Shot Noise Contribution Research Articles

Shot noise and biased tracers: A new look at the halo model

Shot noise is an important ingredient to any measurement or theoretical modeling of discrete tracers of the large scale structure. Recent work has shown that the shot noise in the halo power spectrum becomes increasingly sub-Poissonian at high mass. Interestingly, while the halo model predicts a shot noise power spectrum in qualitative agreement with the data, it leads to an unphysical white noise in the cross halo-matter and matter power spectrum. In this work, we show that absorbing all the halo model sources of shot noise into the halo fluctuation field leads to meaningful predictions for the shot noise contributions to halo clustering statistics and remove the unphysical white noise from the cross halo-matter statistics. Our prescription straightforwardly maps onto the general bias expansion, so that the renormalized shot noise terms can be expressed as combinations of the halo model shot noises. Furthermore, we demonstrate that non-Poissonian contributions are related to volume integrals over correlation functions and their response to long-wavelength density perturbations. This leads to a new class of consistency relations for discrete tracers, which appear to be satisfied by our reformulation of the halo model. We test our theoretical predictions against measurements of halo shot noise bispectra extracted from a large suite of numerical simulations. Our model reproduces qualitatively the observed sub-Poissonian noise, although it underestimates the magnitude of this effect.

Josephson radiation and shot noise of a semiconductor nanowire junction

We measured the Josephson radiation emitted by an InSb semiconductor nanowire junction utilizing photon assisted quasiparticle tunneling in an AC-coupled superconducting tunnel junction. We quantify the action of the local microwave environment by evaluating the frequency dependence of the inelastic Cooper-pair tunneling of the nanowire junction and find the zero frequency impedance $Z(0)=492\,\Omega$ with a cutoff frequency of $f_0=33.1\,$GHz. We extract a circuit coupling efficiency of $\eta\approx 0.1$ and a detector quantum efficiency approaching unity in the high frequency limit. In addition to the Josephson radiation, we identify a shot-noise contribution with a Fano factor $F\approx1$, consistently with the presence of single electron states in the nanowire channel.

Assessment of the information content of the power spectrum and bispectrum

The covariance matrix of the matter and halo power spectrum and bispectrum are studied. Using a large suite of simulations, we find that the non-Gaussianity in the covariance is significant already at mildly nonlinear scales. We compute the leading disconnected non-Gaussian correction to the matter bispectrum covariance using perturbation theory, and find that the corrections result in good agreement in the mildly nonlinear regime. The shot noise contribution to the halo power spectrum and bispectrum covariance is computed using the Poisson model, and the model yields decent agreement with simulation results. However, when the shot noise is estimated from the individual realization, which is usually done in reality, we find that the halo covariance is substantially reduced and gets close to the Gaussian covariance. This is because most of the non-Gaussianity in the covariance arises from the fluctuations in the Poisson shot noise. We use the measured non-Gaussian covariance to access the information content of the power spectrum and bispectrum. The signal-to-noise ratio, S/N, of the matter and halo power spectrum levels off in the mildly nonlinear regime, $k \sim 0.1 - 0.2 \,\mathrm{Mpc} h^{-1}$. In the nonlinear regime the S/N of the matter and halo bispectrum increases but much slower than the Gaussian results suggest. We find that both the S/N for power spectrum and bispectrum are overestimated by the Gaussian covariances, but the problem being much more serious for the bispectrum. Because the bispectrum is affected strongly by nonlinearity and shot noise, inclusion of the bispectrum only adds modest amount of S/N compared to that of the power spectrum.

