A coherent representation has been developed for entanglement and measurement, which is an elegant approach to continuous variable quantum teleportation. In the present paper this frame is used to deal with nonideal elements of the experimental situation, such as inefficiencies of the Bell measurement, loss, and thermal noise in the nonlinear crystal used for producing entangled pairs. A measure of fidelity is introduced for characterizing the quality of nonideal schemes.

A two-level atom interacting with a single radiation mode is considered, without the rotating-wave approximation, in the strong-coupling regime. It is shown that, in agreement with the recent results on Rabi oscillations in a Josephson junction [Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, Phys. Rev. Lett. 87, 246601 (2001)], the Rabi frequency is indeed proportional to first kind integer order Bessel functions in the limit of a large number of photons and the dressed states are macroscopic quantum superposition states. To approach this problem, analytical use of the dual Dyson series and the rotating-wave approximation is made.

We have experimentally investigated the free expansion of a Bose-Einstein condensate in an array of two-dimensional traps created by a one-dimensional optical lattice. If the condensate held in a magnetic trap is loaded adiabatically into the lattice, the increase in chemical potential due to the additional periodic potential is reflected in the expansion of the condensate after switching off the magnetic trap. We have calculated the chemical potential from measurements of the transverse expansion of the condensate as a function of the lattice parameters.

We derive an encoded universality representation for a generalized anisotropic exchange Hamiltonian that contains cross-product terms in addition to the usual two-particle exchange terms. The recently developed algebraic approach is used to show that the minimal universality-generating encodings of one logical qubit are based on three physical qubits. We show how to generate both single- and two-qubit operations on the logical qubits, using suitably timed conjugating operations derived from analysis of the commutator algebra. The timing of the operations is seen to be crucial in allowing simplification of the gate sequences for the generalized Hamiltonian to forms similar to that derived previously for the symmetric $\mathrm{}\left(\mathrm{XY}\right)\mathrm{}$ anisotropic exchange Hamiltonian. The total number of operations needed for a controlled-$Z$ gate up to local transformations is five. A scalable architecture is proposed.

In the framework of the two-step model of Auger decay the orientation of the krypton ${3d}^{-1}$ and xenon ${4d}^{-1}$ primary hole states has been determined as a function of photon energy. This was achieved by carrying out spin-polarization measurements of the Kr $M_{4,5}{N}_{2,3}{N}_{2,3}$ and Xe $N_{4,5}{O}_{2,3}{O}_{2,3}$ Auger electrons after ionization of free atoms by circularly polarized synchrotron radiation of 130–530 eV photon energy. The orientation parameter is found to be strongly influenced by the Cooper minimum in the Xe $4d$ photoionization cross section as demonstrated by the comparison of the Kr and Xe data. Furthermore, the intrinsic parameters for all lines in the Kr $M_{4,5}{N}_{2,3}{N}_{2,3}$ and Xe $N_{4,5}{O}_{2,3}{O}_{2,3}$ Auger groups and for several lines in the Kr $M_{4,5}{N}_1{N}_{2,3}$ Auger group were determined with high accuracy and are compared with previous experiments and calculations. We were also able to measure the spin polarization of most of the low kinetic-energy Kr $M_{4,5}\mathrm{NN}$ and Xe $N_{4,5}\mathrm{OO}$ lines, showing that the assignment of one of the lines should be revisited.

When atoms interact with a phase-modulated field, the probability of finding the atom in the excited-state oscillates at the second harmonic of the modulation frequency, $2{\omega }_m.$ The amplitude of this oscillating probability is a resonant function of the Rabi frequency Ω, and this is termed a β Rabi resonance. In this work, we examine the line shape of the β Rabi resonance both theoretically and experimentally. We find that a small-signal theory of the β-Rabi-resonance condition captures much of the line shape’s character, and, in particular, that the resonance’s “line Q” (i.e., $2\delta {\Omega }_{1/2}/\Omega )$ is proportional to the modulation frequency. This result can be applied to the atomic candle, where β Rabi resonances are employed to stabilize field strength. Considering our results in the context of developing an optical atomic candle, we find that a free-running diode laser’s intensity noise could be improved by orders of magnitude using the atomic candle concept.

