We find that multidimensional determinants “hyperdeterminants,” related to entanglement measures (the so-called concurrence, or 3-tangle for two or three qubits, respectively), are derived from a duality between entangled states and separable states. By means of the hyperdeterminant and its singularities, the single copy of multipartite pure entangled states is classified into an onion structure of every closed subset, similar to that by the local rank in the bipartite case. This reveals how inequivalent multipartite entangled classes are partially ordered under local actions. In particular, the generic entangled class of the maximal dimension, distinguished as the nonzero hyperdeterminant, does not include the maximally entangled states in Bell’s inequalities in general (e.g., in the $n>~4$ qubits), contrary to the widely known bipartite or three-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical n-partite entangled states. Our classification is also useful for the mixed states.

In this paper we calculate with full details Einstein-Podolsky-Rosen spin correlations in the framework of nonrelativistic quantum mechanics. We consider the following situation: two-particle state is prepared (we consider separately distinguishable and identical particles and take into account the space part of the wave function) and two observers in relative motion measure the spin component of the particle along given directions. The measurements are performed in bounded regions of space (detectors), not necessarily simultaneously. The resulting correlation function depends not only on the directions of spin measurements but also on the relative velocity of the observers.

The dynamics of a wave packet incoming on a quantum-mechanical barrier is analyzed in the framework of a fully relativistic model, with particular emphasis on the case of a large spectrum. Some of the characteristic times of tunneling are calculated and compared; they are all of the same order of magnitude and all indicate an apparent superluminal motion, even if causality is maintained. A time-asymptotic expression for the transmitted wave function is derived and its strong validity is shown.

Strong and fast “bang-bang” (BB) pulses have been recently proposed as a means for reducing decoherence in a quantum system. So far theoretical analysis of the BB technique relied on model Hamiltonians. Here we introduce a method for empirically determining the set of required BB pulses, that relies on quantum process tomography. In this manner an experimenter may tailor his or her BB pulses to the quantum system at hand, without having to assume a model Hamiltonian. In addition, the previous work has been extended to a general noiseless evolution via the stabilizer formalism.

We have investigated the $2{}^2{S}_{1/2}–4{}^2{S}_{1/2}$ two-photon transition in atomic lithium by high resolution laser spectroscopy. The frequencies of the two-photon resonances have been measured with an accuracy of better than 1 MHz using a Fabry-Pérot wavemeter. The centers of gravity of the $4{}^2{S}_{1/2}$ levels are 35 012.033 582 (26) ${\mathrm{cm}}^{-1}$ for ${}^7\mathrm{Li}$ and 35 011.544 497 (30) ${\mathrm{cm}}^{-1}$ for ${}^6\mathrm{Li}.$ The transition isotope shift is 14 662.4 (10) MHz. We have also determined the magnetic hyperfine splitting constant for the $4{}^2{S}_{1/2}$ state for both isotopes.

We report calculations of the cross sections for single ionization of the ground $1{}^{1}S$ and excited $2{}^{1}P$ helium states by relativistic impact of a bare uranium ion of charge $Z_p=92\mathrm{}$ with energy 1 GeV/u. The heavy particle collision is treated within the semirelativistic first Born approximation. The nonrelativistic initial and final two-electron correlated atomic states are obtained by numerical procedures from variational principles. The continuum final states are considered below the $n=2\mathrm{}$ threshold of the ${\mathrm{He}}^{+}$ ion. The differential ionization cross section $d\sigma /dE$ is obtained for electron energies $E<~37\mathrm{eV}.$ This energy range includes a wide nonresonant region as well as the resonance structures due to the autoionizing helium states ${(2s}^2){}^{1}S,$ $\mathrm{}\left(2s2p\right)\mathrm{}{}^{1}P$ and ${(2p}^2){}^{1}D.\mathrm{}$

Charge transfer processes due to collisions of ground state ${\mathrm{O}}^{3+}{(2s}^{2}2p{}^{2}P)$ ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial and rotational coupling matrix elements obtained with the spin-coupled valence-bond approach. Total and state-selective cross sections and rate coefficients are presented. Comparison with existing experimental and theoretical data shows our results to be in better agreement with the measurements than the previous calculations, although problems with some of the state-selective measurements are noted. Our calculations demonstrate that rotational coupling is not important for the total cross section, but for state-selective cross sections, its relevance increases with energy. For the ratios of triplet to singlet cross sections, significant departures from a statistical value are found, generally in harmony with experiment.

