Within the framework of relativistic Schrödinger theory (RST), the problem of bound two-particle states is studied and compared to the analogous results of conventional quantum theory. The standard dichotomy of symmetric and antisymmetric quantum states finds its RST analog in the form of the positive and negative mixtures. Similarly the conventional exchange degeneracy has its RST counterpart in the form of a certain mixture degeneracy which, however, is not broken by the interparticle interactions as in the standard quantum theory. The corresponding group of quasilinear mixing transformations turns out to be continuous [in contrast to the discrete operations of (anti)symmetrization in the conventional theory] and is closely related to the Lorentz group SO(1,1) in two dimensions. The group properties can be exploited to generate exact solutions for the mixture dynamics from the pure-state configurations where, however, certain physical quantities remain invariant: scalar densities, currents, energy eigenvalues.

Coherence in an open quantum system is degraded through its interaction with a bath. This decoherence can be avoided by restricting the dynamics of the system to special decoherence-free subspaces. These subspaces are usually constructed under the assumption of spatially symmetric system-bath coupling. Here we show that decoherence-free subspaces may appear without spatial symmetry. Instead, we consider a model of system-bath interactions in which to first order only multiple-qubit coupling to the bath is present, with single-qubit system-bath coupling absent. We derive necessary and sufficient conditions for the appearance of decoherence-free states in this model, and give a number of examples. In a sequel paper we show how to perform universal and fault tolerant quantum computation on the decoherence-free subspaces considered in this paper.

Decoherence-free subspaces (DFSs) shield quantum information from errors induced by the interaction with an uncontrollable environment. Here we study a model of correlated errors forming an Abelian subgroup (stabilizer) of the Pauli group (the group of tensor products of Pauli matrices). Unlike previous studies of DFSs, this type of error does not involve any spatial symmetry assumptions on the system-environment interaction. We solve the problem of universal, fault-tolerant quantum computation on the associated class of DFSs. We do so by introducing a hybrid DFS quantum error-correcting-code approach, where errors that arise due to departure of the codewords from the DFS are corrected actively.

Ionization potentials (IP’s) are evaluated for various excited states of Tl using the relativistic coupled cluster (CCCD) theory in the even-parity pair channel approximation (CCSD-EPC). An average accuracy below half a percent is reached. The effect of deep core electrons on the core-valence correlations is investigated. It is found that electrons in the third subshell $\mathrm{}(n=3\mathrm{})\mathrm{}$ modify the IP’s of the $6p$ orbitals by $100\hspace{0.5em}{\mathrm{cm}}^{-1}.$ By comparison with calculations made in the linearized CCSD (LCCSD) approximation it is demonstrated that nonlinear contributions are mandatory to reach an accuracy below half a percent for the ${6p}_{1/2}$ orbital.

The tungsten $L{\alpha }_{1,2}$ x-ray spectrum was measured with high resolution using photoexcitation by monochromatized synchrotron radiation. The line splitting, widths, and relative intensities were determined from a phenomenological fit by five Voigt functions and compared with previous measurements. A fully split diagram and ${5l}^{-1}$ spectator hole transition multiplets were calculated ab initio using the relativistic multiconfigurational Dirac-Fock method. Fits of various combinations of these multiplets to the measured spectrum show that the line shapes can be well accounted for by the fully split diagram transition ${2p}_{3/2}^{-1}\to {3d}_{3/2,5/2}^{-1}$ alone, without invoking contributions from any spectator hole transition.

$K\alpha$ spectra of heliumlike neon and associated lithiumlike, berylliumlike, and boronlike satellite line emission have been observed with a high-resolution crystal spectrometer on the Lawrence Livermore Electron Beam Ion Trap. The $\mathrm{KLL}$ dielectronic recombination satellites were resolved from their He-like parent lines in electron energy space, and their wavelengths and resonance strengths measured. The wavelength measurements achieved a typical accuracy of a few $\mathrm{m}\AA ,$ with two measurements accurate to better than one part in 10 000. By normalizing to the He-like resonance line, w, we measure Li-like satellite resonance strengths that are 10% to 46% lower than predicted by theoretical models. The wavelengths and relative strengths of Be-like $\mathrm{KLL}$ satellites were also measured, and absolute strengths were obtained by normalizing to the collisionally excited Li-like $\mathrm{qr}$ satellite blend.

