A spatially shifted beam approach to subwavelength focusing

Although negative-refractive-index metamaterials have successfully achieved subwavelength focusing, image resolution is limited by the presence of losses. In this Letter, a metal transmission screen with subwavelength spaced slots is proposed that focuses the near-field beyond the diffraction limit and furthermore, is easily scaled from microwave frequencies to the optical regime. An analytical model based on the superposition of shifted beam patterns is developed that agrees very well with full-wave simulations and is corroborated by experimental results at microwave frequencies.Comment: 5 pages, 7 figures. Content updated following reviewer comments to match final published pape

Solutions to the Jaynes-Cummings model without the rotating-wave approximation

By using extended bosonic coherent states, the solution to the Jaynes-Cummings model without the rotating-wave approximation can be mapped to that of a polynomial equation with a single variable. The solutions to this polynomial equation can give all eigenvalues and eigenfunctions of this model with all values of the coupling strength and the detuning exactly, which can be readily applied to recent circuit quantum electrodynamic systems operating in the ultra-strong coupling regime.Comment: 6 pages,3 figure

The Projective Line Over the Finite Quotient Ring GF(2)[xx]/<x3−x>< x^{3} - x> and Quantum Entanglement I. Theoretical Background

The paper deals with the projective line over the finite factor ring $R\_{\clubsuit} \equiv$ GF(2)[$x$]/$$. The line is endowed with 18 points, spanning the neighbourhoods of three pairwise distant points. As $R\_{\clubsuit}$ is not a local ring, the neighbour (or parallel) relation is not an equivalence relation so that the sets of neighbour points to two distant points overlap. There are nine neighbour points to any point of the line, forming three disjoint families under the reduction modulo either of two maximal ideals of the ring. Two of the families contain four points each and they swap their roles when switching from one ideal to the other; the points of the one family merge with (the image of) the point in question, while the points of the other family go in pairs into the remaining two points of the associated ordinary projective line of order two. The single point of the remaining family is sent to the reference point under both the mappings and its existence stems from a non-trivial character of the Jacobson radical, ${\cal J}\_{\clubsuit}$, of the ring. The factor ring $\widetilde{R}\_{\clubsuit} \equiv R\_{\clubsuit}/ {\cal J}\_{\clubsuit}$ is isomorphic to GF(2) $\otimes$ GF(2). The projective line over $\widetilde{R}\_{\clubsuit}$ features nine points, each of them being surrounded by four neighbour and the same number of distant points, and any two distant points share two neighbours. These remarkable ring geometries are surmised to be of relevance for modelling entangled qubit states, to be discussed in detail in Part II of the paper.Comment: 8 pages, 2 figure

Projective Ring Line Encompassing Two-Qubits

The projective line over the (non-commutative) ring of two-by-two matrices with coefficients in GF(2) is found to fully accommodate the algebra of 15 operators - generalized Pauli matrices - characterizing two-qubit systems. The relevant sub-configuration consists of 15 points each of which is either simultaneously distant or simultaneously neighbor to (any) two given distant points of the line. The operators can be identified with the points in such a one-to-one manner that their commutation relations are exactly reproduced by the underlying geometry of the points, with the ring geometrical notions of neighbor/distant answering, respectively, to the operational ones of commuting/non-commuting. This remarkable configuration can be viewed in two principally different ways accounting, respectively, for the basic 9+6 and 10+5 factorizations of the algebra of the observables. First, as a disjoint union of the projective line over GF(2) x GF(2) (the "Mermin" part) and two lines over GF(4) passing through the two selected points, the latter omitted. Second, as the generalized quadrangle of order two, with its ovoids and/or spreads standing for (maximum) sets of five mutually non-commuting operators and/or groups of five maximally commuting subsets of three operators each. These findings open up rather unexpected vistas for an algebraic geometrical modelling of finite-dimensional quantum systems and give their numerous applications a wholly new perspective.Comment: 8 pages, three tables; Version 2 - a few typos and one discrepancy corrected; Version 3: substantial extension of the paper - two-qubits are generalized quadrangles of order two; Version 4: self-dual picture completed; Version 5: intriguing triality found -- three kinds of geometric hyperplanes within GQ and three distinguished subsets of Pauli operator

Little groups of irreps of O(3), SO(3), and the infinite axial subgroups

Little groups are enumerated for the irreps and their components in any basis of O(3) and SO(3) up to rank 9, and for all irreps of C$_{\infty}$, C$_{\infty h}$, C$_{\infty v}$, D$_{\infty}$ and D$_{\infty h}$. The results are obtained by a new chain criterion, which distinguishes massive (rotationally inequivalent) irrep basis functions and allows for multiple branching paths, and are verified by inspection. These results are relevant to the determination of the symmetry of a material from its linear and nonlinear optical properties and to the choices of order parameters for symmetry breaking in liquid crystals.Comment: 28 pages and 3 figure

Integrable Hamiltonians with D(Dn)D(D_n) symmetry from the Fateev-Zamolodchikov model

A special case of the Fateev-Zamolodchikov model is studied resulting in a solution of the Yang-Baxter equation with two spectral parameters. Integrable models from this solution are shown to have the symmetry of the Drinfeld double of a dihedral group. Viewing this solution as a descendant of the zero-field six-vertex model allows for the construction of functional relations and Bethe ansatz equations

In vitro tooth cleaning efficacy of electric toothbrushes around brackets

This in vitro study assessed the cleaning efficacy of different electric toothbrushes around upper incisor brackets. Standard and Mini Diamond™ brackets were fixed on black-stained teeth. The teeth were coated with white titanium oxide and brushed in a machine twice for 1 minute each. Twelve different brush heads with either a wiping or an oscillating-rotating action were tested. After brushing, the teeth were scanned, the black surfaces were assessed planimetrically and a modified plaque index for orthodontic patients (PIOP) was introduced. Tooth areas, which were black again after brushing indicated tooth surface contact of the filaments and were expressed as a percentage of total area. The remaining white areas around the brackets indicated 'plaque-retentive' niches. Analysis of variance was used for individual comparison of the brush types. Bonferroni/Dunn adjustment was applied for multiple testing. The Sonicare® toothbrush handle with the brush head 'Compact ProResults' (81.7 per cent) and the brush head 'Standard ProResults' (80.8 per cent), as well as the sonic Waterpik® toothbrush SR 800E with the standard brush head (78.2 per cent), showed statistically significantly better cleaning efficacy than all others. The poorest cleaning efficacy was observed for the oscillating-rotating Braun Oral-B Professional Care with the brush head 'Ortho' (less than 50 per cent). The planimetric findings were in correspondence with the results of the PIOP assessment. Cleaning efficacy of electric toothbrushes around brackets on upper incisors was different between the tested brushes. The PIOP was practicable, effective, and easy to use, although it has to be verified in a clinical study