Simplified landscapes for optimization of shaken lattice interferometry

Motivated by recent results using shaken optical lattices to perform atom interferometry, we explore splitting of an atom cloud trapped in a phase-modulated ("shaken") optical lattice. Using a simple analytic model we are able to show that we can obtain the simplest case of $\pm2\hbar k_\mathrm{L}$ splitting via single-frequency shaking. This is confirmed both via simulation and experiment. Furthermore, we are able to split with a relative phase $\theta$ between the two split arms of $0$ or $\pi$ depending on our shaking frequency. Addressing higher-order splitting, we determine that $\pm6\hbar k_\mathrm{L}$ splitting is sufficient to be able to accelerate the atoms in counter-propagating lattices. Finally, we show that we can use a genetic algorithm to optimize $\pm4\hbar k_\mathrm{L}$ and $\pm6\hbar k_\mathrm{L}$ splitting to within $\approx0.1\%$ by restricting our optimization to the resonance frequencies corresponding to single- and two-photon transitions between Bloch bands

The Infrared and Radio Fluxes Densities of Galactic HII Regions

We derive infrared and radio flux densities of all ~1000 known Galactic HII regions in the Galactic longitude range 17.5 < l < 65 degree. Our sample comes from the Wide-Field Infrared Survey Explorer (WISE) catalog of Galactic \hii regions \citep{anderson2014}. We compute flux densities at six wavelengths in the infrared (GLIMPSE 8 microns, WISE 12 microns and 22 microns, MIPSGAL 24 microns, and Hi-GAL 70 microns and 160 microns) and two in the radio (MAGPIS 20 cm and VGPS 21 cm). All HII region infrared flux densities are strongly correlated with their ~20 cm flux densities. All HII regions used here, regardless of physical size or Galactocentric radius, have similar infrared to radio flux density ratios and similar infrared colors, although the smallest regions ($r<1\,$pc), have slightly elevated IR to radio ratios. The colors $\log_{10}(F_{24 micron}/F_{12 micron}) \ge 0$ and $\log_{10}(F_{70 micron}/F_{12 micron}) \ge 1.2$, and $\log_{10}(F_{24 micron}/F_{12 micron}) \ge 0$ and $\log_{10}(F_{160 micron}/F_{70 micron}) \le 0.67$ reliably select HII regions, independent of size. The infrared colors of ~22$\%$ of HII regions, spanning a large range of physical sizes, satisfy the IRAS color criteria of \citet{wood1989} for HII regions, after adjusting the criteria to the wavelengths used here. Since these color criteria are commonly thought to select only ultra-compact HII regions, this result indicates that the true ultra-compact HII region population is uncertain. Comparing with a sample of IR color indices from star-forming galaxies, HII regions show higher $\log_{10}(F_{70 micron}/F_{12 micron})$ ratios. We find a weak trend of decreasing infrared to ~20 cm flux density ratios with increasing $R_{gal}$, in agreement with previous extragalactic results, possibly indicating a decreased dust abundance in the outer Galaxy.Comment: 27 pages, 16 figures, 5 table

Non-unique factorization of polynomials over residue class rings of the integers

We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] is atomic. We reduce the question of factoring arbitrary non-zero polynomials into irreducibles to the problem of factoring monic polynomials into monic irreducibles. The multiplicative monoid of monic polynomials of Z_{p^n}[x] is a direct sum of monoids corresponding to irreducible polynomials in Z_p[x], and we show that each of these monoids has infinite elasticity. Moreover, for every positive integer m, there exists in each of these monoids a product of 2 irreducibles that can also be represented as a product of m irreducibles.Comment: 11 page

OPERA superluminal neutrinos and Kinematics in Finsler spacetime

The OPERA collaboration recently reported that muon neutrinos could be superluminal. More recently, Cohen and Glashow pointed that such superluminal neutrinos would be suppressed since they lose their energies rapidly via bremsstrahlung. In this Letter, we propose that Finslerian nature of spacetime could account for the superluminal phenomena of particles. The Finsler spacetime permits the existence of superluminal behavior of particles while the casuality still holds. A new dispersion relation is obtained in a class of Finsler spacetime. It is shown that the superluminal speed is linearly dependent on the energy per unit mass of the particle. We find that such a superluminal speed formula is consistent with data of OPERA, MINOS and Fermilab-1979 neutrino experiments as well as observations on neutrinos from SN1987a.Comment: 10 pages, 2 figures. Viewpoints of Finslerian special relativity on OPERA superluminal neutrino

Vortex State in Na_xCoO_2.yH_2O: p_x\pm ip_y-wave versus d_{x^2-y^2}\pm id_{xy}-wave Pairing

Based on an effective Hamiltonian specified in the triangular lattice with possible $p_x\pm ip_y$- or $d_{x^2-y^2}\pm id_{xy}$-wave pairing, which has close relevance to the newly discovered Na$_{0.35}$CoO$_2$$\cdot y$H$_2$O, the electronic structure of the vortex state is studied by solving the Bogoliubov-de Gennes equations. It is found that $p_x\pm ip_y$-wave is favored for the electron doping as the hopping integral $t<0$. The lowest-lying vortex bound states are found to have respectively zero and positive energies for $p_x\pm ip_y$- and $d_{x^2-y^2}\pm id_{xy}$-wave superconductors, whose vortex structures exhibit the intriguing six-fold symmetry. In the presence of strong on-site repulsion, the antiferromagnetic and ferromagnetic orders are induced around the vortex cores for the former and the latter, respectively, both of which cause the splitting of the LDOS peaks due to the lifting of spin degeneracy. STM and NMR measurements are able to probe the new features of vortex states uncovered in this work.Comment: 4 pages, 4 figures, The slightly shorter version was submitted to PR

The momentum flux probability distribution function for ion-temperature-gradient turbulence

There has been overwhelming evidence that coherent structures play a critical role in determining the overall transport in a variety of systems. We compute the probability distribution function (PDF) tails of momentum flux and heat flux in ion-temperature-gradient turbulence, by taking into account the interaction among modons, which are assumed to be coherent structures responsible for bursty and intermittent events, contributing to the PDF tails. The tail of PDF of momentum flux R = 〈vxvy〉 is shown to be exponential with the form exp{−ξR3/2}, which is broader than a Gaussian, similar to what was found in the previous local studies. An analogous expression with the same functional dependence is found for the PDF tails of heat flux. Furthermore, we present a detailed numerical study of the dependence of the PDF tail on the temperature and density scale lengths and other physical parameters through the coefficient ξ