We apply the time-dependent close-coupling method to the double photoionization of helium from its $1s2s$ ${}^{1,3}S$ metastable states. Total integral cross sections are in excellent agreement with other nonperturbative theories. Single and triple differential cross sections are also presented which show interesting differences with previous calculations from the ${1s}^2$ ground state of helium. This set of calculations provides a goal for experimentalists to measure absolute total and angular differential cross sections for double ionization processes from excited states of atoms.

The photoionization spectra of isolated chromium clusters from ${\mathrm{Cr}}_4$ to ${\mathrm{Cr}}_{25}$ have been recorded. The vertical ionization energies ${(E}_i^v)$ derived from the spectra decrease discontinuously with increasing cluster size. The $E_i^v$ values determined for ${\mathrm{Cr}}_n$ species were, in most cases, within 0.2 eV of those of the corresponding ${\mathrm{Cr}}_n\mathrm{O}$ and ${\mathrm{Cr}}_n{\mathrm{O}}_2$ species, recently reported by Wang et al. [Appl. Phys. B 73, 417 (2001)], with the largest differences observed for several of the smaller clusters. The $E_i^v$ determined for ${\mathrm{Cr}}_4$ was 0.7 ev larger than that found previously for ${\mathrm{Cr}}_4\mathrm{O},$ suggesting that in this case the bare cluster and oxide have different structures.

Light-induced drift (LID) of a rarefied gas in a cell is studied, and exact analytical closed-form solutions to the model rate equations, which model the gas motion in one dimension, are obtained for cases of both surface LID (SLID) and bulk LID (BLID); the special case of the limit of low radiation absorption by the gas is given particular attention. Similarities and differences among the results for SLID and BLID are discussed. This is part III of a series of papers, parts I and II having studied LID, but concentrating on SLID, with flat-plate and circular-cylindrical cell geometries, respectively [F. O. Goodman, Phys. Rev. A 65, 064309 (2002); 65, 064310 (2002)].

Light-induced drift (LID) of a rarefied gas in a cell is studied, and exact analytical closed-form solutions to the model rate equations are obtained for bulk LID (BLID) in three dimensions, emphasis being placed on the limit of low radiation absorption by the gas. Comparisons are made with an existing model of BLID in one dimension [F. O. Goodman, preceding paper, Phys. Rev. A 67, 013410 (2003)], and we examine whether there are any conditions under which that model is satisfactory. Comparisons are also made with the author’s models of surface LID in one dimension (above reference) and in three dimensions [F. O. Goodman, Phys. Rev. A 65, 063409 (2002); 65, 063410 (2002)].

The asymptotic solution for a hydrogen atom in a uniform magnetic field of arbitrary strength is obtained. It is derived in the form of common exponential factor multiplied by a finite power of radius time a power series in two variables, the sine of the cone angle and the inverse of radius, with explicit recurrent relations for the coefficients of the power series. It is proven that there exists only one physically acceptable solution in this form. Combining this solution at some radius R with similar series solution in the form of a power series in the radial variable with coefficient being polynomials in the sine, determines the binding energies and wave functions of bound states. To illustrate the usefulness of this approach, the ground-state binding energy of the magnetic field $B=100\mathrm{}$ (in units of $2.35\times {10}^9\mathrm{G})$ has been computed with accuracy in ${10}^{-12}$ hartree. The precision required is $\approx 30$ decimal digits, while the previous result of the same accuracy obtained by direct numerical summation of the series using simple exponential decay as the boundary conditions at finite radius R has been computed in high-precision arithmetic of $\approx 280$ decimal digits. The accuracy of the binding energies of the excited state evolving from ${2s}_0$ exceeds that of previous calculations.