We study the quantum properties of the spatially tilted macroscopic signal beams in the transverse pattern formed in a degenerate optical parametric oscillator above threshold. We show that walk-off leads to an imbalance in the intensities and fluctuations of these beams when nonlinear multimode interactions are effective. Still, quantum correlations between the two beams are preserved, so that their intensity difference exhibits sub-Poissonian statistics.

Optimal procedures play an important role in quantum information. It turns out that some naturally occurring processes as emission of light from an atom can realize optimal transformations. Here we study how arbitrary symmetric states of a number of d-level systems can be cloned using a multilevel atomic system. It is shown that optimality is always ensured even though the output number of systems is probabilistic.

We show that a beam splitter of reflectivity one-third can be used to realize a quantum phase gate operation if only the outputs conserving the number of photons on each side are postselected.

Coordinate scaling of each spin density separately is considered in spin-density-functional theory. A virial theorem relates the spin-scaled correlation energy to the spin-scaled correlation potentials. An adiabatic connection formula expresses energies at different spin interaction strengths in terms of spin scaling. Several popular approximate functionals are evaluated on the spin-scaled densities of atoms and of the uniform electron gas. The differences between this and uniform scaling are discussed.

This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine the entanglement and correlation properties guided by the corresponding calculations of concurrence. It is shown that the entropy difference between that of the composite and its marginal density matrices may be of arbitrary sign except under special circumstances when conditional probability can be defined appropriately. This ambiguity is a consequence of the fact that the overlap matrix elements of the eigenstates of the composite density matrix with those of its marginal density matrices also play important roles in the definitions of probabilities and the associated entropies, along with their respective eigenvalues. The general results are illustrated using pure- and mixed-state density matrices of two-qubit systems. Two classes of density matrices are found for which the conditional probability can be defined: (1) density matrices with commuting decompositions and (2) those that are decohered in the representation where the density matrices of the marginals are diagonal. The first class of states encompass those whose separability is currently understood as due to particular symmetries of the states. The second are a class of states that are expected to be useful for understanding separability. Examples of entropy functionals of these decohered states including the crucial isospectral case are discussed.

Decoherence is the main problem to be solved before quantum computers can be built. To control decoherence, it is possible to use error correction methods, but these methods are themselves noisy quantum computation processes. In this work, we study the ability of Steane’s and Shor’s fault-tolerant recovering methods, as well as a modification of Steane’s ancilla network, to correct errors in qubits. We test a way to measure correctly ancilla’s fidelity for these methods, and state the possibility of carrying out an effective error correction through a noisy quantum channel, even using noisy error correction methods.

Suppose that three kinds of quantum systems are given in some unknown states $|f{〉}^{\otimes N},$ $|g_1{〉}^{\otimes K},$ and $|g_2{〉}^{\otimes K},$ and we want to decide which template state $|g_1〉$ or $|g_2〉,$ each representing the feature of the pattern class ${\mathcal{C}}_1$ or ${\mathcal{C}}_2,$ respectively, is closest to the input feature state $|f〉.$ This is an extension of the pattern matching problem into the quantum domain. Assuming that these states are known a priori to belong to a certain parametric family of pure qubit systems, we derive two kinds of matching strategies. The first one is a semiclassical strategy that is obtained by the natural extension of conventional matching strategies and consists of a two-stage procedure: identification (estimation) of the unknown template states to design the classifier (learning process to train the classifier) and classification of the input system into the appropriate pattern class based on the estimated results. The other is a fully quantum strategy without any intermediate measurement, which we might call as the universal quantum matching machine. We present the Bayes optimal solutions for both strategies in the case of $K=1,$ showing that there certainly exists a fully quantum matching procedure that is strictly superior to the straightforward semiclassical extension of the conventional matching strategy based on the learning process.

We perform an improved calculation of the $\alpha$ dependence $(\alpha {=e}^2/hc)$ of the transition frequencies for ions, which are used in a search for the variation of the fine-structure constant $\alpha$ in space-time. We use the Dirac-Hartree-Fock method as a zero approximation and then the many-body perturbation theory and configuration-interaction methods to improve the results. The important problem of level pseudocrossing (as a function of $\alpha )$ is considered. Near the crossing point the derivative of the frequency over $\alpha$ varies strongly (including a change of sign). This makes it very sensitive to the position of the crossing point. We propose a semiempirical solution of the problem, which allows us to obtain accurate results.

