Measurements Of Correlation Function Research Articles

LyaCoLoRe: synthetic datasets for current and future Lyman-α forest BAO surveys

The statistical power of Lyman-α forest Baryon Acoustic Oscillation (BAO) measurements is set to increase significantly in the coming years as new instruments such as the Dark Energy Spectroscopic Instrument deliver progressively more constraining data. Generating mock datasets for such measurements will be important for validating analysis pipelines and evaluating the effects of systematics. With such studies in mind, we present LyaCoLoRe: a package for producing synthetic Lyman-α forest survey datasets for BAO analyses. LyaCoLoRe transforms initial Gaussian random field skewers into skewers of transmitted flux fraction via a number of fast approximations. In this work we explain the methods of producing mock datasets used in LyaCoLoRe, and then measure correlation functions on a suite of realisations of such data. We demonstrate that we are able to recover the correct BAO signal, as well as large-scale bias parameters similar to literature values. Finally, we briefly describe methods to add further astrophysical effects to our skewers—high column density systems and metal absorbers—which act as potential complications for BAO analyses.

Departing from Thermality of Analogue Hawking Radiation in a Bose-Einstein Condensate.

We study the quantum fluctuations in a one-dimensional Bose-Einstein condensate realizing an analogous acoustic black hole. The taking into account of evanescent channels and of zero modes makes it possible to accurately reproduce recent experimental measurements of the density correlation function. We discuss the determination of Hawking temperature and show that in our model the analogous radiation presents some significant departure from thermality.

Angular Correlation Function Estimators Accounting for Contamination from Probabilistic Distance Measurements

Abstract With the advent of surveys containing millions to billions of galaxies, it is imperative to develop analysis techniques that utilize the available statistical power. In galaxy clustering, even small sample contamination arising from distance uncertainties can lead to large artifacts, which the standard estimator for two-point correlation functions does not account for. We first introduce a formalism, termed decontamination, that corrects for sample contamination by utilizing the observed cross-correlations in the contaminated samples; this corrects any correlation function estimator for contamination. Using this formalism, we present a new estimator that uses the standard estimator to measure correlation functions in the contaminated samples but then corrects for contamination. We also introduce a weighted estimator that assigns each galaxy a weight in each redshift bin based on its probability of being in that bin. We demonstrate that these estimators effectively recover the true correlation functions and their covariance matrices. Our estimators can correct for sample contamination caused by misclassification between object types as well as photometric redshifts; they should be particularly helpful for studies of galaxy evolution and baryonic acoustic oscillations, where forward modeling the clustering signal using the contaminated redshift distribution is undesirable.

Cosmological constraints from cosmic shear two-point correlation functions with HSC survey first-year data

Abstract We present measurements of cosmic shear two-point correlation functions (TPCFs) from Hyper Suprime-Cam Subaru Strategic Program (HSC) first-year data, and derive cosmological constraints based on a blind analysis. The HSC first-year shape catalog is divided into four tomographic redshift bins ranging from $z=0.3$ to 1.5 with equal widths of $\Delta z =0.3$. The unweighted galaxy number densities in each tomographic bin are 5.9, 5.9, 4.3, and $2.4\:$arcmin$^{-2}$ from the lowest to highest redshifts, respectively. We adopt the standard TPCF estimators, $\xi _\pm$, for our cosmological analysis, given that we find no evidence of significant B-mode shear. The TPCFs are detected at high significance for all 10 combinations of auto- and cross-tomographic bins over a wide angular range, yielding a total signal-to-noise ratio of 19 in the angular ranges adopted in the cosmological analysis, $7^{\prime }<\theta <56^{\prime }$ for $\xi _+$ and $28^{\prime }<\theta <178^{\prime }$ for $\xi _-$. We perform the standard Bayesian likelihood analysis for cosmological inference from the measured cosmic shear TPCFs, including contributions from intrinsic alignment of galaxies as well as systematic effects from PSF model errors, shear calibration uncertainty, and source redshift distribution errors. We adopt a covariance matrix derived from realistic mock catalogs constructed from full-sky gravitational lensing simulations that fully account for survey geometry and measurement noise. For a flat $\Lambda$ cold dark matter model, we find $S\,_8 \equiv \sigma _8\sqrt{\Omega _{\rm m}/0.3}=0.804_{-0.029}^{+0.032}$, and $\Omega _{\rm m}=0.346_{-0.100}^{+0.052}$. We carefully check the robustness of the cosmological results against astrophysical modeling uncertainties and systematic uncertainties in measurements, and find that none of them has a significant impact on the cosmological constraints.

