Highly charged ions: optical clocks and applications in fundamental physics

Recent developments in frequency metrology and optical clocks have been based on electronic transitions in atoms and singly charged ions as references. These systems have enabled relative frequency uncertainties at a level of a few parts in $10^{-18}$. This accomplishment not only allows for extremely accurate time and frequency measurements, but also to probe our understanding of fundamental physics, such as variation of fundamental constants, violation of the local Lorentz invariance, and forces beyond the Standard Model of Physics. In addition, novel clocks are driving the development of sophisticated technical applications. Crucial for applications of clocks in fundamental physics are a high sensitivity to effects beyond the Standard Model and Einstein's Theory of Relativity and a small frequency uncertainty of the clock. Highly charged ions offer both. They have been proposed as highly accurate clocks, since they possess optical transitions which can be extremely narrow and less sensitive to external perturbations compared to current atomic clock species. The selection of highly charged ions in different charge states offers narrow transitions that are among the most sensitive ones for a change in the fine-structure constant and the electron-to-proton mass ratio, as well as other new physics effects. Recent advances in trapping and sympathetic cooling of highly charged ions will in the future enable high accuracy optical spectroscopy. Progress in calculating the properties of selected highly charged ions has allowed the evaluation of systematic shifts and the prediction of the sensitivity to the "new physics" effects. This article reviews the current status of theory and experiment in the field.Comment: 53 pages, 16 figures, submitted to RM

Quantum gravity corrections to particle interactions

An heuristic semiclassical procedure that incorporates quantum gravity induced corrections in the description of photons and spin 1/2 fermions is reviewed. Such modifications are calculated in the framework of loop quantum gravity and they arise from the granular structure of space at short distances. The resulting effective theories are described by power counting nonrenormalizable actions which exhibit Lorentz violations at Planck length scale. The modified Maxwell and Dirac equations lead to corrections of the energy momentum relations for the corresponding particle at such scale. An action for the relativistic point particle exhibiting such modified dispersion relations is constructed and the first steps towards the study of a consistent coupling between these effective theories are presented.Comment: 12 pages, no figures, MPL LaTeX style; Invited talk at the " First IUCAA Meeting on the Interface of Gravitational and Quantum Realms", Pune, 17-21 December 200

Nuclear-polarization effect to the hyperfine structure in heavy multicharged ions

We have investigated the correction to the hyperfine structure of heavy multicharged ions, which is connected with the nuclear-polarization effect caused by the unpaired bound electron. Numerical calculations are performed for hydrogenlike ions taking into account the dominant collective nuclear excitations. The correction defines the ultimate limit of precision in accurate theoretical predictions of the hyperfine-structure splittings

Magnetic-dipole transition probabilities in B-like and Be-like ions

The magnetic-dipole transition probabilities between the fine-structure levels (1s^2 2s^2 2p) ^2P_1/2 - ^2P_3/2 for B-like ions and (1s^2 2s 2p) ^3P_1 - ^3P_2 for Be-like ions are calculated. The configuration-interaction method in the Dirac-Fock-Sturm basis is employed for the evaluation of the interelectronic-interaction correction with negative-continuum spectrum being taken into account. The 1/Z interelectronic-interaction contribution is derived within a rigorous QED approach employing the two-time Green function method. The one-electron QED correction is evaluated within framework of the anomalous magnetic-moment approximation. A comparison with the theoretical results of other authors and with available experimental data is presented

Hamiltonian LGT in the complete Fourier analysis basis

The main problem in the Hamiltonian formulation of Lattice Gauge Theories is the determination of an appropriate basis avoiding the over-completeness arising from Mandelstam relations. We short-cut this problem using Harmonic analysis on Lie-Groups and intertwining operators formalism to explicitly construct a basis of the Hilbert space. Our analysis is based only on properties of the tensor category of Lie-Group representations. The Hamiltonian of such theories is calculated yielding a sparse matrix whose spectrum and eigenstates could be exactly derived as functions of the coupling $g^2$Comment: LATTICE99 (theoretical developments), 3 page

Quadratic Model Predictive Control Including Input Cardinality Constraints

© 2017 IEEE. This note addresses the problem of feedback control with a constrained number of active inputs. This problem is known as sparse control. Specifically, we describe a novel quadratic model predictive control strategy that guarantees sparsity by bounding directly the l0-norm of the control input vector at each control horizon instant. Besides this sparsity constraint, bounded constraints are also imposed on both control input and system state. Under this scenario, we provide sufficient conditions for guaranteeing practical stability of the closed-loop. We transform the combinatorial optimization problem into an equivalent optimization problem that does not consider relaxation in the cardinality constraints. The equivalent optimization problem can be solved utilizing standard nonlinear programming toolboxes that provides the input control sequence corresponding to the global optimum

Probing the AGN Unification Model at redshift z ∼\sim 3 with MUSE observations of giant Lyα\alpha nebulae

A prediction of the classic active galactic nuclei (AGN) unification model is the presence of ionisation cones with different orientations depending on the AGN type. Confirmations of this model exist for present times, but it is less clear in the early Universe. Here, we use the morphology of giant Ly$\alpha$ nebulae around AGNs at redshift z$\sim$3 to probe AGN emission and therefore the validity of the AGN unification model at this redshift. We compare the spatial morphology of 19 nebulae previously found around type I AGNs with a new sample of 4 Ly$\alpha$ nebulae detected around type II AGNs. Using two independent techniques, we find that nebulae around type II AGNs are more asymmetric than around type I, at least at radial distances $r>30$~physical kpc (pkpc) from the ionizing source. We conclude that the type I and type II AGNs in our sample show evidence of different surrounding ionising geometries. This suggests that the classical AGN unification model is also valid for high-redshift sources. Finally, we discuss how the lack of asymmetry in the inner parts (r$\lesssim$30 pkpc) and the associated high values of the HeII to Ly$\alpha$ ratios in these regions could indicate additional sources of (hard) ionizing radiation originating within or in proximity of the AGN host galaxies. This work demonstrates that the morphologies of giant Ly$\alpha$ nebulae can be used to understand and study the geometry of high redshift AGNs on circum-nuclear scales and it lays the foundation for future studies using much larger statistical samples.Comment: 15 pages, 13 figures, accepted for publication in MNRA