We study the threshold temperature for pairwise thermal entanglement in the spin-1/2 isotropic Heisenberg model up to 11 spins and find that the threshold temperature for odd and even number of qubits approaches the thermal dynamical limit from below and above, respectively. The threshold temperature in the thermodynamical limit is estimated. We investigate the many-particle entanglement in both the ground states and the thermal states of the model up to 11 spins, and find that the ground state in the four-qubit model is a four-particle entangled state and the corresponding thermal state is also a four-particle entangled state before a threshold temperature.

It is shown that the correlations between two qubits selected from a trio prepared in a W state violate the Clauser-Horne-Shimony-Holt inequality more than the correlations between two qubits in any quantum state. Such a violation beyond Cirel’son’s bound is smaller than the one achieved by two qubits selected from a trio in a Greenberger-Horne-Zeilinger state [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. However, it has the advantage that all local observers can know from their own measurements whether or not their qubits belong to the selected pair.

In this paper we analyze the fidelity of the output states in the experimental quantum teleportation of photons, while taking into account the main experimental parameters. In particular, we consider the detector’s ability to distinguish photon numbers, the quantum efficiency of the detectors, and the purity of entangled photon pairs. As a result, it is found that high-fidelity quantum teleportation, without the receiver feedback check, is realizable with multiphoton counters and conventional entangled pairs (visibility=90%) within a day.

The security of quantum key distribution with sub-Poisson light sources is investigated. It is shown that a quantitative analysis of the security of such sources requires only two measured values, the efficiency and second-order correlation. These two numbers represent figures of merit, which characterize the performance of such light sources. We show that sub-Poisson light sources can offer significant improvements in communication rate over Poisson light in the presence of realistic experimental imperfections. We also investigate the amount of channel loss that can be tolerated for secure communication to be possible, and show that this only depends on the second-order correlation, provided the device efficiency exceeds a critical value. If this critical efficiency is exceeded, an inefficient source can perform as well as an efficient one at sufficiently high channel losses.

The cross sections for the production of double K and L vacancy states in Al, Ca, and Co as a result of electron bombardment were determined for impact energies ranging from the double excitation threshold up to 20 keV. The cross sections were derived from the measured intensity ratios $I_{K\alpha L^{\mathrm{}\left(1\right)\mathrm{}}}{:I}_{K\alpha L^{\mathrm{}\left(0\right)\mathrm{}}}$ of the satellite-to-parent-diagram x-ray lines. The specific contributions of the shake and two-step electron-electron processes could be probed by comparing the relative satellite yields observed in the electron-induced spectra to those obtained by photoionization. In particular the energy-dependent cross sections for double K and L excitation resulting from two-step-two processes could be deduced. The measurements were performed by means of high-resolution x-ray spectroscopy, using a reflection-type bent crystal spectrometer.

Doubly excited KLL states were populated by triple electron capture in collisions of fast $(v=4.5\mathrm{}–6.6\mathrm{a}.\mathrm{u}.\mathrm{})$ ${\mathrm{C}}^{6+}$ ions with Ar atoms. Measurements of the Auger-electron emission in the direction of the ion beam were used to determine the absolute single differential cross sections for the triple electron capture to all autoionizing KLL states. The results were compared with cross sections calculated within the independent-particle model, in which the simultaneous capture of all three target electrons was assumed. Single electron capture probabilities, employed by the model, were calculated using the two-center semiclassical close-coupling method, based on an atomic orbital expansion. In order to allow comparison of the measured zero-degree differential cross sections with calculated total cross sections, the Auger-electron emission from the doubly excited KLL states was assumed isotropic. Model calculations were found to be in a good agreement with the experimental data. An adequate description of the triple electron capture by the model implies that the projectile screening and electron-electron correlation effects in multiple electron capture are significantly reduced in fast, highly charged ion-atom collisions.