Higher order correlations in a levitated nanoparticle phonon laser.

We present theoretical and experimental investigations of higher order correlations of mechanical motion in the recently demonstrated optical tweezer phonon laser, consisting of a silica nanosphere trapped in vacuum by a tightly focused optical beam [R. M. Pettit et al., Nature Photonics 13, 402 (2019)]. The nanoparticle phonon number probability distribution is modeled with the master equation formalism in order to study its evolution across the lasing threshold. Up to fourth-order equal-time correlation functions are then derived from the probability distribution. Subsequently, the master equation is transformed into a nonlinear quantum Langevin equation for the trapped particle's position. This equation yields the non-equal-time correlations, also up to fourth order. Finally, we present experimental measurements of the phononic correlation functions, which are in good agreement with our theoretical predictions. We also compare the experimental data to existing analytical Ginzburg-Landau theory where we find only a partial match.

Photon propagation through dissipative Rydberg media at large input rates.

We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency. Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.

Photon-pair characterization using one single-photon detector by time multiplexing

We experimentally demonstrate coincidence measurements as well as g (2) ( nτ ) correlation function measurements with only one single-photon detector (SPD) with the aid of field-programmable gate array and 2 × 2 fast optical switches. Both experiments produced similar results compared to conventional experimental methods, requiring more than one SPD. When detecting correlations between multiple single photons, this technique can be employed to reduce demands for the number of SPDs and potentially would be able to offer new options to researchers and institutions requiring coincidence measurement systems with lower complexity as well as smaller form factors.

Quantum noise radar: superresolution with quantum antennas by accessing spatiotemporal correlations.

We suggest overcoming the "Rayleigh catastrophe" and reaching superresolution for imaging with both spatially and temporally correlated field of a superradiant quantum antenna. Considering far-field radiation of two interacting spontaneously emitting two-level systems, we show that for the measurement of the temporally delayed second-order correlation function of the scattered field, the Fisher information does not tend to zero with diminishing the distance between a pair of scatterers even for non-sharp time-averaged detection. For position estimation of more scatterers, the measurement of the time-delayed function is able to provide a considerable accuracy gain over the zero-delayed function. We also show that the superresolution with the considered quantum antenna can be achieved for both near-field imaging and for estimating the antenna parameters.

First Observation of an Attractive Interaction between a Proton and a Cascade Baryon.

This Letter presents the first experimental observation of the attractive strong interaction between a proton and a multistrange baryon (hyperon) Ξ^{-}. The result is extracted from two-particle correlations of combined p-Ξ^{-}⊕p[over ¯]-Ξ[over ¯]^{+} pairs measured in p-Pb collisions at sqrt[s_{NN}]=5.02 TeV at the LHC with ALICE. The measured correlation function is compared with the prediction obtained assuming only an attractive Coulomb interaction and a standard deviation in the range [3.6, 5.3] is found. Since the measured p-Ξ^{-}⊕p[over ¯]-Ξ[over ¯]^{+} correlation is significantly enhanced with respect to the Coulomb prediction, the presence of an additional, strong, attractive interaction is evident. The data are compatible with recent lattice calculations by the HAL-QCD Collaboration, with a standard deviation in the range [1.8, 3.7]. The lattice potential predicts a shallow repulsive Ξ^{-} interaction within pure neutron matter and this implies stiffer equations of state for neutron-rich matter including hyperons. Implications of the strong interaction for the modeling of neutron stars are discussed.

