizing system. Calcium atoms were excited to a pure ${4p}_{3/2}\mathrm{nd}$ two-electron configuration using a 500-fsec laser pulse. The initial ${4p}_{3/2}\mathrm{nd}$ doubly excited state is energy degenerate with the ${4p}_{1/2}{n}^{\prime }d$ states and several continuum channels. Because of the short-pulse excitation, the initial state of the atom is not an energy eigenstate, but a nonstationary wave packet. As a result, oscillations between the two bound configurations were produced. These oscillations were measured by scanning the timing of a second 500-fsec laser pulse tuned to drive the ${4p}_{1/2}{n}^{\prime }d$ ionic state back down to the ${4sn}^{\prime }d$ singly excited configuration, which was subsequently detected using selective field ionization. A simple theoretical model was used to model the experimental results and produced good agreement with the data.

We have simulated the trapping and cooling of moderated positrons in a Penning trap in which the positrons lose energy through collisions with a simultaneously stored laser-cooled ${}^9{\mathrm{Be}}^{+}$ plasma. Once the positrons are trapped, they cool through sympathetic cooling with the ${}^9{\mathrm{Be}}^{+}$ plasma. After the positrons cool, their motion parallel to the magnetic field reaches a state of thermal equilibrium with the ${}^9{\mathrm{Be}}^{+}$ ions and they rotate about the trap axis at the same frequency as the ${}^9{\mathrm{Be}}^{+}$ ions. Therefore, a centrifugal separation will occur, forcing the positrons to coalesce into a cold column along the trap axis. A simulation which, in part, utilizes Monte Carlo techniques, indicates a capture efficiency of as high as $0.3\%$ for 300 K moderated positrons passing through a ${}^9{\mathrm{Be}}^{+}$ plasma with a density of ${10}^{10}$ atoms ${\mathrm{cm}}^{-3}$ and a column length of 1 cm. This capture efficiency leads to the positron capture rate of $\sim 1000$ positrons per second, assuming a 100 mCi positron source and ${10}^{-3}$ for the efficiency for moderating positrons from the source. The resulting dense reservoirs of cold positrons may be useful for antihydrogen production and for reaching a plasma state in which the mode dynamics must be treated quantum mechanically.

We report an experimental observation of a dark region, around the zero-field point of a spheric quadrupole magnetostatic field, in spatial fluorescence emitted by dilute vapor atoms, which were excited by a circularly polarized traveling-wave laser tuned to a $\overrightarrow{F}F+1\mathrm{}$ transition of ${}^{87}\mathrm{Rb}.$ By ruling out some possible sources, we show that the fluorescence decrease is associated with the three-dimensional nature of the magnetic field; it is a consequence of a precession of magnetic dipole moments induced by the radial magnetic field, which significantly cancels the orientation caused by optical pumping near the point of level crossing in the presence of the axial magnetic field. In an alternative way, the phenomenon can be understood as resulting from a destructive quantum interference, which is related to a coherent double-quantum coupling of atomic levels with two fields; one is the laser field, the other is the magnetic field. Analytic expressions for the half-width and contrast of the dark region have been obtained with a simplified model in the limit of low laser power. A qualitative agreement between the theory and experiment is found. The relevance of our study to laser cooling and trapping in a widely used magneto-optical trap based on such a quadrupole magnetic field is discussed. Finally, some applications of the phenomenon are also presented.

A general stability criterion is derived for the ground states of the Gross-Pitaevskii equation, which describes attractive Bose-Einstein condensates confined in a magnetic trap. These ground states are shown to avoid the collapse in finite time and are proven to be stable in two and three spatial dimensions.

It is shown how the effects of molecular reorientation may be incorporated in a fully quantized quantum-electrodynamical treatment of a high-order nonlinear optical effect. Specifically, a general temporal theory is developed to account for the second-harmonic intensity produced through phase-conjugate six-wave mixing. The theory permits elucidation of the intensity of the second-harmonic radiation for arbitrary arrangements of the generating laser beams and molecular geometry. Several models are considered: a one-dimensional model, linear geometry, and a planar geometry. A comparison is made between the results associated with these models and with those obtained from ultrafast experiments on dilute solutions of substituted stilbenes. We find that the off-axial components of the molecular polarizabilities are necessary to properly describe the orientational dynamics of such molecules.