We present a detailed calculation on $\mathrm{}(1+1)\mathrm{}$-photon resonance-enhanced photodissociation of molecular hydrogen. The first field of frequency ${\omega }_1$ is tuned to excite the ground level $X{}^1{\Sigma }_g^{+}\mathrm{}(v=0,j=0\mathrm{})\mathrm{}$ to either one of the two strongly nonadiabatically coupled intermediate vibrational levels belonging to the electronic states $B{}^1{\Sigma }_u^{+}$ and $C{}^1{\Pi }_u.$ These two levels can absorb a second photon of frequency ${\omega }_2$ and connect to the continua of the $\mathrm{GK}{}^1{\Sigma }_g^{+}$ and $I{}^1{\Pi }_g$ states as well as to the embedded discrete levels of the $H\overline{H}{}^1{\Sigma }_g^{+}$ and $J{}^1{\Delta }_g^{+}$ states. These embedded discrete levels predissociate into the continua of $\mathrm{GK}$ and I states. The differing transition amplitudes to the continua through the different pathways interfere, giving rise to a dissociation line shape as ${\omega }_2$ is varied. The complex interplay between the mixture of bound and continuum states is reflected through this line shape. Further complexity is introduced by the radiative Raman-type coupling between the B and C state levels due to the second field. We have shown how the line shape changes with the change in relative polarizations of the two fields and their intensities in addition to the variable laser detuning. The polarization effects are very different depending on whether ${\omega }_2$ is near resonance or off-resonance with the predissociating levels. The polarization dependence has been explained with reference to the variations in rotational factors of the matrix elements concerned and the consequent change in the dissociation amplitudes through different pathways. It has also been shown that the second field is much more effective than the first field as far as dissociation is concerned.

We present a self-interaction-free time-dependent density-functional theory (TDDFT) for nonperturbative treatment of multiphoton processes of many-electron molecular systems in intense laser fields. The time-dependent exchange-correlation (xc) energy potential with proper short- and long-range potential is constructed by means of the time-dependent optimized effective potential (OEP) method and the incorporation of an explicit self-interaction-correction (SIC) term. The resulting time-dependent OEP/SIC equations are structurally similar to the time-dependent Hartree-Fock equations, but include the many-body effects through an orbital-independent single-particle local time-dependent xc potential. A numerical time-propagation technique is introduced for accurate and efficient solution of the TDDFT/OEP-SIC equations for two-center diatomic molecular systems. This procedure involves the use of a generalized pseudospectral method for nonuniform optimal grid discretization of the Hamiltonian in prolate spheroidal coordinates and a split-operator scheme in the energy representation for the time development of the electron orbital wave functions. High-precision time-dependent wave functions can be obtained by this procedure with the use of only a modest number of spatial grid points. The theory is applied to a detailed study of high-order harmonic generation (HHG) processes of ${\mathrm{H}}_2$ molecules in intense pulsed laser fields. Particular attention is paid to the exploration of the spectral and temporal structures of HHG by means of the wavelet time-frequency analysis. The results reveal striking details of the spectral and temporal fine structures of HHG, providing new insights regarding the detailed HHG mechanisms in different energy regimes.

The sonic analog of a gravitational black hole in dilute-gas Bose-Einstein condensates is investigated. It is shown that there exist both dynamically stable and unstable configurations which, in the hydrodynamic limit, exhibit behaviors completely analogous to that of gravitational black holes. The dynamical instabilities involve the creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models, namely, a long, thin condensate with an outcoupler laser beam providing an “atom sink,” and a tight ring-shaped condensate. We also simulate the creation of a stable sonic black hole by solving the Gross-Pitaevskii equation numerically for a condensate subject to a trapping potential which is adiabatically deformed. A sonic black hole could, in this way, be created experimentally with state-of-the-art or planned technology.

We consider the damping of condensate collective modes in the collisionless regime at finite temperatures arising from lack of equilibrium between the condensate and the noncondensate atoms, an effect that is ignored in the usual discussion of the collisionless region. As a first approximation, we ignore the dynamics of the thermal cloud. Our calculations should be applicable to collective modes of the condensate that are oscillating out-of-phase with the thermal cloud. We obtain a generalized Stringari equation of motion for the condensate at finite temperatures, which includes a damping term associated with the fact that the condensate is not in diffusive equilibrium with the static thermal cloud. This intercomponent collisional damping of the condensate modes is comparable in magnitude to the Landau damping considered in the recent literature.

A renormalization-group method is developed with which thermodynamic properties of a weakly interacting, finite-size Bose gas can be investigated. Thereby effects originating from a confining potential are taken into account by periodic boundary conditions and by treating the resulting discrete energy levels of the confined degrees of freedom properly. The resulting density of states modifies the flow equations of the renormalization group in momentum space. It is shown that as soon as the characteristic length of confinement becomes comparable to the thermal wavelength of a weakly interacting and trapped Bose gas its thermodynamic properties are changed significantly. This is exemplified by investigating characteristic bunching properties of the interacting Bose gas which manifest themselves in the second-order coherence factor.

We develop a full numerical as well as an approximate analytic solution for two-step holographic recording with high intensity pulses in ${\mathrm{LiNbO}}_3:\mathrm{F}\mathrm{e}$ crystals. We find the unknown material parameters by fitting the numerical solution to the experimental results. The two important parameters that were unknown so far and found in this work are the bulk photovoltaic coefficient and absorption cross section for the excitation of the electrons from small polarons in ${\mathrm{LiNbO}}_3$ with infrared light. We show that the approximate analytic solution agrees very well with the numerical solution (as well as the experimental results) for most practical applications. We use the analytic solution to explain the experimental observations that were not understood before.

