Relativistic wave and Green's functions for hydrogen--like ions

The \textsc{Greens} library is presented which provides a set of C++ procedures for the computation of the (radial) Coulomb wave and Green's functions. Both, the nonrelativistic as well as relativistic representations of these functions are supported by the library. However, while the wave functions are implemented for all, the bound and free--electron states, the Green's functions are provided only for bound--state energies $(E < 0$). Apart from the Coulomb functions, moreover, the implementation of several special functions, such as the Kummer and Whittaker functions of the first and second kind, as well as a few utility procedures may help the user with the set--up and evaluation of matrix elements.Comment: 21 page

Evolution equation of entanglement for multi-qubit systems

We discuss entanglement evolution of a multi-qubit system when one of its qubits is subjected to a general noisy channel. For such a system, an evolution equation of entanglement for a lower bound for multi-qubit concurrence is derived. Using this evolution equation, the entanglement dynamics of an initially mixed three-qubit state composed of a GHZ and a W state is analyzed if one of the qubits is affected by a phase, an amplitude or a generalized amplitude damping channel.Comment: 3 figures, 28 reference

High-fidelity copies from a symmetric 1 to 2 quantum cloning machine

A symmetric 1 to 2 quantum cloning machine (QCM) is presented that provides high-fidelity copies with $0.90 \le F \le 0.95$ for all pure (single-qubit) input states from a given meridian of the Bloch sphere. \cor{Emphasize is placed especially on the states of the (so-called) Eastern meridian, that includes the computational basis states \ketm{0}, \ketm{1} together with the diagonal state \ketm{+} = \frac{1}{\sqrt{2}} (\ketm{0} + \ketm{1}), for which suggested cloning transformation is shown to be optimal.} In addition, we also show how this QCM can be utilized for eavesdropping in Bennett's B92 protocol for quantum key distribution with a substantial higher success rate than obtained for universal or equatorial quantum copying.Comment: 2 figures, 20 reference

Relativistic central--field Green's functions for the RATIP package

From perturbation theory, Green's functions are known for providing a simple and convenient access to the (complete) spectrum of atoms and ions. Having these functions available, they may help carry out perturbation expansions to any order beyond the first one. For most realistic potentials, however, the Green's functions need to be calculated numerically since an analytic form is known only for free electrons or for their motion in a pure Coulomb field. Therefore, in order to facilitate the use of Green's functions also for atoms and ions other than the hydrogen--like ions, here we provide an extension to the Ratip program which supports the computation of relativistic (one--electron) Green's functions in an -- arbitrarily given -- central--field potential \rV(r). Different computational modes have been implemented to define these effective potentials and to generate the radial Green's functions for all bound--state energies $E < 0$. In addition, care has been taken to provide a user--friendly component of the Ratip package by utilizing features of the Fortran 90/95 standard such as data structures, allocatable arrays, or a module--oriented design.Comment: 20 pages, 1 figur

Bessel beams of two-level atoms driven by a linearly polarized laser field

We study Bessel beams of two-level atoms that are driven by a linearly polarized laser field. Starting from the Schroedinger equation, we determine the states of two-level atoms in a plane-wave field respecting propagation directions both of the atom and the field. For such laser-driven two-level atoms, we construct Bessel beams beyond the typical paraxial approximation. We show that the probability density of these atomic beams obtains a non-trivial, Bessel-squared-type behavior and can be tuned under the special choice of the atom and laser parameters, such as the nuclear charge, atom velocity, laser frequency, and propagation geometry of the atom and laser beams. Moreover, we spatially and temporally characterize the beam of hydrogen and selected (neutral) alkali-metal atoms that carry non-zero orbital angular momentum (OAM). The proposed spatiotemporal Bessel states (i) are able to describe, in principle, twisted states of any two-level system which is driven by the radiation field and (ii) have potential applications in atomic, nuclear processes and quantum communication.Comment: 13 pages, 5 figures, appeared as a EPJD highlight on Thursday, 01 August 2013 http://www.epj.org/index.php?option=com_content&view=article&id=684%3Aepjd-highlight-novel-beams-made-of-twisted-atoms&catid=112%3Aepj-d&Itemid=466&lang=e

