Conditional detection of pure quantum states of light after storage in a Tm-doped waveguide

We demonstrate the conditional detection of time-bin qubits after storage in and retrieval from a photon-echo-based waveguide quantum memory. Each qubit is encoded into one member of a photon pair produced via spontaneous parametric down-conversion, and the conditioning is achieved by the detection of the other member of the pair. By performing projection measurements with the stored and retrieved photons onto different bases, we obtain an average storage fidelity of 0.885±0.020, which exceeds the relevant classical bounds and shows the suitability of our integrated light-matter interface for future applications of quantum information processing.     

Dielectric-barrier discharges in two-dimensional lattice potentials

We use a pin-grid electrode to introduce a corrugated electrical potential into a planar dielectric-barrier discharge (DBD) system, so that the amplitude of the applied electric field has the profile of a two-dimensional square lattice. The lattice potential provides a template for the spatial distribution of plasma filaments in the system and has pronounced effects on the patterns that can form. The positions at which filaments become localized within the lattice unit cell vary with the width of the discharge gap. The patterns that appear when filaments either overfill or underfill the lattice are reminiscent of those observed in other physical systems involving 2D lattices. We suggest that the connection between lattice-driven DBDs and other areas of physics may benefit from the further development of models that treat plasma filaments as interacting particles.     

Realizing optical magnetism from dielectric metamaterials

We demonstrate, for the first time, an all-dielectric metamaterial composite in the midinfrared based on micron-sized, high-index tellurium dielectric resonators. Dielectric resonators are desirable compared to conventional metallodielectric metamaterials at optical frequencies as they are largely angular invariant, free of Ohmic loss, and easily integrated into three-dimensional volumes. Measurements and simulation provide evidence of optical magnetism, which could be used for infrared magnetic mirrors, hard or soft surfaces, and subwavelength cavities.     

The structuring of personal example spaces

This paper elaborates the notion of a personal example space as the set of mathematical objects and construction techniques that a learner has access to as examples of a concept while working on a given task. This is different from the conventional space of examples that is represented by the worked examples and exercises in textbooks. We refer to three studies spanning the age range of learners, from school-age learners to pre-service teachers learning maths and professional mathematicians. Their constructions of examples are used as evidence of their personal example spaces. From these, we identify characteristics of such spaces that provide insight into learning mathematics. This perspective informs teaching by giving access to how personal knowledge is structured and what might enhance that structure.     

Approximation Algorithms for Two-State Anti-Ferromagnetic Spin Systems on Bounded Degree Graphs

We show that for the anti-ferromagnetic Ising model on the Bethe lattice, weak spatial mixing implies strong spatial mixing. As a by-product of our analysis, we obtain what is to the best of our knowledge the first rigorous proof of the uniqueness threshold for the anti-ferromagnetic Ising model (with non-zero external field) on the Bethe lattice. Following a method due to Weitz [15], we then use the equivalence between weak and strong spatial mixing to give a deterministic fully polynomial time approximation scheme for the partition function of the anti-ferromagnetic Ising model with arbitrary field on graphs of degree at most  $d$ , throughout the uniqueness region of the Gibbs measure on the infinite $d$ -regular tree. By a standard correspondence, our results translate to arbitrary two-state anti-ferromagnetic spin systems with soft constraints. Subsequent to a preliminary version of this paper, Sly and Sun [13] have shown that our results are optimal in the sense that, under standard complexity theoretic assumptions, there does not exist a fully polynomial time approximation scheme for the partition function of such spin systems on graphs of maximum degree  $d$ for parameters outside the uniqueness region. Taken together, the results of [13] and of this paper therefore indicate a tight relationship between complexity theory and phase transition phenomena in two-state anti-ferromagnetic spin systems.     

Frequency comb velocity-modulation spectroscopy

We have demonstrated a new technique that provides massively parallel comb spectroscopy sensitive specifically to ions through the combination of cavity-enhanced direct frequency comb spectroscopy with velocity-modulation spectroscopy. Using this novel system, we have measured electronic transitions of HfF? and achieved a fractional absorption sensitivity of 3×10?? recorded over 1500 simultaneous channels spanning 150 cm?1 around 800 nm with an absolute frequency accuracy of 30 MHz (0.001 cm?1). A fully sampled spectrum consisting of interleaved measurements is acquired in 30 min.     

