Ion–laser interactions: The most complete solution

Trapped ions are considered one of the best candidates to perform quantum information processing. By interacting them with laser beams they are, somehow, easy to manipulate, which makes them an excellent choice for the production of nonclassical states of their vibrational motion, the reconstruction of quasiprobability distribution functions, the production of quantum gates, etc. However, most of these effects have been produced in the so-called low intensity regime, this is, when the Rabi frequency (laser intensity) is much smaller than the trap frequency. Because of the possibility to produce faster quantum gates in other regimes it is of importance to study this system in a more complete manner, which is the motivation for this contribution. We start by studying the way ions are trapped in Paul traps and review the basic mechanisms of trapping. Then we show how the problem may be completely solved for trapping states; i.e., we find (exact) eigenstates of the full Hamiltonian. We show how, in the low intensity regime, Jaynes–Cummings and anti-Jaynes–Cummings interactions may be obtained, without using the rotating wave approximation and analyze the medium and high intensity regimes where dispersive Hamiltonians are produced. The traditional approach (low intensity regime) is also studied and used for the generation of non-classical states of the vibrational wavefunction. In particular, we show how to add and subtract vibrational quanta to an initial state, how to produce specific superpositions of number states and how to generate NOON states for the two-dimensional vibration of the ion. It is also shown how squeezing may be measured. The time dependent problem is studied by using Lewis–Ermakov methods. We give a solution to the problem when the time dependence of the trap is considered and also analyze a specific (artificial) time dependence that produces squeezing of the initial vibrational wave function. A way to mimic the ion–laser interaction via classical optics is also introduced.     

Dominions in varieties generated by simple groups

We determine the dominion (in the sense of Isbell) of a subgroup H of a finite nonabelian simple group S in Var(S). We also obtain necessary and suficient conditions for H to be epimorphically embedded in S, and derive several examples, which generalize an example of B. H. Neumann. Finally, we extend the results to a variety generated by a family of finite nonabelian simple groups. Received May 12, 1999; accepted in final form April 9, 2002.     

Mössbauer spectra of “stannite group” minerals

Stannite group minerals were studied by means of Mössbauer spectroscopy. In particular we examined the problem of stannite-kesterite miscibility. From the behaviour of the Mössbauer linewidth as a function of the mineral composition it follows that all the samples have a single phase structure, in disagreement with the existence of a miscibility gap.     

A T-matrix method and computer code for randomly oriented, axially symmetric coated scatterers

A computer code is described for the calculation of light-scattering properties of randomly oriented, axially symmetric coated particles, in the framework of the T-matrix theory. The underlying mathematical background is outlined briefly and convergence procedures are discussed. After outlining the input-output interaction between user and code, benchmark results are presented for two distinct shapes: coated, centered spheroids and offset coated spheres.     

Direct interfacial Y731 oxidation in α2 by a photoβ2 subunit of E. coli class Ia ribonucleotide reductase

Proton-coupled electron transfer (PCET) is a fundamental mechanism important in a wide range of biological processes including the universal reaction catalysed by ribonucleotide reductases (RNRs) in making de novo, the building blocks required for DNA replication and repair. These enzymes catalyse the conversion of nucleoside diphosphates (NDPs) to deoxynucleoside diphosphates (dNDPs). In the class Ia RNRs, NDP reduction involves a tyrosyl radical mediated oxidation occurring over 35 Å across the interface of the two required subunits (β₂ and α₂) involving multiple PCET steps and the conserved tyrosine triad [Y₃₅₆(β₂)–Y₇₃₁(α₂)–Y₇₃₀(α₂)]. We report the synthesis of an active photochemical RNR (photoRNR) complex in which a Re(i)-tricarbonyl phenanthroline ([Re]) photooxidant is attached site-specifically to the Cys in the Y₃₅₆C-(β₂) subunit and an ionizable, 2,3,5-trifluorotyrosine (2,3,5-F₃Y) is incorporated in place of Y₇₃₁ in α₂. This intersubunit PCET pathway is investigated by ns laser spectroscopy on [Re₃₅₆]-β₂:2,3,5-F₃Y₇₃₁-α₂ in the presence of substrate, CDP, and effector, ATP. This experiment has allowed analysis of the photoinjection of a radical into α₂ from β₂ in the absence of the interfacial Y₃₅₆ residue. The system is competent for light-dependent substrate turnover. Time-resolved emission experiments reveal an intimate dependence of the rate of radical injection on the protonation state at position Y₇₃₁(α₂), which in turn highlights the importance of a well-coordinated proton exit channel involving the key residues, Y₃₅₆ and Y₇₃₁, at the subunit interface.     