Cross-correlation of galaxies and galaxy clusters in the Sloan Digital Sky Survey and the importance of non-Poissonian shot noise

We present measurements of angular cross power spectra between galaxies and optically-selected galaxy clusters in the final photometric sample of the Sloan Digital Sky Survey (SDSS). We measure the auto- and cross-correlations between galaxy and cluster samples, from which we extract the effective biases and study the shot noise properties. We model the non-Poissonian shot noise by introducing an effective number density of tracers and fit for this quantity. We find that we can only describe the cross-correlation of galaxies and galaxy clusters, as well as the auto-correlation of galaxy clusters, on the relevant scales using a non-Poissonian shot noise contribution. The values of effective bias we finally measure for a volume-limited sample are $b_{cc}=4.09 \pm 0.47$ for the cluster auto-correlation and $b_{gc}=2.15 \pm 0.09$ for the galaxy-cluster cross-correlation. We find that these results are consistent with expectations from the auto-correlations of galaxies and clusters and are in good agreement with previous studies. The main result is two-fold: firstly we provide a measurement of the cross-correlation of galaxies and clusters, which can be used for further cosmological analysis, and secondly we describe an effective treatment of the shot noise.

Pushing phase and amplitude sensitivity limits in interferometric microscopy.

Sensitivity of the amplitude and phase measurements in interferometric microscopy is influenced by factors such as instrument design and environmental interferences. Through development of a theoretical framework followed by experimental validation, we show photon shot noise is often the limiting factor in interferometric microscopy measurements. Thereafter, we demonstrate how a state-of-the-art camera with million-level electrons full well capacity can significantly reduce shot noise contribution resulting in a stability of optical path length down to a few picometers even in a near-common-path interferometer.

One- and two-mode squeezed light in correlated interferometry

We study in detail a system of two interferometers aimed to the detection of extremely faint phase-fluctuations. This system can represent a breakthrough for detecting a faint correlated signal that would remain otherwise undetectable even using the most sensitive individual interferometric devices, that are limited by the shot noise. If the two interferometers experience identical phase-fluctuations, like the ones introduced by the so called "holographic noise", this signal should emerge if their output signals are correlated, while the fluctuations due to shot noise and other independent contributions will vanish. We show how the injecting quantum light in the free ports of the interferometers can reduce the photon noise of the system beyond the shot-noise, enhancing the resolution in the phase-correlation estimation. We analyze both the use of two-mode squeezed vacuum or twin-beam state (TWB) and of two independent squeezing states. Our results basically confirms the benefit of using squeezed beams together with strong coherent beams in interferometry, even in this correlated case. However, mainly we concentrate on the possible use of TWB, discovering interesting and probably unexplored areas of application of bipartite entanglement and in particular the possibility of reaching in principle surprising uncertainty reduction.

Forward-bias diode parameters, electronic noise, and photoresponse of graphene/silicon Schottky junctions with an interfacial native oxide layer

Metal-semiconductor Schottky junction devices composed of chemical vapor deposition grown monolayer graphene on p-type silicon substrates are fabricated and characterized. Important diode parameters, such as the Schottky barrier height, ideality factor, and series resistance, are extracted from forward bias current-voltage characteristics using a previously established method modified to take into account the interfacial native oxide layer present at the graphene/silicon junction. It is found that the ideality factor can be substantially increased by the presence of the interfacial oxide layer. Furthermore, low frequency noise of graphene/silicon Schottky junctions under both forward and reverse bias is characterized. The noise is found to be 1/f dominated and the shot noise contribution is found to be negligible. The dependence of the 1/f noise on the forward and reverse current is also investigated. Finally, the photoresponse of graphene/silicon Schottky junctions is studied. The devices exhibit a peak responsivity of around 0.13 A/W and an external quantum efficiency higher than 25%. From the photoresponse and noise measurements, the bandwidth is extracted to be ∼1 kHz and the normalized detectivity is calculated to be 1.2×109 cm Hz1/2 W−1. These results provide important insights for the future integration of graphene with silicon device technology.

Magnetic field enhancement of generation-recombination and shot noise in organic light emitting diodes

We have studied the effect of magnetic field on noise in series of 2-methoxy-5-(2′-ethylhexyloxy)-1,4-phenylenevinylene-based organic light emitting diodes with dominant hole injection, dominant electron injection, and balanced electron and hole injection. The noise spectra of the balanced devices revealed the generation-recombination (g-r) noise term, which we associated with bimolecular electron-hole recombination. The presence of the g-r noise term is correlated with the strong organic magnetoresistance (up to 25%) observed in the balanced devices. The noise spectra also have the shot noise contribution with the Fano factor 0.25–0.4. We found that time constant of the g-r term decreases and the magnitude of shot noise increases when magnetic field is applied. This behavior can be consistently explained within the polaron-polaron model of organic magnetoresistance. We have not found any evidence that the magnetoresistance in studied devices is affected by traps.