Electrochemical, spectroscopic, and photophysical properties of structurally diverse polyazine-bridged Ru(II),Pt(II) and Os(II),Ru(II),Pt(II) supramolecular motifs

Five new tetrametallic supramolecules of the motif [{(TL)(2)M(dpp)}(2)Ru(BL)PtCl(2)](6+) and three new trimetallic light absorbers [{(TL)(2)M(dpp)}(2)Ru(BL)](6+) (TL = bpy = 2,2'-bipyridine or phen = 1,10-phenanthroline; M = Ru(II) or Os(II); BL = dpp = 2,3-bis(2-pyridyl)pyrazine, dpq = 2,3-bis(2-pyridyl)quinoxaline, or bpm = 2,2'-bipyrimidine) were synthesized and their redox, spectroscopic, and photophysical properties investigated. The tetrametallic complexes couple a Pt(II)-based reactive metal center to Ru and/or Os light absorbers through two different polyazine BL to provide structural diversity and interesting resultant properties. The redox potential of the M(II/III) couple is modulated by M variation, with the terminal Ru(II/III) occurring at 1.58-1.61 V and terminal Os(II/III) couples at 1.07-1.18 V versus Ag/AgCl. [{(TL)(2)M(dpp)}(2)Ru(BL)](PF(6))(6) display terminal M(dπ)-based highest occupied molecular orbitals (HOMOs) with the dpp(π*)-based lowest unoccupied molecular orbital (LUMO) energy relatively unaffected by the nature of BL. The coupling of Pt to the BL results in orbital inversion with localization of the LUMO on the remote BL in the tetrametallic complexes, providing a lowest energy charge separated (CS) state with an oxidized terminal Ru or Os and spatially separated reduced BL. The complexes [{(TL)(2)M(dpp)}(2)Ru(BL)](6+) and [{(TL)(2)M(dpp)}(2)Ru(BL)PtCl(2)](6+) efficiently absorb light throughout the UV and visible regions with intense metal-to-ligand charge transfer (MLCT) transitions in the visible at about 540 nm (M = Ru) and 560 nm (M = Os) (ε ≈ 33,000-42,000 M(-1) cm(-1)) and direct excitation to the spin-forbidden (3)MLCT excited state in the Os complexes about 720 nm. All the trimetallic and tetrametallic Ru-based supramolecular systems emit from the terminal Ru(dπ)→dpp(π*) (3)MLCT state, λ(max)(em) ≈ 750 nm. The tetrametallic systems display complex excited state dynamics with quenching of the (3)MLCT emission at room temperature to populate the lowest-lying (3)CS state population of the emissive (3)MLCT state.     

Guided ultrasonic waves in composite cylinders

The ultrasonic nondestructive evaluation of composite cylinders requires a thorough understanding of the propagation of waves in these materials. In this paper, the propagation of flexural and longitudinal guided waves in fiber-reinforced composite (FRC) rods with transversely isotropic symmetry properties is studied. The frequency equations obtained for free cylinders and the effect of increased fiber volume fraction (increased anisotropy) on the dispersion characteristics of the rod are explored. The numerical results reveal a number of previously unnoticed characteristics of dispersion curves for composite cylinders. The mode shapes of longitudinal waves propagating in glass/epoxy cylinders are also plotted. These plots can be used to choose an appropriate strategy for inspecting composite cylinders by ultrasonic nondestructive evaluation techniques. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 411–426, May–June, 2007.     

Aesthetics as a liberating force in mathematics education?

This article investigates different meanings associated with contemporary scholarship on the aesthetic dimension of inquiry and experience, and uses them to suggest possibilities for challenging widely held beliefs about the elitist and/or frivolous nature of aesthetic concerns in mathematics education. By relating aesthetics to emerging areas of interest in mathematics education such as affect, embodiment and enculturation, as well as to issues of power and discourse, this article argues for aesthetic awareness as a liberating, and also connective force in mathematics education.     

Further Paradoxes in Generalized Levy Problems

The classical solution of Levy's plate problem breaks down for a critical plate angle, with both stress and displacement fields becoming unbounded throughout the plate. The same sort of paradoxical response occurs in traditional solutions for other critical angles if the pressure in Levy's original problem is replaced by a constant shear traction. These breakdowns can be rectified by suitably supplementing classical fields. In this note, a further generalization of Levy's problem is considered. This entails clamping the plate edge without applied tractions. Critical angles for which traditional analysis breaks down are identified, and new solutions are developed for these angles. This revised version was published online in July 2006 with corrections to the Cover Date.