Figure of Merit for Dark Energy Constraints from Current Observational Data

Choosing the appropriate figure of merit (FoM) for dark energy (DE) constraints is key in comparing different DE experiments. Here we show that for a set of DE parameters {f_i}, it is most intuitive to define FoM = 1/\sqrt{Cov(f1,f2,f3,...)}, where Cov(f1,f2,f3,...) is the covariance matrix of {f_i}. The {f_i} should be minimally correlated. We demonstrate two useful choices of {f_i} using 182 SNe Ia (compiled by Riess et al. 2007), [R(z_*), l_a(z_*), \Omega_b h^2] from the five year Wilkinson Microwave Anisotropy Probe (WMAP) observations, and SDSS measurement of the baryon acoustic oscillation (BAO) scale, assuming the HST prior of H_0=72+/-8 km/s Mpc^{-1} and without assuming spatial flatness. We find that the correlation of (w_0,w_{0.5}) [w_0=w_X(z=0), w_{0.5}=w_X(z=0.5), w_X(a) = 3w_{0.5}-2w_0+3(w_0-w_{0.5})a] is significantly smaller than that of (w_0,w_a) [w_X(a)=w_0+(1-a)w_a]. In order to obtain model-independent constraints on DE, we parametrize the DE density function X(z)=\rho_X(z)/\rho_X(0) as a free function with X_{0.5}, X_{1.0}, and X_{1.5} [values of X(z) at z=0.5, 1.0, and 1.5] as free parameters estimated from data. If one assumes a linear DE equation of state, current data are consistent with a cosmological constant at 68% C.L. If one assumes X(z) to be a free function parametrized by (X_{0.5}, X_{1.0}, X_{1.5}), current data deviate from a cosmological constant at z=1 at 68% C.L., but are consistent with a cosmological constant at 95% C.L.. Future DE experiments will allow us to dramatically increase the FoM of constraints on (w_0,w_{0.5}) and of (X_{0.5}, X_{1.0}, X_{1.5}). This will significantly shrink the DE parameter space to enable the discovery of DE evolution, or the conclusive evidence for a cosmological constant.Comment: 7 pages, 3 color figures. Submitte

Model-Independent Distance Measurements from Gamma-Ray Bursts and Constraints on Dark Energy

Gamma-Ray Bursts (GRB) are the most energetic events in the Universe, and provide a complementary probe of dark energy by allowing the measurement of cosmic expansion history that extends to redshifts greater than 6. Unlike Type Ia supernovae (SNe Ia), GRBs must be calibrated for each cosmological model considered, because of the lack of a nearby sample of GRBs for model-independent calibration. For a flat Universe with a cosmological constant, we find Omega_m=0.25^{+0.12}_{-0.11} from 69 GRBs alone. We show that the current GRB data can be summarized by a set of model-independent distance measurements, with negligible loss of information. We constrain a dark energy equation of state linear in the cosmic scale factor using these distance measurements from GRBs, together with the "Union" compilation of SNe Ia, WMAP five year observations, and the SDSS baryon acoustic oscillation scale measurement. We find that a cosmological constant is consistent with current data at 68% confidence level for a flat Universe. Our results provide a simple and robust method to incorporate GRB data in a joint analysis of cosmological data to constrain dark energy.Comment: 8 pages, 5 color figures. Version expanded and revised for clarification, and typo in Eqs.(3)(4)(12) corrected. PRD, in pres

Three-Way Entanglement and Three-Qubit Phase Gate Based on a Coherent Six-Level Atomic System

We analyze the nonlinear optical response of a six-level atomic system under a configuration of electromagnetically induced transparency. The giant fifth-order nonlinearity generated in such a system with a relatively large cross-phase modulation effect can produce efficient three-way entanglement and may be used for realizing a three-qubit quantum phase gate. We demonstrate that such phase gate can be transferred to a Toffoli gate, facilitating practical applications in quantum information and computation.Comment: 10 pages, 2 figure

The UNAM-KIAS Catalog of Isolated Galaxies

A new catalog of isolated galaxies from The Sloan Digital Sky Survey (DR5) is presented. 1520 isolated galaxies were found in 1.4 steradians of sky. The selection criteria in this so called UNAM-KIAS catalog was implemented from a variation on the criteria developed by Karachentseva 1973 including full redshift information. Through an image processing pipeline that takes advantage from the high resolution (~ 0.4 ''/pix) and high dynamic range of the SDSS images, a uniform g band morphological classification for all these galaxies is presented. We identify 80% (SaSm) spirals (50% later than Sbc types) on one hand, and a scarce population of early-type E(6.5%) and S0(8%) galaxies amounting to 14.5% on the other hand. This magnitude-limited catalog is ~ 80% complete at 16.5, 15.6, 15.0, 14.6 and 14.4 magnitudes in the ugriz bands respectively. Some representative physical properties including SDSS magnitudes and color distributions, color-color diagrams, absolute magnitude-color, and concentration-color diagrams as a function of morphological type are presented. The UNAM-KIAS Morphological Atlas is also released along with this paper. For each galaxy of type later than Sa, a mosaic is presented that includes: (1) a g-band logarithmic image, (2) a g band filtered-enhanced image where a Gaussian kernel of various sizes was applied and (3) an RGB color image from the SDSS database. For E/S0/Sa galaxies, in addition to the images in (1), (2) and (3), plots of r band surface brightness and geometric profiles (ellipticity, Position Angle PA and A4/B4 coefficients of the Fourier series expansions of deviations of a pure ellipse) are provided...Comment: 40 pages, 17 figures and 3 table