Effective second-order correlation function and single-photon detection

Quantum-optical research on semiconductor single-photon sources puts special emphasis on the measurement of the second-order correlation function g(2)(τ), arguing that g(2)(0) < 1/2 implies the source field represents a good single-photon light source. We analyze the gain of information from g(2)(0) with respect to single photons. Any quantum state, for which the second-order correlation function falls below 1/2, has a nonzero projection on the single-photon Fock state. The amplitude p of this projection is arbitrary, independent of g(2)(0). However, one can extract a lower bound on the single-to-multi-photon-projection ratio. A vacuum contribution in the quantum state of light artificially increases the value of g(2)(0), cloaking actual single-photon projection. Thus, we propose an effective second-order correlation function , which takes the influence of vacuum into account and also yields lower and upper bounds on p. We consider the single-photon purity as a standard figure of merit in experiments, reinterpret it within our results and provide an effective version of that physical quantity. Besides comparing different experimental and theoretical results, we also provide a possible measurement scheme for determining .

Dark Energy Survey Year 1 Results: Cross-correlation between Dark Energy Survey Y1 galaxy weak lensing and South Pole Telescope +Planck CMB weak lensing

We cross-correlate galaxy weak lensing measurements from the Dark Energy Survey (DES) year-one (Y1) data with a cosmic microwave background (CMB) weak lensing map derived from South Pole Telescope (SPT) and Planck data, with an effective overlapping area of 1289 deg$^{2}$. With the combined measurements from four source galaxy redshift bins, we reject the hypothesis of no lensing with a significance of $10.8\sigma$. When employing angular scale cuts, this significance is reduced to $6.8\sigma$, which remains the highest signal-to-noise measurement of its kind to date. We fit the amplitude of the correlation functions while fixing the cosmological parameters to a fiducial $\Lambda$CDM model, finding $A = 0.99 \pm 0.17$. We additionally use the correlation function measurements to constrain shear calibration bias, obtaining constraints that are consistent with previous DES analyses. Finally, when performing a cosmological analysis under the $\Lambda$CDM model, we obtain the marginalized constraints of $\Omega_{\rm m}=0.261^{+0.070}_{-0.051}$ and $S_{8}\equiv \sigma_{8}\sqrt{\Omega_{\rm m}/0.3} = 0.660^{+0.085}_{-0.100}$. These measurements are used in a companion work that presents cosmological constraints from the joint analysis of two-point functions among galaxies, galaxy shears, and CMB lensing using DES, SPT and Planck data.

Dark Energy Survey year 1 results: Joint analysis of galaxy clustering, galaxy lensing, and CMB lensing two-point functions

We perform a joint analysis of the auto and cross-correlations between three cosmic fields: the galaxy density field, the galaxy weak lensing shear field, and the cosmic microwave background (CMB) weak lensing convergence field. These three fields are measured using roughly 1300 sq. deg. of overlapping optical imaging data from first year observations of the Dark Energy Survey and millimeter-wave observations of the CMB from both the South Pole Telescope Sunyaev-Zel'dovich survey and Planck. We present cosmological constraints from the joint analysis of the two-point correlation functions between galaxy density and galaxy shear with CMB lensing. We test for consistency between these measurements and the DES-only two-point function measurements, finding no evidence for inconsistency in the context of flat $\Lambda$CDM cosmological models. Performing a joint analysis of five of the possible correlation functions between these fields (excluding only the CMB lensing autospectrum) yields $S_{8}\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3} = 0.782^{+0.019}_{-0.025}$ and $\Omega_{\rm m}=0.260^{+0.029}_{-0.019}$. We test for consistency between these five correlation function measurements and the Planck-only measurement of the CMB lensing autospectrum, again finding no evidence for inconsistency in the context of flat $\Lambda$CDM models. Combining constraints from all six two-point functions yields $S_{8}=0.776^{+0.014}_{-0.021}$ and $\Omega_{\rm m}= 0.271^{+0.022}_{-0.016}$. These results provide a powerful test and confirmation of the results from the first year DES joint-probes analysis.

