Pure spin-angular momentum coefficients for non-scalar one-particle operators in jj-coupling

A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version of the Anco program now provides these coefficients for both, scalar as well as non-scalar one-particle operators as they arise frequently in the study of transition probabilities, photoionization and electron capture processes, the alignment transfer through excited atomic states, collision strengths, and in many other investigations. The program is based on a recently developed formalism [G.Gaigalas, Z.Rudzikas, and C.F.Fischer, J. Phys. B 30 (1997) 3747], which combines techniques from second quantization in coupled tensorial form, the theory of quasispin, and the use of reduced coefficients of fractional parentage, in order to derive the spin-angular coefficients for complex atomic shell structures more efficiently. By making this approach now available also for non-scalar interactions, therefore, studies on a whole field of new properties and processes are likely to become possible even for atoms and ions with a complex structure

Controlling quantum random walk with a step-dependent coin

We report on the possibility of controlling quantum random walks with a step-dependent coin. The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for this walk including: complete localization, Gaussian and asymmetric likes. In addition, we explore the entropy of walk in two contexts; for probability density distributions over position space and walker's internal degrees of freedom space (coin space). We show that entropy of position space can decrease for a step-dependent coin with the step-number, quite in contrast to a walk with step-independent coin. For entropy of coin space, a damped oscillation is found for walk with step-independent coin while for a step-dependent coin case, the behavior of entropy depends on rotation angle. In general, we demonstrate that quantum walks with simple initiatives may exhibit a quite complex and varying behavior if step-dependent coins are applied. This provides the possibility of controlling quantum random walk with a step-dependent coin.Comment: 17 pages, 9 figure

Compton scattering of twisted light: angular distribution and polarization of scattered photons

Compton scattering of twisted photons is investigated within a non-relativistic framework using first-order perturbation theory. We formulate the problem in the density matrix theory, which enables one to gain new insights into scattering processes of twisted particles by exploiting the symmetries of the system. In particular, we analyze how the angular distribution and polarization of the scattered photons are affected by the parameters of the initial beam such as the opening angle and the projection of orbital angular momentum. We present analytical and numerical results for the angular distribution and the polarization of Compton scattered photons for initially twisted light and compare them with the standard case of plane-wave light

Maple procedures for the coupling of angular momenta. VI. LS-jj transformations

Transformation matrices between different coupling schemes are required, if a reliable classification of the level structure is to be obtained for open-shell atoms and ions. While, for instance, relativistic computations are traditionally carried out in jj-coupling, a LSJ coupling notation often occurs much more appropriate for classifying the valence-shell structure of atoms. Apart from the (known) transformation of single open shells, however, further demand on proper transformation coefficients has recently arose from the study of open d- and f-shell elements, the analysis of multiple--excited levels, or the investigation on inner-shell phenomena. Therefore, in order to facilitate a simple access to LS jj transformation matrices, here we present an extension to the Racah program for the set-up and the transformation of symmetry-adapted functions. A flexible notation is introduced for defining and for manipulating open-shell configurations at different level of complexity which can be extended also to other coupling schemes and, hence, may help determine an optimum classification of atomic levels and processes in the future

Multipartite W states for chains of atoms conveyed through an optical cavity

We propose and work out a scheme to generate the entangled W states for a chain of N four-level atoms which are transported through an optical cavity by means of an optical lattice. This scheme is based on the combined laser-cavity mediated interaction between distant and equally separated atoms and works in a completely deterministic way for qubits encoded by two hyperfine levels of the atoms. Only two parameters, namely the distance between the atoms and the velocity of the chain, determine the effective interaction among the atoms and, therefore, the degree of entanglement that is obtained for the overall chain of N qubits. In particular, we work out the parameter regions for which the W states are generated most reliably for chains of N = 2,3,4 and 5 atoms. In addition, we analyze the sensitivity in the formation of entanglement for such chains of qubits due to uncertainties produced by the oscillations of atoms in optical lattices.Comment: 12 pages, revised version accepted in PR