The UNAM-KIAS Catalog of Isolated Galaxies

A new catalog of isolated galaxies from The Sloan Digital Sky Survey (DR5) is presented. 1520 isolated galaxies were found in 1.4 steradians of sky. The selection criteria in this so called UNAM-KIAS catalog was implemented from a variation on the criteria developed by Karachentseva 1973 including full redshift information. Through an image processing pipeline that takes advantage from the high resolution (~ 0.4 ''/pix) and high dynamic range of the SDSS images, a uniform g band morphological classification for all these galaxies is presented. We identify 80% (SaSm) spirals (50% later than Sbc types) on one hand, and a scarce population of early-type E(6.5%) and S0(8%) galaxies amounting to 14.5% on the other hand. This magnitude-limited catalog is ~ 80% complete at 16.5, 15.6, 15.0, 14.6 and 14.4 magnitudes in the ugriz bands respectively. Some representative physical properties including SDSS magnitudes and color distributions, color-color diagrams, absolute magnitude-color, and concentration-color diagrams as a function of morphological type are presented. The UNAM-KIAS Morphological Atlas is also released along with this paper. For each galaxy of type later than Sa, a mosaic is presented that includes: (1) a g-band logarithmic image, (2) a g band filtered-enhanced image where a Gaussian kernel of various sizes was applied and (3) an RGB color image from the SDSS database. For E/S0/Sa galaxies, in addition to the images in (1), (2) and (3), plots of r band surface brightness and geometric profiles (ellipticity, Position Angle PA and A4/B4 coefficients of the Fourier series expansions of deviations of a pure ellipse) are provided...Comment: 40 pages, 17 figures and 3 table

Uncorrelated Measurements of the Cosmic Expansion History and Dark Energy from Supernovae

We present a method for measuring the cosmic expansion history H(z) in uncorrelated redshift bins, and apply it to current and simulated type Ia supernova data assuming spatial flatness. If the matter density parameter Omega_m can be accurately measured from other data, then the dark energy density history X(z)=rho_X(z)/rho_X(0) can trivially be derived from this expansion history H(z). In contrast to customary ``black box'' parameter fitting, our method is transparent and easy to interpret: the measurement of H(z)^{-1} in a redshift bin is simply a linear combination of the measured comoving distances for supernovae in that bin, making it obvious how systematic errors propagate from input to output. We find the Riess et al. (2004) ``gold'' sample to be consistent with the ``vanilla'' concordance model where the dark energy is a cosmological constant. We compare two mission concepts for the NASA/DOE Joint Dark Energy Mission (JDEM), the Joint Efficient Dark-energy Investigation (JEDI), and the Supernova Accelaration Probe (SNAP), using simulated data including the effect of weak lensing (based on numerical simulations) and a systematic bias from K-corrections. Estimating H(z) in seven uncorrelated redshift bins, we find that both provide dramatic improvements over current data: JEDI can measure H(z) to about 10% accuracy and SNAP to 30-40% accuracy.Comment: 7 pages, 4 color figures. Expanded and revised version; PRD in pres

Discovery of Molecular Gas in the Outflow and Tidal Arms around M82

We present the first fully sampled map of 12CO (1-0) emission from M82 covering the entire galaxy. Our map contains a 12 x 15 kpc^2 area. We find that extraplanar CO emission, previously reported at short distances above the galactic plane, extends to heights of up to 6 kpc above the disk. Some of this emission is associated with tidal arms seen in HI, implying either that M82 contained substantial amounts of molecular gas in the outer disk, or that molecular gas formed after the tidal features. CO emission along the direction of the outflow extends to distances of 3 kpc above and below the disk. At this distance, the line is shifted in velocity about 100 km/s, and has the same sense as the galactic outflow from the central starburst. This implies that molecular gas may be entrained into the outflow.Comment: 4 pages, 6 figures. Uses emulateapj5. Accepted by ApJ Letter

Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

Wavelength-swept Tm-doped fiber laser operating in the two-micron wavelength band

A wavelength-swept thulium-doped silica fiber laser using an intracavity rotating slotted-disk wavelength scanning filter in combination with an intracavity solid etalon for passive control of temporal and spectral profiles is reported. The laser yielded a wavelength swept output in a step-wise fashion with each laser pulse separated from the previous pulse by a frequency interval equal to the free-spectral-range of the etalon and with an instantaneous linewidth of <0.05 nm. Scanning ranges from 1905 nm to 2049 nm for a cladding-pumping laser configuration, and from 1768 nm to 1956 nm for a core-pumping laser configuration were achieved at average output powers up to ~1 W