Lagrangian bias in the local bias model

It is often assumed that the halo-patch fluctuation field can be written as a Taylor series in the initial Lagrangian dark matter density fluctuation field. We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function. This statement is exact and valid on all scales; there are no higher order contributions, e.g., from terms proportional to products or convolutions of two-point functions, which one might have thought would appear upon truncating the Taylor series of the halo bias function. In addition, the auto-correlation function of locally biased tracers can be written as a Taylor series in the auto-correlation function of the mass; there are no terms involving, e.g., derivatives or convolutions. Moreover, although the leading order coefficient, the linear bias factor of the auto-correlation function is just the square of that for the cross-correlation, it is the same as that obtained from expanding the mean number of halos as a function of the local density only in the large-scale limit. In principle, these relations allow simple tests of whether or not halo bias is indeed local in Lagrangian space. We discuss why things are more complicated in practice. We also discuss our results in light of recent work on the renormalizability of halo bias, demonstrating that it is better to renormalize than not. We use the Lognormal model to illustrate many of our findings.Comment: 14 pages, published on JCA

Competitive formation of spiro and ansa derivatives in the reactions of tetrafluorobutane-1,4-diol with hexachlorocyclotriphosphazene: a comparison with butane-1,4-diol

Reaction of hexachlorocyclotriphosphazene, N3P3Cl6 (1), in two stoichiometries (1:1.2 and 1:3) with the sodium derivative of the fluorinated diol, 2,2,3,3-tetrafluorobutane-1,4-diol, (2), in THF solution at room temperature afforded six products, whose structures have been characterized by X-ray crystallography and 1H, 19F and 31P NMR spectroscopy: the mono-spiro compound, N3P3Cl4(OCH2CF2CF2CH2O), (3), its ansa isomer, (4), a di-spiro derivative N3P3Cl2(OCH2CF2CF2CH2O)2, (5), its spiro-ansa (6) and non-gem cis bis-ansa (7) isomers and a tri-spiro compound N3P3(OCH2CF2CF2CH2O)3, (8). The tri-spiro derivative (8) was also formed in the reaction of the ansa compound (4) with diol (2) in a 1:3 ratio in THF at room temperature. The reactions of (1) with step-wise additions of (2) were also investigated at low temperature (-780C) to give the same range of products as at room temperature. The results of all reactions are compared with previous work on the reactions of (1) with butane-1,4-diol/pyridine mixtures and with the reaction of hexafluorocyclotriphosphazene, N3P3F6 (9), with the silyl derivative of the diol (2), (Me3SiOCH2CF2)2, in a 1:0.4 mole ratio in the same solvent, THF

Stereoisomerism in pentaerythritol-bridged cyclotriphosphazene tri-spiranes: spiro and ansa 1,3-propanediyldioxy disubstituted derivatives

Four isomeric products were isolated and purified from the reaction of 1,3-propanediol with the tetra-spirane cyclophosphazene-organophosphate compound (1): viz. the di-monospiro (2a), di-monoansa (2b) and two monospiro-monoansa derivatives (2c) and (2d). It is shown by 31P NMR spectroscopy on addition of a chiral solvating agent (CSA) that both the di-monospiro (2a) and di-monoansa (2b) derivatives are racemates, as expected, whereas no splitting of NMR signals occurred on addition of CSA to solutions of (2c) and (2d). It is found by X-ray crystallography that the two monospiro-monoansa spirane derivatives, (2c) and (2d), are meso diastereoisomers, which represent a new case of the stereochemistry of bis di-substituted cyclophosphazene derivatives of (1). It is also observed from the 31P NMR spectrum of the reaction mixture, supported by the yields of pure compounds, that formation of a spiro group is about 4.5 times more likely than that of an ansa moiety under the conditions of the reaction

Monolithic integration of a quantum emitter with a compact on-chip beam-splitter

A fundamental component of an integrated quantum optical circuit is an on-chip beam-splitter operating at the single-photon level. Here, we demonstrate the monolithic integration of an on-demand quantum emitter in the form of a single self-assembled InGaAs quantum dot (QD) with a compact (>10 μm), air clad, free standing directional coupler acting as a beam-splitter for anti-bunched light. The device was tested by using single photons emitted by a QD embedded in one of the input arms of the device. We verified the single-photon nature of the QD signal by performing Hanbury Brown-Twiss measurements and demonstrated single-photon beam splitting by cross-correlating the signal from the separate output ports of the directional coupler

Path-dependent initialization of a single quantum dot exciton spin in a nanophotonic waveguide

We demonstrate a scheme for in-plane initialization of a single exciton spin in an InGaAs quantum dot (QD) coupled to a GaAs nanobeam waveguide. The chiral coupling of the QD and the optical mode of the nanobeam enables spin initialization fidelity approaching unity in magnetic field B=1 T and >0.9 without the field. We further show that this in-plane excitation scheme is independent of the incident excitation laser polarization and depends solely on the excitation direction. This scheme provides a robust in-plane spin excitation basis for a photon-mediated spin network for quantum information applications