We analyze the dynamical interactions of swift heavy projectiles and solid inner-shell electrons. The dielectric formalism employed to deal with the free-electron gas is extended to account for the core electrons, by using the local plasma approximation. Results for stopping power, energy straggling, and inner-shell ionization in collisions of bare ions with metals are displayed, showing very good accord with the experimental data. Simultaneous excitations of projectile and target electrons are also analyzed. In the high-energy range we find a similar contribution of target core and valence electrons to the probability of projectile-electron loss. The problem of no excitation threshold within the local plasma approximation and the possibility of collective excitations of the shells are discussed.

A versatile semiclassical approximation for intense laser-atom processes is presented. This uniform approximation is no more complicated than the frequently used multidimensional saddle-point approximation and far superior, since it applies for all energies, both close to as well as away from the classical cutoffs. In the latter case, it reduces to the standard saddle-point approximation. The uniform approximation agrees accurately with numerical evaluations for potentials, for which these are feasible, and constitutes a practicable method of calculation, in general. The method is applied to the calculation of high-order above-threshold ionization spectra with various binding potentials: Coulomb, Yukawa, and shell potentials which may model ${\mathrm{C}}_{60}$ molecules or clusters. The shell potentials generate rescattering spectra that are more structured and may feature an apparently higher cutoff.

In this paper, a method for state measurement in atomic waveguides is presented. Matter waves exiting a terminated waveguide are allowed to expand ballistically. Measurement is performed by spatially resolved detection of laser-induced fluorescence. We describe in detail the motion of wave packets both in the guiding potential and in the region of free expansion. It is shown that different modes can be distinguished in a straightforward manner and that the same is true for coherent superpositions after introduction of a controlled phase shift. The sensitivity of the transition from adiabatic guiding to free expansion is investigated in detail. It is found that adiabatic readjustment, which will distort the original state, can be considerable but may be avoided by proper choice of potential parameters. The method proposed here is shown to be feasible for experiments in atom optics through utilizing numerical estimates.

With the help of a microscopic model we investigate the effects of collisions and atomic recoil on the behavior of absorbing atoms placed inside a bidirectional resonator and driven by an external injected field. This model complements and generalizes earlier studies of the collective atomic recoil laser and of optical bistability. According to our model, even in the presence of collisions, the resonator can support bidirectional propagation. In particular, for appropriate selection of the parameters, we predict the existence of stationary solutions such that the cavity field that copropagates with the injected signal is locked in frequency with the external source, while the counterpropagating field is frequency shifted from both, even in steady state. The early stage of growth of the counterpropagating field is accompanied by a spatial modulation (grating structure) in the density of the medium, but this modulation decays away in a time roughly of the order of the average interval between collisions.

We investigate the connection between a multiple-scale approach recently applied to anharmonic oscillators to avoid secular terms in the time-dependent perturbation series, and a frequency-operator method developed earlier for the same purpose.

We present a scheme to produce an entangled four-photon W state by using linear optical elements. The symmetrical setup of linear optical elements consists of four beam splitters, four polarization beam splitters, and four mirrors. A photon Einstein-Podolsky-Rosen pair and two single photons are required as the input modes. The projection on the W state can be made by a four-photon coincidence measurement. Further, we show that by means of a horizontally oriented polarizer in front of one detector, the W state of three photons can be generated.

We study the entanglement of unitary operators on $d_1\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified by the concept of concurrence.

We examine a dilute two-component atomic Fermi gas trapped in a harmonic potential in the superfluid phase. For experimentally realistic parameters, the trapping potential is shown to have crucial influence on various properties of the gas. Using an effective Hamiltonian, analytical results for the critical temperature, the temperature dependence of the superfluid gap, and the energy of the lowest collective modes are derived. These results are shown to agree well with numerical calculations. We also discuss in more detail a previously proposed method to experimentally observe the superfluid transition by looking at the collective-mode spectrum. Our results are aimed at the present experimental effort to observe a superfluid phase transition in a trapped atomic Fermi gas.