A mixed-classical-quantum approach to describe laser-induced excitation, fragmentation and, in particular, ionization of one-electron molecular dimers is presented. Self-consistent equations of motion for the classical nuclear dynamics and the quantum-mechanical electronic evolution are derived. They are solved using a combined set of basis functions for the electronic wave function consisting of atomic orbitals and chainlike arranged Gaussians to account for a realistic description of the continuum dynamics of the ionized electron. For the molecular benchmark system ${\mathrm{H}}_2^{+},$ the obtained results are in good agreement with those of full-quantum-mechanical calculations, which are available for relatively short laser pulses. For longer pulses, the present calculation signals a transient effect of molecular stabilization against fragmentation at corresponding (low) laser intensities.

We consider an electron that is bound by a zero-range potential and a constant magnetic field and which becomes disturbed by a monochromatic laser beam with elliptical polarization. The exact solution of the Schrödinger equation for an electron in the presence of an arbitrary electromagnetic wave and a static magnetic field is obtained. Exact expressions have been found for the complex energy, whose real and imaginary parts yield the level position and the width of an electron in a zero-range force field, a constant magnetic field, and a monochromatic electromagnetic field. These expressions have been analyzed in details for the case of a circularly polarized laser light.

We study the scattering properties of a Bose-Einstein condensate held in a finite depth well when the incoming particles are identical to the ones in the condensate. We calculate phase shifts and corresponding transmission and reflection coefficients, and we show that the transmission times can be negative, i.e., the atomic wave packet seemingly leaves the condensate before it arrives.

Development of a theoretical treatment of multiple coherent light scattering in an ultracold atomic gas is reported. Specific application is made to coherent backscattering of a weak-radiation field from realistically modeled samples of ultracold atomic ${}^{85}\mathrm{Rb}.$ Comprehensive Monte Carlo simulations of the spatial, spectral, and polarization dependence of the backscattering line shape are made and compared with available experimental results.

The effect of the carrier-envelope phase of a few-cycle driving laser field on the generation and measurement of high-order harmonic attosecond pulses is investigated theoretically. We find that the position of the generated attosecond soft-x-ray pulse in the cutoff region is locked to the oscillation of the driving laser field, but not to the envelope of the laser pulse. This property ensures the success of the width measurement of an attosecond soft-x-ray pulse based on the cross correlation between the attosecond pulse and its driving laser pulse [M. Hentschel et al., Nature (London) 414, 509 (2001)]. However, there still exists a timing jitter of the order of tens of attoseconds between the attosecond pulse and its driving laser field. We also propose a method to detect the carrier-envelope phase of the driving laser field by measuring the spatial distribution of the photoelectrons induced by the attosecond soft-x-ray pulse and its driving laser pulse.

High-order harmonic generation from a solid target surface has been investigated using femtosecond laser pulses focused to intensities greater than ${10}^{18}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ The experiments show that the harmonics are very intense, with a conversion efficiency that is one or two orders of magnitude larger than that of harmonics generated in gases. Beside the observation of presently the shortest wavelength harmonics from femtosecond-laser solid target interaction, i.e., down to 22 nm, an anomaly has been observed in the harmonic spectrum. In contrast to the expected well-known continuous “roll off” of the high-harmonic orders, the harmonic intensity decreases with the increase of harmonic order, but in between shows minima which are significantly less intense than the neighboring harmonics. Furthermore, the order of the harmonic minima depend on target material. Additional calculations using numerical kinetic particle simulations and a simpler oscillating mirror model show that the physical origin of these modulations is an intricate interplay of resonance absorption and ponderomotive force which leads to a complex electron density profile evolution. Furthermore, this is emphasized by a spectral line analysis of the harmonics. In agreement with the theory, broad lines have been observed and, in particular for the harmonics in the minima, a complex interference structure is present.

A quantum-information-processing scheme is proposed with semiconductor quantum dots located in a high-$Q$ single-mode QED cavity. The spin degrees of freedom of one excess conduction electron of the quantum dots are employed as qubits. Excitonic states, which can be produced ultrafast with optical operation, are used as auxiliary states in the realization of quantum gates. We show how properly tailored ultrafast laser pulses and Pauli-blocking effects can be used to achieve a universal encoded quantum computing.

We present a detailed study of the method recently proposed by Yang and Gea-Banacloche [Phys. Rev. A 64, 032309 (2000)] to protect a maximally entangled state of n atomic qubits against spontaneous-emission-induced decoherence. We compare this to an approach based on nonradiative states, in the case where the number of thermal photons in the environment is nonzero.