The Synthesis of Some Fused Pyrazolo‐1,4‐Naphthoquinones

New fused pyrazolo‐1,4‐naphthoquinones were prepared from the reaction of hydrazines with 6‐(4‐methyl‐3‐pentenyl)‐1,4‐naphthoquinone. The reaction was extended to hydroxylamine to afford the corresponding isoxazolo‐1,4‐napthoquinone compound.     

The development of an artificial organic networks toolkit for LabVIEW

Two of the most challenging problems that scientists and researchers face when they want to experiment with new cutting‐edge algorithms are the time‐consuming for encoding and the difficulties for linking them with other technologies and devices. In that sense, this article introduces the artificial organic networks toolkit for LabVIEW? (AON‐TL) from the implementation point of view. The toolkit is based on the framework provided by the artificial organic networks technique, giving it the potential to add new algorithms in the future based on this technique. Moreover, the toolkit inherits both the rapid prototyping and the easy‐to‐use characteristics of the LabVIEW? software (e.g., graphical programming, transparent usage of other softwares and devices, built‐in programming event‐driven for user interfaces), to make it simple for the end‐user. In fact, the article describes the global architecture of the toolkit, with particular emphasis in the software implementation of the so‐called artificial hydrocarbon networks algorithm. Lastly, the article includes two case studies for engineering purposes (i.e., sensor characterization) and chemistry applications (i.e., blood–brain barrier partitioning data model) to show the usage of the toolkit and the potential scalability of the artificial organic networks technique. © 2015 Wiley Periodicals, Inc.     

On the Meromorphic Functions in the Punctured Plane Without Multiple Values

The study of meromorphic functions without multiple values in the plane started by F. Nevanlinna is extended to meromorphic functions in the punctured plane \({\mathbb {C}}^{{*}}.\) It is a classical result that a meromorphic function \(f\left( z\right) \) can be obtained as quotient of solutions of the second order differential equation \(u^{{\prime \prime }}+\left\{ f\left( z\right) ,z\right\} u=0,\) where \(\left\{ f\left( z\right) ,z\right\} \) is the Schwarzian derivative of \(f\left( z\right) \). In our hypothesis of meromorphic functions of finite order without multiple values in the puntured plane, the Schwarzian derivative \(\left\{ f\left( z\right) , z\right\} \) turns out to be a rational function with only possible poles at 0 and \(\infty \). In these conditions the asymptotic behaviour of \(f\left( z\right) \) can be described by a result of Hille (Lectures on Ordinary Differential Equations in the complex plane, Addison Wesley, Boston, 1969) on ordinary differential equations in the complex plane. The results obtained are framed in the value distribution theory of meromorphic functions, in particular in the punctured plane we shall consider the work of Khrystiyanin and Kondratyuk (Mat Stud 23(1):19–30, 2005; Mat Stud 23(1):57–68, 2005) and Korhonen (Nevanlinna theory on an annulus. Value distribution theory and related topics. Adv. Complex analysis and applications, Kluwer Academic Publishers, Dordrecht, 2004).     

Diels-Alder reactions of N-tosylpirroles developed in protic ionic liquids. Theoretical studies using DFT methods

N-Tosyl-2-nitropirrole and N-tosyl-3-nitropirrole react with poorly and activated dienes using protic ionic liquids as reaction media. They exhibit a dienophile character producing the corresponding indoles through a Diels-Alder process. In all cases the presence of protic ionic liquids as reaction media improves the yields with respect to use of molecular solvent, while the temperature and the reaction time decrease. Part of this work is specifically concerned with theoretical studies using DFT methods. The global and local electrophilicity and nucleophilicity indices were calculated for the dienophiles and dienes used in this study in order to evaluate reactivity and regioselectivity.