Diffraction of atoms by lasers is a very important tool for matter wave optics. Although the process is well understood, the phase shifts induced by this diffraction process are not well known. In this paper, we make analytical calculations of these phase shifts in some simple cases and use these results to model the contrast interferometer recently built by Pritchard and co-workers. We thus show that the values of the diffraction phases are large and that they probably contribute to the phase noise observed in this experiment.

A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence for two qubits and the 3-tangle for three qubits), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover, a natural extension of the definition of Greenberger-Horne-Zeilinger states to, e.g., $2\times 2\times N$ systems is obtained.

We examine the quantum states produced through parametric amplification with internal quantum noise. The internal diffusion arises by coupling both modes of light to a reservoir for the duration of the interaction time. The Wigner function for the diffused two-mode squeezed state is calculated. The nonlocality, separability, and purity of these quantum states of light are discussed. In addition, we conclude by studying the nonlocality of two other continuous-variable states: the Werner state and the phase-diffused state for two light modes.

A significant branch of classical cryptography deals with the problems which arise when mistrustful parties need to generate, process, or exchange information. As Kilian showed a while ago, mistrustful classical cryptography can be founded on a single protocol, oblivious transfer, from which general secure multiparty computations can be built. The scope of mistrustful quantum cryptography is limited by no-go theorems, which rule out, inter alia, unconditionally secure quantum protocols for oblivious transfer or general secure two-party computations. These theorems apply even to protocols which take relativistic signaling constraints into account. The best that can be hoped for, in general, are quantum protocols which are computationally secure against quantum attack. Here a method is described for building a classically certified bit commitment, and hence every other mistrustful cryptographic task, from a secure coin-tossing protocol. No security proof is attempted, but reasons are sketched why these protocols might resist quantum computational attack.

Bipartite correlations in multiqubit systems cannot be shared freely. The presence of entanglement or classical correlation on certain pairs of qubits may imply correlations on other pairs. We present a method of characterization of bipartite correlations in multiqubit systems using a concept of entangled graphs which has been introduced in our earlier work [M. Plesch and V. Bužek, Phys. Rev. A 67, 012322 (2003)]. In entangled graphs, each qubit is represented by a vertex while the entanglement and classical correlations are represented by two types of edges. We prove by construction that any entangled graph with classical correlations can be represented by a mixed state of N qubits. However, not all entangled graphs with classical correlations can be represented by a pure state.

We present a systematic study of the purity for Gaussian states of single-mode continuous variable systems. We prove the connection of purity to observable quantities for these states, and show that the joint measurement of two conjugate quadratures is necessary and sufficient to determine the purity at any time. The statistical reliability and the range of applicability of the proposed measurement scheme are tested by means of Monte Carlo simulated experiments. We then consider the dynamics of purity in noisy channels. We derive an evolution equation for the purity of general Gaussian states both in thermal and in squeezed thermal baths. We show that purity is maximized at any given time for an initial coherent state evolving in a thermal bath, or for an initial squeezed state evolving in a squeezed thermal bath whose asymptotic squeezing is orthogonal to that of the input state.

An experimental scheme is proposed to test Bell’s inequality by using superconducting nanocircuits. In this scheme, quantum entanglement of a pair of charge qubits separated by a sufficiently long distance may be created by cavity quantum electrodynamic techniques; the population of qubits is experimentally measurable by dc currents through the probe junctions, and one measured outcome may be recorded for every experiment. Therefore, both locality and detection-efficiency loopholes should be closed in the same experiment. We also propose a useful method to measure the amount of entanglement based on the concurrence between Josephson qubits. The measurable variables for Bell’s inequality as well as the entanglement are expressed in terms of a useful phase-space Q function.

The adiabatic connection can be used in density functional theory to define the unknown (exchange and) correlation density functional. Using conventional wave-function techniques, accurate estimates of thus defined (exchange and) correlation energy densities can be obtained for specified systems. In this paper, numerical results are presented for the He and the Be atom, as well as the isoelectron Ne ions. A generalized gradient approximation is tested against these results. The comparison shows that the generalized gradient approximation has the ability to detect local features (the shell structure). In one case $\left({\mathrm{Ne}}^{6+}\right),$ however, it turns out that the accurate correlation energy per particle is lower than that obtained within the local-density approximation, and thus not properly corrected by the generalized gradient approximation.

