arXiv subjects

Stephan Fritzsche

Publications and source records attributed to Stephan Fritzsche.

68 records · Page 4Linked to original sources

arXiv2012

Relativistic polarization analysis of Rayleigh scattering by atomic hydrogen

A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second order perturbation theory. The relativistic atomic states used for the calculations are obtained by making use of the finite basis set method and expressed in terms of $B$ splines and $B$ polynomials. We introduce two experimental scenarios in which the light is circularly and linearly polarized, respectively. For each of these scenarios, the polarization-dependent angular distribution and the degrees of circular and linear polarization of the scattered light are investigated as a function of scattering angle and photon energy. Analytical expressions are derived for the polarization-dependent angular distribution which can be used for scattering by both hydrogenic as well as many-electron systems. Detailed computations are performed for Rayleigh scattering by atomic hydrogen within the incident photon energy range 0.5 to 10 keV. Particular attention is paid to the effects that arise from higher (nondipole) terms in the expansion of the electron-photon interaction.

physics.atom-ph↗

arXiv2012

Mass- and field-shift isotope parameters for the $2s - 2p$ resonance doublet of lithium-like ions

It was recently shown that dielectronic recombination measurements can be used for accurately inferring changes in the nuclear mean-square charge radii of highly-charged lithium-like neodymium [Brandau et al., Phys. Rev. Lett. 100 073201 (2008)]. To make use of this method to derive information about the nuclear charge distribution for other elements and isotopes, accurate electronic isotope shift parameters are required. In this work, we calculate and discuss the relativistic mass- and field-shift factors for the two $2s ^{2}S_{1/2} - 2p ^{2}P^{o}_{1/2,3/2}$ transitions along the lithium isoelectronic sequence. Based on the multiconfiguration Dirac-Hartree-Fock method, the electron correlation and the Breit interaction are taken into account systematically. The analysis of the isotope shifts for these two transitions along the isoelectronic sequence demonstrates the importance and competition between the mass shifts and the field shifts.

physics.atom-ph↗

arXiv2011

Quantum computing with mixed states

We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no efficient classical algorithms are known. We suggest a new implementation of quantum computation with initially mixed states in which an algorithm realization is achieved by means of optimal basis independent transformations of qubits.

quant-ph↗

arXiv2010

Quantum correlations in the two-photon decay of few-electron ions

A theoretical study of the polarization entanglement of two photons emitted in the decay of metastable ionic states is performed within the framework of density matrix theory and second-order perturbative approach. Particular attention is paid to relativistic and non-dipole effects that become important for medium- and high-$Z$ ions. To analyze these effects, the degree of entanglement is evaluated both in the dipole approximation and within the rigorous relativistic theory. Detailed calculations are performed for the two-photon $2s_{1/2}\to 1s_{1/2}$ transition in hydrogen-like, as well as for the $1s_{1/2}\, 2s_{1/2} \; {}^1S_0 \to 1s_{1/2}^2 \; {}^1S_0$, $1s_{1/2} \, 2s_{1/2} \; {}^3S_1\to 1s_{1/2}^2 \; {}^1S_0$ and $1s_{1/2} \, 2p_{1/2} \; {}^3P_0\to 1s_{1/2}^2 \; {}^1S_0$ transitions in helium-like ions.

physics.atom-ph↗

arXiv2010

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.

quant-ph↗

arXiv2010

Universal quantum Controlled-NOT gate

An investigation of an optimal universal unitary Controlled-NOT gate that performs a specific operation on two unknown states of qubits taken from a great circle of the Bloch sphere is presented. The deep analogy between the optimal universal C-NOT gate and the `equatorial' quantum cloning machine (QCM) is shown. In addition, possible applications of the universal C-NOT gate are briefly discussed.

quant-ph↗

arXiv2010

Entanglement dynamics of three-qubit states in noisy channels

We study entanglement dynamics of the three-qubit system which is initially prepared in pure Greenberger-Horne- Zeilinger (GHZ) or W state and transmitted through one of the Pauli channels $σ_z, \, σ_x, \, σ_y$ or the depolarizing channel. With the help of the lower bound for three-qubit concurrence we show that the W state preserves more entanglement than the GHZ state in transmission through the Pauli channel $σ_z$. For the Pauli channels $σ_x, \, σ_y$ and the depolarizing channel, however, the entanglement of the GHZ state is more resistant against decoherence than the W-type entanglement. We also briefly discuss how the accuracy of the lower bound approximation depends on the rank of the density matrix under consideration.

quant-ph↗

arXiv2010

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.

quant-ph↗

arXiv2009

MCDHF calculations of the electric dipole moment of radium induced by the nuclear Schiff moment

The multiconfiguration Dirac-Hartree-Fock theory (MCDHF) has been employed to calculate the electric dipole moment of the 7s6d 3D2 state of radium induced by the nuclear Schiff moment. The results are dominated by valence and core-valence electron correlation effects. We show that the correlation effects can be evaluated in a converged series of multiconfiguration expansions.

physics.atom-ph↗

arXiv2008

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.

physics.atom-ph↗

arXiv2007

Angular distribution studies on the two-photon ionization of hydrogen-like ions: Relativistic description

The angular distribution of the emitted electrons, following the two-photon ionization of the hydrogen-like ions, is studied within the framework of second order perturbation theory and the Dirac equation. Using a density matrix approach, we have investigated the effects which arise from the polarization of the incoming light as well as from the higher multipoles in the expansion of the electron--photon interaction. For medium- and high-Z ions, in particular, the non-dipole contributions give rise to a significant change in the angular distribution of the emitted electrons, if compared with the electric-dipole approximation. This includes a strong forward emission while, in dipole approxmation, the electron emission always occurs symmetric with respect to the plane which is perpendicular to the photon beam. Detailed computations for the dependence of the photoelectron angular distributions on the polarization of the incident light are carried out for the ionization of H, Xe$^{53+}$, and U$^{91+}$ (hydrogen-like) ions.

physics.atom-ph↗

arXiv2005

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.

quant-ph↗

arXiv2005

Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen--like ions

Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen--like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb--field) solutions, here we present the Dirac program which has been developed originally for studying the properties and dynamical behaviour of the (hydrogen--like) ions. In the present version, a set of Maple procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the Dirac program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion--atom and ion--photon collisions.

physics.atom-ph↗

arXiv2003

Relativistic and retardation effects in the two--photon ionization of hydrogen--like ions

The non-resonant two-photon ionization of hydrogen-like ions is studied in second-order perturbation theory, based on the Dirac equation. To carry out the summation over the complete Coulomb spectrum, a Green function approach has been applied to the computation of the ionization cross sections. Exact second-order relativistic cross sections are compared with data as obtained from a relativistic long-wavelength approximation as well as from the scaling of non-relativistic results. For high-Z ions, the relativistic wavefunction contraction may lower the two-photon ionization cross sections by a factor of two or more, while retardation effects appear less pronounced but still give rise to non-negligible contributions.

physics.atom-ph↗