Modeling and Jitter Improvement of SRD-Based Ultra-Wideband Pulse Generator

Step recovery diode (SRD)-based ultra-wide band (UWB) pulse generators (PGs) suffer from jitter caused by AM-to-PM conversion, SRD shot noise, and clock jitter. These noise sources significantly impact the accuracy of UWB systems if very high precision ranging/positioning is required. Jitter behavior caused by the transmitter and receiver is mostly detrimental in the equivalent time-sampling receiver. Thus, a mathematical model for simulation of the jitter and amplitude variation effect in the equivalent time-sampling technique has been developed and used in SystemVue simulations. A criterion as an estimate of system accuracy is defined as signal-to-distortion ratio (SDR) and used. Similarly, a model for AM and PM noise analysis for an SRD-based UWB PG is developed that was validated experimentally. In addition, SRD shot-noise contribution on output jitter was evaluated using the proposed model. Based on these models, methods to reduce the output jitter of the system have been recommended. Simulation showed that clock jitter and SRD shot noise led to pronounced output jitter, with shot noise the primary cause. For a typical SRD-based UWB PG, an output jitter of around 3 ps has been achieved using improvement techniques based on the proposed method, compared to a 15-ps jitter before improvement. These measured results are in good agreement with our predictions.

Noise reduction and hyperfine level coherence in spontaneous noise spectroscopy of atomic vapor

We develop a system for measurements of power spectra of transmitted light intensity fluctuations, in which the extraneous noise, including shot noise, is reduced. In essence, we just apply light, measure the power of the transmitted light and derive its power spectrum. We use this to observe the spontaneous noise spectra of photon atom interactions. Applying light with frequency modulation, we can also observe the spontaneous noise reflecting the coherence between the hyperfine levels in the excited state. There are two in novel components in the measurement system, the noise reduction scheme and the stabilization of the laser system. The noise reduction mechanism can be used to reduce the shot noise contribution to arbitrarily low levels through averaging, in principle. This is combined with differential detection to keep unwanted noise at low levels. The laser system is stabilized to obtain spectral width below 1\,kHz without high frequency ($\gtrsim10\,$MHz) noise. These methods are described systematically and the performance of the asurement system is examined through experimental results.

High frequency noise of epitaxial graphene grown on sapphire

AbstractMicrowave noise technique is applied to study in‐plane electronic properties of epitaxial graphene grown on sapphire by chemical vapor deposition and subjected to high electric field applied in the plane. The noise spectrum is measured in the field direction at room temperature. While a 1/f1.25‐type dependence is observed in the 200 MHz–2.5 GHz band, a shot noise contribution is resolved at 10 GHz. The shot noise is possibly associated with hole jumps across the potential barriers located in the graphene layer. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Weak-value amplification in a shot-noise-limited interferometer

We study the weak-value amplification (WVA) in a phase measurement with an optical interferometer in which shot noise limits the sensitivity. We compute the signal and the shot noise including the full-order interaction terms of the WVA, and show that the shot-noise contribution to a phase shift in a pointer variable is always larger than the final variance of the pointer variable. This yields difference in estimating noise level up to a factor of 1.5. To clarify an advantage for practical uses of the WVA, we discuss signal-to-noise ratio and its optimization in the presence of the shot noise.