Efficient demultiplexed single-photon source with a quantum dot coupled to a nanophotonic waveguide

Planar nanostructures allow near-ideal extraction of emission from a quantum emitter embedded within, thereby realizing deterministic single-photon sources. Such a source can be transformed into M single-photon sources by implementing active temporal-to-spatial mode demultiplexing. We report on the realization of such a demultiplexed source based on a quantum dot embedded in a nanophotonic waveguide. Efficient outcoupling (&amp;gt;60%) from the waveguide into a single mode optical fiber is obtained with high-efficiency grating couplers. As a proof-of-concept, active demultiplexing into M = 4 spatial channels is demonstrated by the use of electro-optic modulators with an end-to-end efficiency of &amp;gt;81% into single-mode fibers. Overall, we demonstrate four-photon coincidence rates of &amp;gt;1 Hz even under nonresonant excitation of the quantum dot. The main limitation of the current source is the residual population of other exciton transitions, which corresponds to a finite preparation efficiency of the desired transition. We quantitatively extract a preparation efficiency of 15% using the second-order correlation function measurements. The experiment highlights the applicability of planar nanostructures as efficient multiphoton sources through temporal-to-spatial demultiplexing and lays out a clear path way of how to scale up toward demonstrating quantum advantages with the quantum dot sources.

Magnetic monopole noise.

Magnetic monopoles1-3 are hypothetical elementary particles with quantized magnetic charge. In principle, a magnetic monopole can be detected by the quantized jump in magnetic flux that it generates upon passage through a superconducting quantum interference device (SQUID)4. Following the theoretical prediction that emergent magnetic monopoles should exist in several lanthanide pyrochlore magnetic insulators5,6, including Dy2Ti2O7, the SQUID technique has been proposed for their direct detection6. However, this approach has been hindered by the high number density and the generation-recombination fluctuations expected of such thermally generated monopoles. Recently, theoretical advances have enabled the prediction of the spectral density of magnetic-flux noise from monopole generation-recombination fluctuations in these materials7,8. Here we report the development of a SQUID-based flux noise spectrometer and measurements of the frequency and temperature dependence of magnetic-flux noise generated by Dy2Ti2O7 crystals. We detect almost all of the features of magnetic-flux noise predicted for magnetic monopole plasmas7,8, including the existence of intense magnetization noise and its characteristic frequency and temperature dependence. Moreover, comparisons of simulated and measured correlation functions of the magnetic-flux noise indicate that the motions of magnetic charges are strongly correlated. Intriguingly, because the generation-recombination time constant for Dy2Ti2O7 is in the millisecond range, magnetic monopole flux noise amplified by SQUID is audible to humans.

Relaxation dynamics induced in glasses by absorption of hard x-ray photons

X-ray photon correlation is used to probe the slow dynamics of the glass-former B2O3 across the glass transition. In the undercooled liquid phase the decay times of the measured correlation functions are consistent with visible light scattering results and independent of the incoming flux; in the glass they are instead temperature independent and show a definite dependence on the X-ray flux. This dependence can be exploited to obtain information on the volume occupied by the atoms that move in the glass following an absorption event. The length scale derived in this way, of the order of the nanometer, is consistent with that reported for the dynamical heterogeneities, suggesting the existence of a new scheme to get access to this fundamental quantity.

Graph Database Solution for Higher-order Spatial Statistics in the Era of Big Data

Abstract We present an algorithm for the fast computation of the general N-point spatial correlation functions of any discrete point set embedded within an Euclidean space of . Utilizing the concepts of kd-trees and graph databases, we describe how to count all possible N-tuples in binned configurations within a given length scale, e.g., all pairs of points or all triplets of points with side lengths &lt; r MAX. Through benchmarking, we show the computational advantage of our new graph-based algorithm over more traditional methods. We show measurements of the three-point correlation function up to scales of ∼200 Mpc (beyond the baryon acoustic oscillation scale in physical units) using current Sloan Digital Sky Survey (SDSS) data. Finally, we present a preliminary exploration of the small-scale four-point correlation function of 568,776 SDSS Constant (stellar) Mass (CMASS) galaxies in the northern Galactic cap over the redshift range of 0.43 &lt; z &lt; 0.7. We present the publicly available code GRAMSCI (GRAph Made Statistics for Cosmological Information; bitbucket.org/csabiu/gramsci), under a Gnu is Not Unix (GNU) General Public License.