Resonance fluorescence of a driven Jaynes-Cummings system is studied theoretically when the cavity is driven by a classical field of arbitrary strength. In the regime of strong atom-cavity coupling, there occur anomalous resonance peaks at $\pm \sqrt{2}{g}^{\prime },\pm \sqrt{3}{g}^{\prime },$ etc., with the modified vacuum Rabi frequency $g^{\prime }.$ These new peaks and the observed shift of the vacuum Rabi splitting are to be explained in the language of the quasienergy levels induced dynamically by the strong driving field. In the presence of significant damping the spectrum reflects the photon-number distribution inside the cavity, and particularly, a bimodality of the distribution results in a unique quintuplet resonance fluorescence spectrum.

The entanglement dependence of the noncyclic geometric phase is analyzed. A pair of noninteracting spin-$\frac{1}{2}$ particles prepared in an arbitrarily entangled state and precessing in an external time-independent uniform magnetic field is considered. It is shown that the geometric phase reduces to a sum of one-particle geometric phases for product states and takes on the two values corresponding to the phase factors $\pm 1$ for maximally entangled states. If only one of the particles is affected by the magnetic field it is demonstrated that the influence of entanglement on the geometric phase may be interpreted as an effective reduction of the degree of polarization of the affected particle. The generalization to more than two precessing spin-$\frac{1}{2}$ particles, in the particular case where Schmidt decompositions exists, is briefly outlined. The geometric phase for a pair of spin-$\frac{1}{2}$ particles with a spin-spin interaction is calculated. In this model we show that the noncyclic geometric phase for a certain class of states may be interpreted solely in terms of the solid angle enclosed by the geodesically closed curve on a two-sphere parametrized by the evolving Schmidt coefficients. This suggests a geometric interpretation of Schmidt decompositions for spin-$\frac{1}{2}$ pairs analogous to that of the Poincaré sphere for a single spin $\frac{1}{2}.$

The mapped Fourier grid method, using a coordinate adapted to the local de Broglie wavelength associated to the vibrational motion in a molecule, and recently developed by Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)], is used to compute the perturbed binding energies and rotational constants of the ${\mathrm{Cs}}_2{0}_u^{+}(6s+6p{}^2{P}_{1/2,3/2})$ photoassociation spectrum below the lower dissociation limit. The results are shown to be very sensitive to the molecular potential curves and spin-orbit coupling. In the case of ${\mathrm{Rb}}_2{0}_u^{+}(5s+5p{}^2{P}_{1/2,3/2}),$ a strong isotopic effect is also predicted. The results can be interpreted in the framework of generalized two-channel quantum defect theory, and generalized Lu-Fano plots are presented. This work suggests that parameters could easily be fitted to experimental spectra, eliminating the difficulties caused by limitations in the accuracy of the short-range molecular potentials.

Branching fractions were measured for electric-dipole transitions from the $5p$ upper levels to the $5s$ levels in neutral krypton atoms. The measurements were made with a wall-stabilized electric arc and a 2-m monochromator for the spectral lines in the visible, and with a hollow cathode lamp and the NIST 2-m Fourier-transform spectrometer for the lines in the near infrared. A semiempirical calculation, based on accurately known lifetimes for six upper levels, was used to calculate lifetimes for which accurate measurements do not exist. This resulted in a complete set of lifetimes for all $5p$ levels. Branching fractions and lifetimes were used to calculate transition rates for the $5p-5s$ transitions. The relative uncertainties of the transition rates range from less than 1% for the strongest lines to about 10% for the weakest lines. Our data also reveal that most of the previous measurements appear to have been affected by opacity effects in the light sources.

Isotope shifts and hyperfine structure have been measured in the ${4f}^7{5d6s}^2$ ${}^9{D}_6\to X$ ${}^9{D}_6$ (38 024.792 ${\mathrm{cm}}^{-1})$ transition in atomic gadolinium using high-resolution resonance ionization mass spectroscopy. Excitation was performed as a resonance-enhanced two-photon transition with the ${4f}^{7}5d6s6p$ ${}^9{F}_7$ state as an intermediate level. Selective population of hyperfine states in the first excitation step allowed assignment of all transitions in the complex hyperfine spectrum of the odd isotopes ${}^{155,157}\mathrm{Gd}$ and evaluation of the magnetic dipole and electric quadrupole hyperfine structure constants for the X ${}^9{D}_6$ state. Measured values for the isotope shifts of all stable Gd isotopes have been used to derive specific mass-shift and field-shift factors. The obtained spectroscopic information leads to the conclusion that the X ${}^9{D}_6$ state is a ${4f}^{7}5d6s8s$ configuration.