Recently, experiments have been reported where a geometrical interference pattern was observed when photoelectrons ejected in the threshold photoionization of xenon were detected in a velocity-map imaging apparatus [C. Nicole et al., Phys. Rev. Lett. 88, 133001 (2002)]. This technique, called photoionization microscopy, relies on the existence of interferences between various trajectories by which the electron moves from the atom to the plane of observation. Unlike previous predictions relevant to the hydrogenic case, the structure of the interference pattern evolves smoothly with the excess energy above the saddle point and is only weakly affected by the presence of continuum Stark resonances. In this paper, we describe a semiclassical analysis of this process and present numerical simulations in excellent agreement with the experimental results. It is shown that the background contribution dominates in the observations, as opposed to the behavior expected for hydrogenic systems where the interference pattern is qualitatively different on quasidiscrete Stark resonances.

The nonstationary Schrödinger equation is considered in a finite basis of states. The model Hamiltonian matrix corresponds to a single diabatic potential curve with a Coulombic $\sim 1/t$ time dependence. An arbitrary number of other diabatic potential curves are flat, i.e., time independent and have arbitrary energies. Related states are coupled by constant interactions with the Coulomb state. The resulting nonstationary Schrödinger equation is solved by the method of contour integral. Probabilities of transitions to any other state are obtained as $\overrightarrow{t}\infty$ in a simple analytical form for the case when the Coulomb state is populated initially (at instant of time $\overrightarrow{t}+0).\mathrm{}$ The formulas apply both to the cases when a horizontal diabatic potential curve is crossed by the Coulomb one and to a noncrossing situation. In the limit of weak coupling, the transition probabilities are interpreted in terms of a sequence of pairwise Landau-Zener-type transitions. Mapping of the Coulomb model onto an exactly solvable exponential multistate model is established. For the special two-state case, the well-known Nikitin model is recovered.

The angular anisotropy parameter $\beta$ for the $3p$ and $3d$ photoionization of krypton was investigated in the photon energy range from 325 eV to 1000 eV. Using the new UE52 undulator at the BESSY II storage ring the results were obtained by rotating the polarization axis of the linearly polarized synchrotron radiation. With this method high-precision measurements of $\beta$ are possible, showing significant deviations between experiment and theoretical calculations. This gives strong evidence for the importance of intrachannel and interchannel electron correlations for the photoionization processes of Kr.

A calculation is performed in order to analyze the charge-state dependence of the kinetic electron emission induced by slow ions in metals. All stages of the emission process are included: the excitation of the electrons, the neutralization of the projectile during its passage through the solid, and the transport of the excited electrons from where they are created to the surface. It is shown that the number of excited electrons depends strongly on the ion charge state. Nevertheless, due to the fast neutralization of the ions within the escape depth of the excited electrons, no significant initial charge-state dependence is expected in the kinetic electron yield. This result is consistent with available experimental data.

In the Stark effect for the inverted δ-function potential, there are two kinds of field-induced resonances: the resonance stemming from the bound state supported by the bare potential, and a doubly infinite family of resonances originating from the continuum threshold. In this paper, we derive asymptotic expressions for the real and the imaginary parts (positions and halfwidths) of all these resonances as functions of the applied electric field, and then numerically track their behavior with changing field strength.

The existence of strongly localized matter solitons, intrinsic localized modes (ILM’s), in an array of atomic-molecular Bose-Einstein condensates (AMBEC’s) is shown. The theory is based on the Wannier function expansion of the system order parameter and predicts the possibility of strong localization of the atomic and molecular components whose relative populations are determined by the Raman detuning parameter and by the atom-molecule conversion rate. ILM’s can possess different symmetries and spatial distributions of the components. In this context AMBEC arrays can be viewed as potential compressors and separators of atomic and molecular condensates.