The Zeeman $g_J$ factors are calculated for the $2^2{P}_J$ and $3^2{P}_J$ states of lithium and lithiumlike ions, including relativistic corrections of order ${\alpha }^2,$ using variational wave functions in Hylleraas coordinates. Comparison with other calculations is made.

Starting from the microscopic semiconductor Bloch equations including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell’s equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole $(e$-$h)$ and carrier–LO-phonon $(c$-LO) scatterings are directly used to derive the momentum and energy relaxation rates. These rates, expressed as functions of temperatures and densities, lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-$h$ scattering dominates over $c$–LO-phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-$h$ scattering, even though the diffusion coefficients of individual components depend sensitively on the e-$h$ scattering rates. Our discussions lead to deeper insights into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization, which in turn couples to the laser field.

We present numerical results for the diffusion coefficients (DCs) in the coupled diffusion model derived [J. Li and C. Z. Ning, preceding paper, Phys. Rev. A 66, 023802 (2002)] for a semiconductor quantum well. These include self- and mutual-diffusion coefficients in the general two-component case, as well as density- and temperature-related DCs under the single-component approximation. The results are analyzed from the viewpoint of the free Fermi gas theory with many-body effects incorporated. We discuss in detail the dependence of these DCs on densities and temperatures in order to identify different roles played by the free-carrier contributions including carrier statistics and carrier–LO-phonon scattering, and many-body corrections including band-gap renormalization and electron-hole $(e-h)$ scattering. In the general two-component case, it is found that the self- and mutual-diffusion coefficients are determined mainly by the free-carrier contributions, but with significant many-body corrections near the transition density where carrier statistics changes from the Maxwell to the Fermi-Dirac distribution. Carrier–LO-phonon scattering is dominant at low density, whereas e-$h$ scattering becomes important in determining their density dependence above the electron transition density. In the single-component case, it is found that many-body effects decrease the density coefficients but enhance the temperature coefficients. The modification is on the order of $10\%$ and reaches a maximum of over $20\%$ [C. Z. Ning and J. Li, Phys. Rev. B $65,$ 201305(R) (2002)] for the density coefficients. Overall, temperature elevation enhances the diffusive capability of carriers (DCs) linearly, and such an enhancement grows with density. The complete data set of various DCs as functions of carrier densities and temperatures provides necessary ingredients for future applications of the model to various spatially inhomogeneous optoelectronic devices.

We show that a micromaser can work as an effective source of highly correlated atoms. We consider a one-photon micromaser pumped by a Poissonian beam of atomic pairs. We show that the atoms forming the pairs leave the micromaser’s cavity in entangled states and that they can violate the Bell inequality. We consider two aspects of the violation of the Bell inequality: we study the maximal value ${\mathbf{B}}_{\max }$ of an expression appearing in the Bell inequality and we evaluate a vector-dependent $\mathbf{B}(\overrightarrow{a},a^{\prime },\overrightarrow{b},b^{\prime })$ depending upon experimental setup. We calculate the entanglement of the formation of states of the atomic pairs. We show that the pairs of atoms, which fly out from the micromaser cavity, are entangled for almost all values of control parameters characterizing the considered two-atom micromaser. This happens even if they do not violate the Bell inequality.

We study high-order harmonic generation for ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_2$ model molecules in linearly polarized laser pulses by numerical solution of the Schrödinger equation. Maxima and minima due to intramolecular interference are found in the dependence of the harmonic intensities on the internuclear distance and on the orientation of the molecules. These extrema can be approximately predicted by regarding them as the result of interference between two radiating point sources located at the positions of the nuclei.

We present a multiparty quantum clock synchronization protocol that utilizes shared prior entanglement and broadcast of classical information to synchronize spatially separated clocks. Notably, it is necessary only for any one party to publish classical information. Consequently, the efficacy of the method is independent of the relative location of the parties. The suggested protocol is robust and does not require precise sequencing of procedural steps.