On-chip resonantly-driven quantum emitter with enhanced coherence

Advances in nanotechnology provide techniques for the realisation of integrated quantum-optical circuits for on-chip quantum information processing(QIP). The indistinguishable single photons, required for such devices can be generated by parametric down-conversion, or from quantum emitters such as colour centres and quantum dots(QDs). Among these, semiconductor QDs offer distinctive capabilities including on-demand operation, coherent control, frequency tuning and compatibility with semiconductor nanotechnology. Moreover, the coherence of QD photons can be significantly enhanced in resonance fluorescence(RF) approaching at its best the coherence of the excitation laser. However, the implementation of QD RF in scalable on-chip geometries remains challenging due to the need to suppress stray laser photons. Here we report on-chip QD RF coupled into a single-mode waveguide with negligible resonant laser background and show that the coherence is enhanced compared to off-resonant excitation. The results pave the way to a novel class of integrated quantum-optical devices for on-chip QIP with embedded resonantly-driven quantum emitters

On-chip resonantly-driven quantum emitter with enhanced coherence

Advances in nanotechnology provide techniques for the realisation of integrated quantum-optical circuits for on-chip quantum information processing(QIP). The indistinguishable single photons, required for such devices can be generated by parametric down-conversion, or from quantum emitters such as colour centres and quantum dots(QDs). Among these, semiconductor QDs offer distinctive capabilities including on-demand operation, coherent control, frequency tuning and compatibility with semiconductor nanotechnology. Moreover, the coherence of QD photons can be significantly enhanced in resonance fluorescence(RF) approaching at its best the coherence of the excitation laser. However, the implementation of QD RF in scalable on-chip geometries remains challenging due to the need to suppress stray laser photons. Here we report on-chip QD RF coupled into a single-mode waveguide with negligible resonant laser background and show that the coherence is enhanced compared to off-resonant excitation. The results pave the way to a novel class of integrated quantum-optical devices for on-chip QIP with embedded resonantly-driven quantum emitters

Genus Topology of the Cosmic Microwave Background from WMAP

We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen by the Wilkinson Microwave Anisotropy Probe (WMAP). A genus analysis of the WMAP data indicates consistency with Gaussian random-phase initial conditions, as predicted by standard inflation.Comment: PDF: http://www.astro.virginia.edu/~wnc5c/WMAPtopology.pd

Single-photon electroluminescence for on-chip quantum networks

An electrically driven single-photon source has been monolithically integrated with nano-photonic circuitry. Electroluminescent emission from a single InAs/GaAs quantum dot (QD) is channelled through a suspended nanobeam waveguide. The emission line has a linewidth of below 6 μeV, demonstrating the ability to have a high coherence, electrically driven, waveguide coupled QD source. The single-photon nature of the emission is verified by g(2) (τ) correlation measurements. Moreover, in a cross-correlation experiment, with emission collected from the two ends of the waveguide, the emission and propagation of single photons from the same QD is confirmed. This work provides the basis for the development of electrically driven on-chip single-photon sources, which can be readily coupled to waveguide filters, directional couplers, phase shifters, and other elements of quantum photonic networks

Roles of Fast-Cyclotron and Alfven-Cyclotron Waves for the Multi-Ion Solar Wind

Using linear Vlasov theory of plasma waves and quasi-linear theory of resonant wave-particle interaction, the dispersion relations and the electromagnetic field fluctuations of fast and Alfven waves are studied for a low-beta multi-ion plasma in the inner corona. Their probable roles in heating and accelerating the solar wind via Landau and cyclotron resonances are quantified. We assume that (1) low-frequency Alfven and fast waves have the same spectral shape and the same amplitude of power spectral density; (2) these waves eventually reach ion cyclotron frequencies due to a turbulence cascade; (3) kinetic wave-particle interaction powers the solar wind. The existence of alpha particles in a dominant proton/electron plasma can trigger linear mode conversion between oblique fast-whistler and hybrid alpha-proton cyclotron waves. The fast-cyclotron waves undergo both alpha and proton cyclotron resonances. The alpha cyclotron resonance in fast-cyclotron waves is much stronger than that in Alfven-cyclotron waves. For alpha cyclotron resonance, an oblique fast-cyclotron wave has a larger left-handed electric field fluctuation, a smaller wave number, a larger local wave amplitude, and a greater energization capability than a corresponding Alfven-cyclotron wave at the same wave propagation angle \theta, particularly at $80^\circ$ < \theta < $90^\circ$. When Alfven-cyclotron or fast-cyclotron waves are present, alpha particles are the chief energy recipient. The transition of preferential energization from alpha particles to protons may be self-modulated by differential speed and temperature anisotropy of alpha particles via the self-consistently evolving wave-particle interaction. Therefore, fast-cyclotron waves as a result of linear mode coupling is a potentially important mechanism for preferential energization of minor ions in the main acceleration region of the solar wind.Comment: 29 pages, 10 figures, 3 tables. Accepted for publication in Solar Physic