In the analysis of experiments designed to reveal violation of Bell-type inequalities, it is usually assumed that any hidden variables associated with the $n\mathrm{th}$ particle pair would be independent of measurement choices and outcomes for the first $\left(n-1\right)$ pairs. Models which violate this assumption exploit what we call the memory loophole. We focus on the strongest type of violation, which uses the two-sided memory loophole, in which the hidden variables for pair n can depend on the previous measurement choices and outcomes in both wings of the experiment. We show that the two-sided memory loophole allows a systematic violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality when the data are analyzed in the standard way, but cannot produce a violation if a CHSH expression depending linearly on the data is used. In the first case, the maximal CHSH violation becomes small as the number of particle pairs tested becomes large. Hence, although in principle the memory loophole implies a slight flaw in the existing analyses of Bell experiments, the data still strongly confirm quantum mechanics against local hidden variables. We consider also a related loophole, the simultaneous measurement loophole, which applies if all measurements on each side are carried out simultaneously. We show that this can increase the probability of violating the linearized CHSH inequality as well as other Bell-type inequalities.

We explore the role played by the phase in an accurate description of the entanglement of bipartite systems. We first present an appropriate polar decomposition that leads to a truly Hermitian operator for the phase of a single qubit. We also examine the positive operator-valued measures that can describe the qubit phase properties. When dealing with two qubits, the relative phase seems to be a natural variable to understand entanglement. In this spirit, we propose a measure of entanglement based on this variable.

We investigate the dynamics of entanglement between two continuous variable quantum systems. The model system consists of two atoms in a harmonic trap which are interacting by a simplified s-wave scattering. We show, that the dynamically created entanglement changes in a steplike manner. Moreover, we introduce local operators which allow us to violate a Bell-Clauser-Horne-Shimony-Holt inequality adapted to the continuous variable case. The correlations show nonclassical behavior and almost reach the maximal quantum-mechanical value. This is interesting since the states prepared by this interaction are very different from any Einstein-Podolsky-Rosen–like state.

We discuss several methods for unambiguous state discrimination of N symmetric coherent states using linear optics and photodetectors. One type of measurement is shown to be optimal in the limit of small photon numbers for any N. For the special case of $N=4\mathrm{}$ this measurement can be fruitfully used by the receiving end (Bob) in an implementation of the Bennett-Brassard 1984 (BB84) quantum key distribution protocol using faint laser pulses. In particular, if Bob detects only a single photon the procedure is equivalent to the standard measurement that he would have to perform in a single-photon implementation of BB84, if he detects two photons Bob will unambiguously know the bit sent to him in 50% of the cases without having to exchange basis information, and if three photons are detected, Bob will know unambiguously which quantum state was sent.

Differential direct and charge-transfer scattering cross sections are calculated for collisions of ${\mathrm{H}}^{+}$ with ${\mathrm{N}}_2$ using the electron nuclear dynamics formalism. The calculated cross sections are compared to direct scattering measurements which are also reported here and to the experimental charge transfer data of Gao et al. [R. S. Gao, L. K. Johnson, C. L. Hakes, K. A. Smith, and R. F. Stebbings, Phys. Rev. A 41, 5929 (1990)]. Cross sections are presented for projectile energies of 0.5, 1.5, and 5.0 keV and scattering angles of $0.01°$ to $10°.$ The differential cross section reveals considerable structure over this angular range which is a consequence of small angle quantum interference and the glory and rainbow effects. For the case of charge transfer, we find that at least 90% of charge transfer events result in the hydrogen atom leaving the system in the $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ state.

Starting from the hydrodynamic equations of superfluids, we calculate the frequencies of the collective oscillations of a harmonically trapped Bose-Einstein gas for various one-dimensional configurations at zero temperature. These include the mean-field regime described by Gross-Pitaevskii theory and the beyond-mean-field regime at small densities described by the Lieb-Liniger theory. The relevant combinations of the physical parameters governing the transition between the different regimes as well as the conditions of applicability of the hydrodynamic equations are discussed.