Erasing Distinguishability Using Quantum Frequency Up-Conversion

The frequency distinguishability of two single photons was successfully erased using single photon frequency up-conversion. A frequency non-degenerate photon pair generated via spontaneous four-wave mixing in a dispersion shifted fiber was used to emulate two telecom-band single photons that were in the same temporal mode but in different frequency modes. The frequencies of these photons were converted to the same frequency by using the sum frequency generation process in periodically poled lithium niobate waveguides, while maintaining their temporal indistinguishability. As a result, the two converted photons exhibited a non-classical dip in a Hong-Ou-Mandel quantum interference experiment. The present scheme will add flexibility to networking quantum information systems that use photons with various wavelengths.Comment: 4 pages, 5 figure

Piecewise-linear maps with heterogeneous chaos

Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic invariant set is heterogeneous when arbitrarily close to each point of the set there are different periodic points with different numbers of unstable dimensions. We call such dynamics heterogeneous chaos (or hetero-chaos), While we believe it is common for physical systems to be hetero-chaotic, few explicit examples have been proved to be hetero-chaotic. Here we present two more explicit dynamical systems that are particularly simple and tractable with computer. It will give more intuition as to how complex even simple systems can be. Our maps have one dense set of periodic points whose orbits are 1D unstable and another dense set of periodic points whose orbits are 2D unstable. Moreover, they are ergodic relative to the Lebesgue measure.Comment: 16 pages, 9 figure

Einstein--de Haas Effect in Dipolar Bose-Einstein Condensates

The general properties of the order parameter for a dipolar spinor Bose-Einstein condensate are discussed based on symmetries of interactions. An initially spin-polarized dipolar condensate is shown to dynamically generate a non-singular vortex via spin-orbit interactions -- a phenomenon reminiscent of the Einstein--de Haas effect in ferromagnets.Comment: 4 pages, 4 figures; Final versio

Spontaneous Circulation in Ground-State Spinor Dipolar Bose-Einstein Condensates

We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the non-local Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all these phases can be observed in the spin-1 $^{87}$Rb condensate by changing the number of atoms or the trap frequency.Comment: final versio

Topological defect formation in quenched ferromagnetic Bose-Einstein condensates

We study the dynamics of the quantum phase transition of a ferromagnetic spin-1 Bose-Einstein condensate from the polar phase to the broken-axisymmetry phase by changing magnetic field, and find the spontaneous formation of spinor domain walls followed by the creation of polar-core spin vortices. We also find that the spin textures depend very sensitively on the initial noise distribution, and that an anisotropic and colored initial noise is needed to reproduce the Berkeley experiment [Sadler et al., Nature 443, 312 (2006)]. The dynamics of vortex nucleation and the number of created vortices depend also on the manner in which the magnetic field is changed. We point out an analogy between the formation of spin vortices from domain walls in a spinor BEC and that of vortex-antivortex pairs from dark solitons in a scalar BEC.Comment: 10 pages, 11 figure

Interrater reliability in visual identification of interictal high-frequency oscillations on electrocorticography and scalp EEG.

High-frequency oscillations (HFOs), including ripples (Rs) and fast ripples (FRs), are promising biomarkers of epileptogenesis, but their clinical utility is limited by the lack of a standardized approach to identification. We set out to determine whether electroencephalographers experienced in HFO analysis can reliably identify and quantify interictal HFOs. Two blinded raters independently reviewed 10 intraoperative electrocorticography (ECoG) samples from epilepsy surgery cases, and 10 scalp EEG samples from epilepsy monitoring unit evaluations. HFOs were visually marked using bandpass filters (R, 80-250 Hz; FR, 250-500 Hz) with a sampling frequency of 2,000 Hz. There was agreement as to the presence or absence of epileptiform discharges (EDs), Rs, and FRs, in 17, 18, and 18 cases, respectively. Interrater reliability (IRR) was favorable with κ = 0.70, 0.80, and 0.80, respectively, and similar for ECoG and scalp electroencephalography (EEG). Furthermore, interclass correlation for rates of Rs (0.99, 95% confidence interval [CI] 0.96-0.99) and FRs (0.77, 95% CI 0.41-0.91) were superior in comparison to EDs (0.37, 95% CI -0.60 to 0.75). Our data suggest that HFO identification and quantification are reliable among experienced electroencephalographers. Our findings support the reliability of utilizing HFO data in both research and clinical arenas

Spin-polarized electronic structures and transport properties of Fe-Co alloys

The electrical resistivities of Fe-Co alloys owing to random alloy disorder are calculated using the Kubo-Greenwood formula. The obtained electrical esistivities agree well with experimental data quantitatively at low temperature. The spin-polarization of Fe50Co50 estimated from the conductivity (86%) has opposite sign to that from the densities of the states at the Fermi level (-73%). It is found that the conductivity is governed mainly by s-electrons, and the s-electrons in the minority spin states are less conductive due to strong scattering by the large densities of the states of d-electrons than the majority spin electrons.Comment: 3 pages, 4 figure

Best Complete Approximations of Preference Relations

We investigate the problem of approximating an incomplete preference relation $\succsim$ on a finite set by a complete preference relation. We aim to obtain this approximation in such a way that the choices on the basis of two preferences, one incomplete, the other complete, have the smallest possible discrepancy in the aggregate. To this end, we use the top-difference metric on preferences, and define a best complete approximation of $\succsim$ as a complete preference relation nearest to $\succsim$ relative to this metric. We prove that such an approximation must be a maximal completion of $\succsim$, and that it is, in fact, any one completion of $\succsim$ with the largest index. Finally, we use these results to provide a sufficient condition for the best complete approximation of a preference to be its canonical completion. This leads to closed-form solutions to the best approximation problem in the case of several incomplete preference relations of interest