Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schroedinger-like equation which provides a semiclassical Hamiltonian picture of the evolution of a `quantum of space', as shown by the authors in a recent paper. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed.Comment: 10 pages, talk given at "Physics and Mathematics of Nonlinear Phenomena" (PMNP2013), to appear in J. Phys. Conf. Serie

Sequential modular position and momentum measurements of a trapped ion mechanical oscillator

The non-commutativity of position and momentum observables is a hallmark feature of quantum physics. However this incompatibility does not extend to observables which are periodic in these base variables. Such modular-variable observables have been suggested as tools for fault-tolerant quantum computing and enhanced quantum sensing. Here we implement sequential measurements of modular variables in the oscillatory motion of a single trapped ion, using state-dependent displacements and a heralded non-destructive readout. We investigate the commutative nature of modular variable observables by demonstrating no-signaling-in-time between successive measurements, using a variety of input states. In the presence of quantum interference, which we enhance using squeezed input states, measurements of different periodicity show signaling-in-time. The sequential measurements allow us to extract two-time correlators for modular variables, which we use to violate a Leggett-Garg inequality. The experiments involve control and coherence of multi-component superpositions of up to 8 coherent, squeezed or Fock state wave-packets. Signaling-in-time as well as Leggett-Garg inequalities serve as efficient quantum witnesses which we probe here with a mechanical oscillator, a system which has a natural crossover from the quantum to the classical regime.Comment: 6 pages, 3 figures and supplemental informatio

Orbital magnetism in axially deformed sodium clusters: From scissors mode to dia-para magnetic anisotropy

Low-energy orbital magnetic dipole excitations, known as scissors mode (SM), are studied in alkali metal clusters. Subsequent dynamic and static effects are explored. The treatment is based on a self-consistent microscopic approach using the jellium approximation for the ionic background and the Kohn-Sham mean field for the electrons. The microscopic origin of SM and its main features (structure of the mode in light and medium clusters, separation into low- and high-energy plasmons, coupling high-energy M1 scissors and E2 quadrupole plasmons, contributions of shape isomers, etc) are discussed. The scissors M1 strength acquires large values with increasing cluster size. The mode is responsible for the van Vleck paramagnetism of spin-saturated clusters. Quantum shell effects induce a fragile interplay between Langevin diamagnetism and van Vleck paramagnetism and lead to a remarkable dia-para anisotropy in magnetic susceptibility of particular light clusters. Finally, several routes for observing the SM experimentally are discussed.Comment: 21 pages, 7 figure

Time-dependent Hamiltonian estimation for Doppler velocimetry of trapped ions

The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control. Though spectroscopic methods allow time-independent Hamiltonians to be recovered, for time-dependent Hamiltonians this task is more challenging. Here, using a single trapped ion, we experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. The method involves measuring the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. In our system the initially unknown Hamiltonian arises from transporting an ion through a static, near-resonant laser beam. Hamiltonian estimation allows us to estimate the spatial dependence of the laser beam intensity and the ion's velocity as a function of time. This work is of direct value in optimizing transport operations and transport-based gates in scalable trapped ion quantum information processing, while the estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high operational fidelities in quantum control.Comment: 10 pages, 8 figure

Librarianship from an International Point of View

published or submitted for publicatio

Testing the specificity of predictors of reading, spelling and maths: a new model of the association among learning skills based on competence, performance and acquisition

In a previous study (Zoccolotti et al., 2020) we examined reading, spelling, and maths skills in an unselected group of 129 Italian children attending fifth grade by testing various cognitive predictors; results showed a high degree of predictors’ selectivity for each of these three behaviors. In the present study, we focused on the specificity of the predictors by performing cross-analyses on the same dataset; i.e., we predicted spelling and maths skills based on reading predictors, reading based on maths predictors and so on. Results indicated that some predictors, such as the Orthographic Decision and the Arithmetic Facts tests, predicted reading, spelling and maths skills in similar ways, while others predicted different behaviors but only for a specific parameter, such as fluency but not accuracy (as in the case of RAN), and still others were specific for a single behavior (e.g., Visual-auditory Pseudo-word Matching test predicted only spelling skills). To interpret these results, we propose a novel model of learning skills separately considering factors in terms of competence, performance and acquisition (automatization). Reading, spelling and calculation skills would depend on the development of discrete and different abstract competences (accounting for the partial dissociations among learning disorders reported in the literature). By contrast, overlap among behaviors would be accounted for by defective acquisition in automatized responses to individual “instances”; this latter skill is item specific but domain independent. Finally, performance factors implied in task’s characteristics (such as time pressure) may contribute to the partial association among learning skills. It is proposed that this new model may provide a useful base for interpreting the diffuse presence of comorbidities among learning disorders

A network analysis of the relationship among reading, spelling and maths skills

Background. Skill learning (e.g., reading, spelling and maths) has been predominantly treated separately in the neuropsychological literature. However, skills (as well as their corresponding deficits), tend to partially overlap. We recently proposed a multi-level model of learning skills (based on the distinction among competence, performance, and acquisition) as a framework to provide a unitary account of these learning skills. In the present study, we examined the performance of an unselected group of third-to fifth-grade children on standard reading, spelling, and maths tasks, and tested the relationships among these skills with a network analysis, i.e., a method particularly suited to analysing relations among different domains. Methods. We administered a battery of reading, spelling, and maths tests to 185 third-, fourth-, and fifth-grade children (103 M, 82 F). Results. The network analysis indicated that the different measures of the same ability (i.e., reading, spelling, and maths) formed separate clusters, in keeping with the idea that they are based on different competences. However, these clusters were also related to each other, so that three nodes were more central in connecting them. In keeping with the multi-level model of learning skills, two of these tests (arithmetic facts subtest and spelling words with ambiguous transcription) relied heavily on the ability to recall specific instances, a factor hypothesised to underlie the co-variation among learning skills. Conclusions. The network analysis indicated both elements of association and of partial independence among learning skills. Interestingly, the study was based on standard clinical instruments, indicating that the multi-level model of learning skills might provide a framework for the clinical analysis of these learning skills