Covariance matrices for halo number counts and correlation functions

We study the mean number counts and two-point correlation functions, along with their covariance matrices, of cosmological surveys such as for clusters. In particular, we consider correlation functions averaged over finite redshift intervals, which are well suited to cluster surveys or populations of rare objects, where one needs to integrate over nonzero redshift bins to accumulate enough statistics. We develop an analytical formalism to obtain explicit expressions of all contributions to these means and covariance matrices, taking into account both shot-noise and sample-variance effects. We compute low-order as well as high-order (including non-Gaussian) terms. We derive expressions for the number counts per redshift bins both for the general case and for the small window approximation. We estimate the range of validity of Limber's approximation and the amount of correlation between different redshift bins. We also obtain explicit expressions for the integrated 3D correlation function and the 2D angular correlation. We compare the relative importance of shot-noise and sample-variance contributions, and of low-order and high-order terms. We check the validity of our analytical results through a comparison with the Horizon full-sky numerical simulations, and we obtain forecasts for several future cluster surveys.

Unifying intensity noise and second-order coherence properties of amplified spontaneous emission sources

We present joint investigations of relative intensity noise (RIN) and second-order coherence properties of amplified spontaneous emission (ASE) generated by a superluminescent diode. We introduce a generalized intensity noise description for ASE sources that contains the shot noise contribution but also accounts for first- and second-order coherence properties reflecting the process of light generation. We find excellent agreement between pump-current-dependent RIN values and this new description, with the perspective of particular interesting consequences for the realization of low-noise broadband emitters.

Bayesian non-linear large-scale structure inference of the Sloan Digital Sky Survey Data Release 7

In this work, we present the first non-linear, non-Gaussian full Bayesian large-scale structure analysis of the cosmic density field conducted so far. The density inference is based on the Sloan Digital Sky Survey (SDSS) Data Release 7, which covers the northern galactic cap. We employ a novel Bayesian sampling algorithm, which enables us to explore the extremely high dimensional non-Gaussian, non-linear lognormal Poissonian posterior of the three-dimensional density field conditional on the data. These techniques are efficiently implemented in the Hamiltonian Density Estimation and Sampling (hades) computer algorithm and permit the precise recovery of poorly sampled objects and non-linear density fields. The non-linear density inference is performed on a 750-Mpc cube with roughly 3-Mpc grid resolution, while accounting for systematic effects, introduced by survey geometry and selection function of the SDSS, and the correct treatment of a Poissonian shot noise contribution. Our high-resolution results represent remarkably well the cosmic web structure of the cosmic density field. Filaments, voids and clusters are clearly visible. Further, we also conduct a dynamical web classification and estimate the web-type posterior distribution conditional on the SDSS data.

Observability of radiation-pressure shot noise in optomechanical systems

We present a theoretical study of an experiment designed to detect radiation pressure shot noise in an optomechanical system. Our model consists of a coherently driven optical cavity mode that is coupled to a mechanical oscillator. We examine the cross-correlation between two quadratures of the output field from the cavity. We determine under which circumstances radiation pressure shot noise can be detected by a measurement of this cross-correlation. This is done in the general case of nonzero detuning between the frequency of the drive and the cavity resonance frequency. We study the qualitative features of the different contributions to the cross-correlator and provide quantitative figures of merit for the relative importance of the radiation pressure shot noise contribution to other contributions. We also propose a modified setup of this experiment relevant to the "membrane-in-the-middle" geometry, which potentially can avoid the problems of static bistability and classical noise in the drive.

Detection of Structural Dynamics by FRET: A Photon Distribution and Fluorescence Lifetime Analysis of Systems with Multiple States

Two complementary methods in confocal single-molecule fluorescence spectroscopy are presented to analyze conformational dynamics by Forster resonance energy transfer (FRET) measurements considering simulated and experimental data. First, an extension of photon distribution analysis (PDA) is applied to characterize conformational exchange between two or more states via global analysis of the shape of FRET peaks for different time bins. PDA accurately predicts the shape of FRET efficiency histograms in the presence of FRET fluctuations, taking into account shot noise and background contributions. Dynamic-PDA quantitatively recovers FRET efficiencies of the interconverting states and relaxation times of dynamics on the time scale of the diffusion time t(d) (typically milliseconds), with a dynamic range of the method of about +/-1 order of magnitude with respect to t(d). Correction procedures are proposed to consider the factors limiting the accuracy of dynamic-PDA, such as brightness variations, shortening of the observation time due to diffusion, and a contribution of multimolecular events. Second, an analysis procedure for multiparameter fluorescence detection is presented, where intensity-derived FRET efficiency is correlated with the fluorescence lifetime of the donor quenched by FRET. If a maximum likelihood estimator is applied to compute a mean fluorescence lifetime of mixed states, one obtains a fluorescence weighted mean lifetime. Thus a mixed state is detected by a characteristic shift of the fluorescence lifetime, which becomes longer than that expected for a single species with the same intensity-derived FRET efficiency. Analysis tools for direct visual inspection of two-dimensional diagrams of FRET efficiency versus donor lifetime are presented for the cases of static and dynamic FRET. Finally these new techniques are compared with fluorescence correlation spectroscopy.