Calculation of reduced coefficients and matrix elements in jj-coupling

A program RCFP will be presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. The list of quantities wich are supported by the present program includes the coefficients of fractional parentage, the reduced coefficients of fractional parentage, the reduced matrix elements of the unit operator T^{(k)} as well as the completely reduced matrix elements of the operator W^{(k_jk_q)} in jj-coupling. These quantities are now available for all subshells (nj) with j \leq 9/2 including partially filled 9/2-shells. Our program is based on a recently developed new approach on the spin-angular integration which combines second quantization and quasispin methods with the theory of angular momentum in order to obtain a more efficient evaluation of many-electron matrix elements. An underlying Fortran 90/95 module can directly be used also in (other) atomic structure codes to accelerate the computation for open-shell atoms and ions

Atomic ionization by twisted photons: Angular distribution of emitted electrons

We investigate the angular distribution of electrons that are emitted in the ionization of hydrogen-like ions by twisted photons. Analysis is performed based on the first-order perturbation theory and the non-relativistic Schr\"odinger equation. Special attention is paid to the dependence of the electron emission pattern on the impact parameter b of the ion with respect to the centre of the twisted wave front. In order to explore such a dependence, detailed calculations were carried out for the photoionization of the 1s ground and 2 py excited states of neutral hydrogen atoms. Based on these calculations, we argue that for relatively small impact parameters the electron angular distributions may be strongly affected by altering the position of the atom within the wave front. In contrast, if the atom is placed far from the front centre, the emission pattern of the electrons is independent on the impact parameter b and resembles that observed in the photoionization by plane wave photons.Comment: 23 pages, 6 figure

Program to calculate pure angular momentum coefficients in jj-coupling

A program for computing pure angular momentum coefficients in relativistic atomic structure for any scalar one- and two-particle operator is presented. The program, written in Fortran 90/95 and based on techniques of second quantization, irreducible tensorial operators, quasispin and the theory of angular momentum, is intended to replace existing angular coefficient modules from GRASP92. The new module uses a different decomposition of the coefficients as sums of products of pure angular momentum coefficients, which depend only on the tensor rank of the interaction but not on its details, with effective interaction strengths of specific interactions. This saves memory and reduces the computational cost of big calculations signficantly

The effect of bound state dressing in laser assisted radiative recombination

We present a theoretical study on the recombination of a free electron into the ground state of a hydrogen-like ion in the presence of an external laser field. Emphasis is placed on the effects caused by the laser dressing of the residual ionic bound state. To investigate how this dressing affects the total and angle-differential cross section of laser assisted radiative recombination (LARR) we apply first-order perturbation theory and the separable Coulomb-Volkov-continuum ansatz. Using this approach detailed calculations were performed for low-$Z$ hydrogen like ions and laser intensities in the range from $I_L=10^{11}\text{W/cm}^2$ to $I_L=10^{13}\text{W/cm}^2$. It is seen that the total cross section as a function of the laser intensity is remarkably affected by the bound state dressing. Moreover the laser dressing becomes manifest as asymmetries in the angular distribution and the (energy) spectrum of the emitted recombination photons.Comment: 9 pages, 5 figure

Hyperfine-induced effects on the linear polarization of the Kα1\alpha_1 emission from helium-like ions

The linear polarization of the characteristic photon emission from few-electron ions is studied for its sensitivity with regard to the nuclear spin and magnetic moment of the ions. Special attention is paid, in particular, to the K$\alpha_1$ (1s 2p_{3/2} ^{1,3}P_{1,2} \to 1s^2 ^1S_0) decay of selected helium-like ions following the radiative electron capture into initially hydrogen-like species. Based on the density matrix theory, a unified description is developed that includes both, the many-electron and hyperfine interactions as well as the multipole-mixing effects arising from the expansion of the radiation field. It is shown that the polarization of the K$\alpha_1$ line can be significantly affected by the mutipole mixing between the leading $M2$ and hyperfine-induced $E1$ components of 1s2p ^3P_2, F_i \to 1s^2 ^1S_0, F_f transitions. This $E1$-$M2$ mixing strongly depends on the nuclear properties of the considered isotopes and can be addressed experimentally at existing heavy-ion storage rings