Broadband quantum light on a fiber-optic platform: from biphotons and heralded single photons to bright squeezed vacuum

Four-wave mixing (FWM) of ultrashort laser pulses in a highly nonlinear photonic-crystal fiber is shown to provide a multimodal source of broadband quantum states of light. In the regime of low pump powers, generation of two-photon states and heralded single photons with a bandwidth up to ≈6 THz is demonstrated within an FWM-sideband tunability range of ≈55 THz. In the modality of heralded single-photon generation, three-detector measurements of the conditional second-order correlation function reveal a strong antibunching in the signal-photon channel, with more than 99.2% of the signal counts identified as truly single-photon states. At high pump powers, two-detector signal-idler correlation function measurements indicate broadband bright squeezed vacuum generation.

Diffusional Dynamics of Tetraalkylphosphonium Ionic Liquid Films Measured by Fluorescence Correlation Spectroscopy.

Fluorescence correlation spectroscopy (FCS) is applied to investigate the diffusional dynamics of hydrophilic (Atto 590) and amphiphilic (DiD) fluorophores in a series of alkylphosphonium ionic liquid (IL) films ([P4448][Cl], [P6668][Cl], [P66614][Cl], and [P66614][NTf2]) in order to determine diffusional parameters and to elucidate nanoscale structural heterogeneities within the IL. From the measured correlation functions, the diffusion coefficients of the fluorescent molecules are estimated, rendering values that span from 0.39 to 1.2 and 0.146 to 5.2 μm2/s for Atto 590 and DiD, respectively. An increase in the diffusion coefficient values is correlated to the increase in the alkyl chain length, which in turn is correlated with a decrease in their viscosity. Interestingly, deviations from Brownian diffusion behavior of the fluorescent probes in the ILs are observed, showing a time-dependent diffusion coefficient in most of the cases. These deviations can be attributed to the presence of nanoscale structural heterogeneities in the tetraalkylphosphonium ILs. These results experimentally confirm the presence of nanosegregation in tetraalkylphosphonium ILs, which has been previously observed in molecular dynamics studies.

Cosmological forecasts from photometric measurements of the angular correlation function for the Legacy Survey of Space and Time

AbstractWe aim to do forecasts for the Legacy Survey of Space and Time (LSST) with a theoretical modeling of the two point angular correlation function. The Fisher matrix is the starting point. This is a square matrix over the cosmological parameters, whose diagonal contains direct informations on the parameters expected uncertainties.

Measurement of marked correlation functions in SDSS-III Baryon Oscillation Spectroscopic Survey using LOWZ galaxies in Data Release 12

Marked correlation functions, which are sensitive to the clustering of galaxies in different environments, have been proposed as constraints on modified gravity models. We present measurements of the marked correlation functions of galaxies in redshift space using 361,761 LOWZ ($z_{\rm eff} = 0.32$) galaxies from the Sloan Digital Sky Survey III (SDSS III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) and compare them to $\Lambda$CDM+General Relativity simulations. We apply mass cuts to find the best match between the redshift space autocorrelation function of subhaloes in the simulation and in the observations. We then compare the marked correlation functions, finding no significant evidence for deviations of the marked correlation functions of LOWZ galaxies from $\Lambda$CDM on scales $6 \ h^{-1}$Mpc $ \leq s \leq$ $69 \ h^{-1}$Mpc. The constraining power of marked correlation functions in our analysis is limited by our ability to model the autocorrelation function of galaxies on small scales including the effect of redshift distortions. The statistical errors are well below the differences seen between marked correlation functions of $f$(R) gravity models and $\Lambda$CDM in recent publications (Armijo et al., Hern\'{a}ndez-Aguayo et al.) indicating that improved future theoretical analyses should be able to rule out some models definitively.