A scheme for obtaining laser in the deep x-ray regime is proposed based on the principle of gain without inversion. A ladder scheme is proposed in ${\mathrm{Ar}}^{+8\mathrm{}}$ system. In this system, conventional lasing with population inversion has been obtained in a neonlike fashion. This lasing field is proposed for the drive field on the higher transition of the ladder. A coherent field obtained in the high harmonics ultrashort laser provides the probe field to be amplified. This will be selected to best match the frequency needed for the transition from lower level of the present x-ray lasing to the ground state. Numerical calculations in the bare state picture exhibit possible gain at resonance, and at the Rabi side bands, for appropriate choice of system parameters, i.e., the strength of the driving field, the strength of the incoherent pump that provides the required energy needed for the inversionless amplification and the deexcitation rate. The latter rate is detrimental to lasing as it increases. It is quite interesting to note that the system exhibits surprisingly high stability for gain without inversion even for quite high rate of the incoherent deexcitation processes. Real and imaginary parts of the coherences were also obtained for detuned drive and probe fields. These provide insight into the role played by the quantum interference. The present theoretical calculations give high confidence in the quantum interference process as a candidate for realizing very short wavelength laser.

In this paper, we present a theoretical and experimental analysis of stochastic effects observed in polarization switching vertical-cavity surface-emitting lasers. We make a thorough comparison between theoretical predictions and experiments, comparing measured quasipotentials and dwell times. The correspondence between our theoretical model based on stochastic intensity rate equations and the experiments is found to be very good.

We present an all-optical implementation of quantum computation using semiconductor quantum dots. Quantum memory is represented by the spin of an excess electron stored in each dot. Two-qubit gates are realized by switching on trion-trion interactions between different dots. State selectivity is achieved via conditional laser excitation exploiting Pauli exclusion principle. Read out is performed via a quantum-jump technique. We analyze the effect on our scheme’s performance of the main imperfections present in real quantum dots: exciton decay, hole mixing, and phonon decoherence. We introduce an adiabatic gate procedure that allows one to circumvent these effects and evaluate quantitatively its fidelity.

The effect of random fields on the internal dynamics of trapped ions is studied analytically. General characteristics of the dependence of the dephasing on the noise statistics are identified: the form of the initial decay of the coherences is determined by the probability distribution; effects of noise color, in particular, collapses and revivals rooted in spectral concentration of the fluctuations, are apparent in a transient regime; at large times, exponential decay sets in for widely different noise properties. The study is particularized to magnetic-field fluctuations: features distinctive of the linear and quadratic Zeeman shifts are traced. The scaling of the dephasing with the number of ions is analyzed; the implications for the realization of decoherence-free states are discussed.

An optical-model potential for systematic calculations of elastic scattering of electrons and positrons by atoms and positive ions is proposed. The electrostatic interaction is determined from the Dirac-Hartree-Fock self-consistent atomic electron density. In the case of electron projectiles, the exchange interaction is described by means of the local-approximation of Furness and McCarthy. The correlation-polarization potential is obtained by combining the correlation potential derived from the local density approximation with a long-range polarization interaction, which is represented by means of a Buckingham potential with an empirical energy-dependent cutoff parameter. The absorption potential is obtained from the local-density approximation, using the Born-Ochkur approximation and the Lindhard dielectric function to describe the binary collisions with a free-electron gas. The strength of the absorption potential is adjusted by means of an empirical parameter, which has been determined by fitting available absolute elastic differential cross-section data for noble gases and mercury. The Dirac partial-wave analysis with this optical-model potential provides a realistic description of elastic scattering of electrons and positrons with energies in the range from $\sim 100\mathrm{eV}$ up to $\sim 5\mathrm{keV}.$ At higher energies, correlation-polarization and absorption corrections are small and the usual static-exchange approximation is sufficiently accurate for most practical purposes.

We investigate a double-well tunneling process in Bose condensates of two interacting species. We show that particles of different species can tunnel as pairs through the potential barrier between the two wells in opposite directions. Such a correlated motion of tunneling atoms leads to the generation of quantum entanglement between two macroscopically coherent systems. The strong correlations are manifested in the particle number sum and the phase difference variables.