The plane-wave dynamics of $3\overrightarrow{\omega }2\omega ,\omega$ subharmonic optical parametric oscillators containing a second-harmonic generator of the idler-wave ω is analyzed analytically by using the mean-field approximation and numerically by taking into account the field propagation inside the media. The resonant ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}(-3\omega ;2\mathrm{}\omega ,\omega ):{\chi }^{\mathrm{}\left(2\right)\mathrm{}}(-2\omega ;\omega ,\omega )$ cascaded second-order nonlinearities induce a mutual injection locking of the signal and idler waves that leads to coherent self-phase locking of the pump and subharmonic waves, freezing the phase diffusion noise. In case of signal-and-idler resonant devices, largely detuned subthreshold states occur due to a subcritical bifurcation, broadening out the self-locking frequency range to a few cavity linewidths.

We analyze pattern formation in doubly resonant second-harmonic generation in the presence of a competing parametric process, also named the internally pumped optical parametric oscillator. Different scenarios are established where either the up- or down-conversion processes dominate the spatiotemporal behavior. The possibility of obtaining exact solutions above threshold for the parametric oscillation process allows detailed analytical investigations of the parametric instability, that are supplemented by numerical analysis. We identify secondary instabilities that lead to formation of negative patterns and gray solitons. Estimates of the thresholds for pattern formation under experimentally relevant conditions are given.

We have investigated electron transfer and fragmentation of ${\mathrm{C}}_{60}$ molecules in slow $(1q–2q$ keV) collisions with ${\mathrm{C}}_{60}^{q+}$ projectiles $(q=2\mathrm{}–5)$ and atomic ${\mathrm{C}}^{q+}$ projectiles at somewhat higher velocities. While the latter give the characteristic fragment distributions the former only yield intact ${\mathrm{C}}_{60}^{r+}$ target molecules. Further, the atomic carbon projectiles ionize the target ${\mathrm{C}}_{60}$ up to their incident charges, $r_{\max }=q,$ while the maximum target charges are limited to $r_{\max }=\mathrm{Int}\left[\mathrm{}\right(q+1\mathrm{})/2\mathrm{}]$ for ${\mathrm{C}}_{60}^{q+}$ projectiles. The latter results are explained by considering the energy minima for q charges distributed on the equipotential surfaces of two touching spheres.

In a previous article [J. R. Walkup, M. Dunn, and D. K. Watson, Phys. Rev. A 58, 4668 (1998)] dimensional perturbation theory (DPT) was applied to circular Rydberg states of diamagnetic hydrogen to investigate avoided crossings in its energy spectrum as both the field strength and magnetic quantum number m were swept. Because the DPT perturbation parameter $\delta =1/(D+2\mathrm{}|m|+1),$ where D is the dimensionality of the system, is inversely related to m, one might assume that for a given field strength DPT would be effective only when m is large. However, the field-strength expression used in DPT is scaled as a function of m, so it is not obvious a priori whether the effectiveness of DPT diminishes when m is significantly reduced for a given physical field strength. It is shown that for many states of diamagnetic hydrogen DPT can still produce strongly convergent and accurate energy values when m is small, even when $m=0\mathrm{}$ $(\delta =1/2).\mathrm{}$ For those regions where even Padé summation failed to converge adequately, a technique is presented based on economized rational approximants.

We have observed the bichromatic force on metastable He using fiber amplifiers to produce the high power of light needed at $\lambda =1.083\mathrm{}\hspace{0.5em}\mu \mathrm{m}.$ We have done deflection experiments to confirm that the very large magnitude of the force scales to He, and preliminary deceleration experiments for eventual trap loading. Our measurements support earlier experiments in Rb. Helium is ideally suited for this kind of beam slowing because its slowing length with the usual radiative force is more than a factor of 100 larger than with the bichromatic force. Thus, loading a MOT will be much more effective because of the much larger angular capture range associated with the shorter distance.

We investigate the behavior of a two-component Bose-Einstein condensate (BEC) driven by a strong time-dependent resonant magnetic field. The external resonant field couples two hyperfine states via a one-photon transition. It is shown that a first-order parametric instability of a BEC appears if the local atomic number density exceeds a threshold value that is proportional to the driving field. It is shown that the spatial-dependent increment of instability is proportional to the square of the local atomic density. This instability is determined by the nonlinearity of the BEC associated with the short-range interactions between the atoms.

We investigate the entanglement properties of multiparticle systems, concentrating on the case where the entanglement is robust against the disposal of particles. Two qubits—belonging to a multipartite system—are entangled in this sense if their reduced density matrix is entangled. We introduce a family of multiqubit states, for which one can choose for any pair of qubits independently whether they should be entangled or not as well as the relative strength of the entanglement, thus providing the possibility to construct all kinds of “entanglement molecules.” For some particular configurations, we also give the maximal amount of entanglement achievable.

By applying an intense 28-fs laser pulse to a helium gas jet, spectrally resolved high-order harmonics originating from different quantum paths were obtained. The selection of high-order harmonics from a single quantum path could be achieved by controlling the phase-matching condition. Comparison of the observed harmonic spectrum with a calculation indicated that an attosecond pulse train with a single attosecond pulse per half-optical cycle was produced.