Rigidity of spherical codes

A packing of spherical caps on the surface of a sphere (that is, a spherical code) is called rigid or jammed if it is isolated within the space of packings. In other words, aside from applying a global isometry, the packing cannot be deformed. In this paper, we systematically study the rigidity of spherical codes, particularly kissing configurations. One surprise is that the kissing configuration of the Coxeter-Todd lattice is not jammed, despite being locally jammed (each individual cap is held in place if its neighbors are fixed); in this respect, the Coxeter-Todd lattice is analogous to the face-centered cubic lattice in three dimensions. By contrast, we find that many other packings have jammed kissing configurations, including the Barnes-Wall lattice and all of the best kissing configurations known in four through twelve dimensions. Jamming seems to become much less common for large kissing configurations in higher dimensions, and in particular it fails for the best kissing configurations known in 25 through 31 dimensions. Motivated by this phenomenon, we find new kissing configurations in these dimensions, which improve on the records set in 1982 by the laminated lattices.Comment: 39 pages, 8 figure

Nanowire quantum dots tuned to atomic resonances

Quantum dots tuned to atomic resonances represent an emerging field of hybrid quantum systems where the advantages of quantum dots and natural atoms can be combined. Embedding quantum dots in nanowires boosts these systems with a set of powerful possibilities, such as precise positioning of the emitters, excellent photon extraction efficiency and direct electrical contacting of quantum dots. Notably, nanowire structures can be grown on silicon substrates, allowing for a straightforward integration with silicon-based photonic devices. In this work we show controlled growth of nanowire-quantum-dot structures on silicon, frequency tuned to atomic transitions. We grow GaAs quantum dots in AlGaAs nanowires with a nearly pure crystal structure and excellent optical properties. We precisely control the dimensions of quantum dots and their position inside nanowires, and demonstrate that the emission wavelength can be engineered over the range of at least $30\,nm$ around $765\,nm$. By applying an external magnetic field we are able to fine tune the emission frequency of our nanowire quantum dots to the $D_{2}$ transition of $^{87}$Rb. We use the Rb transitions to precisely measure the actual spectral linewidth of the photons emitted from a nanowire quantum dot to be $9.4 \pm 0.7 \mu eV$, under non-resonant excitation. Our work brings highly-desirable functionalities to quantum technologies, enabling, for instance, a realization of a quantum network, based on an arbitrary number of nanowire single-photon sources, all operating at the same frequency of an atomic transition.Comment: main text (20 pages, 3 figures) plus supplementary information, Nano Letters (2018

Growth of self-catalyzed inas/insb axial heterostructured nanowires: Experiment and theory

The growth mechanisms of self-catalyzed InAs/InSb axial nanowire heterostructures are thoroughly investigated as a function of the In and Sb line pressures and growth time. Some interesting phenomena are observed and analyzed. In particular, the presence of In droplet on top of InSb segment is shown to be essential for forming axial heterostructures in the self-catalyzed vapor-liquid-solid mode. Axial versus radial growth rates of InSb segment are investigated under different growth conditions and described within a dedicated model containing no free parameters. It is shown that widening of InSb segment with respect to InAs stem is controlled by the vapor-solid growth on the nanowire sidewalls rather than by the droplet swelling. The In droplet can even shrink smaller than the nanowire facet under Sb-rich conditions. These results shed more light on the growth mechanisms of self-catalyzed heterostructures and give clear route for engineering the morphology of InAs/InSb axial nanowire heterostructures for different applications

Case of Collecting Tick \u3ci\u3eAmblyoma lepidum\u3c/i\u3e Dönitz, 1909, in Azerbaijan

First paragraph: On 18 May 1954, (a specimen of) Burhinus oedicnemus (L.) was killed in the Lenkoransky region of Azerbaijan S.S.R.; on its head a male Amblyomma lepidum Dönitz, 1909, was found. Morphological characters of this tick, size and shape of body, characteristic light and dark ornamentation of dorsal shield, punctation, shape, and two colors of festoons, size and shape of cervical and lateral grooves, hypostome, peritreme, projection on coxae, and spherical orbited eyes correspond to those in the description of A. lepidum, given in Robinson monograph. Only on four anterior festoons a small light spot is found (in description by Robinson festoons are all one color, dark). This may be an individual variation