Influence of the operating parameters and of the sample introduction system on time correlation of line intensities using an axially viewed CCD-based ICP-AES system

The influence of the acquisition and operating parameters on time correlation between emission line intensities was investigated using axially viewed inductively coupled plasma-multichannel-based emission spectrometry and various sample introduction systems. It was found that to obtain flicker-noise limited signals, necessary to compensate for time-correlated signal fluctuations by internal standardization, the flicker-noise magnitude of the sample introduction system, the integration time and the emission line intensity had to be considered. The highest correlation between lines was observed for ultrasonic nebulization with desolvatation, the noisiest system among those considered, for which the contribution of the uncorrelated shot-noise was negligible. In contrast, for sample introduction systems characterized by lower flicker-noise levels, shot-noise led to high, non-correlated RSD values, making the internal standard method to be much less efficient. To minimize shot-noise, time correlation was improved by increasing the emission line intensities and the integration time. Improvement in repeatability did not depend only on time correlation, but also on the ratio between the relative standard deviations of the analytical and reference lines. The best signal compensation was obtained when RSD values of the reference and analytical lines were similar, which is usually obtained when the system is flicker-noise limited, while departure from similarity can lead to a degradation of repeatability when using the internal standard method. Moreover, the use of so-called robust plasma conditions, i.e. a high power (1500 W) along with a low carrier gas flow rate (0.8 L/min) improved also the compensation. Finally, high correlation and consequent improvement in repeatability by internal standardization was observed also in the presence of complex matrices (sediment and soil samples), although a matrix-induced degradation of the correlation between lines was generally observed when using ultrasonic nebulization.

Impact of point source clustering on cosmological parameters with CMB anisotropies

The faint radio point sources that are unresolved in cosmic microwave background (CMB) anisotropy maps are likely to be a biased tracer of the large-scale structure dark matter distribution. While the shot-noise contribution to the angular power spectrum of unresolved radio point sources is included either when optimally constructing the CMB angular power spectrum, as with WMAP data, or when extracting cosmological parameters, we suggest that clustering part of the point source power spectrum should also be included. This is especially necessary at high frequencies above 150 GHz, where the clustering of far-IR sources is expected to dominate the shot-noise level of the angular power spectrum at tens of arcminute angular scales of both radio and sub-mm sources. We make an estimate of source clustering of unresolved radio sources in both WMAP and ACBAR, and marginalize over the amplitude of source clustering in each CMB data set when model fitting for cosmological parameters. For the combination of WMAP 5-year data and ACBAR, we find that the spectral index changes from the value of $0.963\ifmmode\pm\else\textpm\fi{}0.014$ to $0.959\ifmmode\pm\else\textpm\fi{}0.014$ (at 68% C.L.) when the clustering power spectrum of point sources is included in model fits. While we find that the differences are marginal with and without source clustering in current data, it may be necessary to account for source clustering with future data sets such as Planck, especially to properly model fit anisotropies at arcminute angular scales. If clustering is not accounted and point sources are modeled with a shot noise only out to $l\ensuremath{\sim}2000$, the spectral index will be biased by about $1.5\ensuremath{\sigma}$.

Characterizing Multiple Molecular States in Single-Molecule Multiparameter Fluorescence Detection by Probability Distribution Analysis

Probability distribution analysis (PDA) [M. Antonik et al., J. Phys. Chem. B 2006, 110, 6970] allows one to quantitatively analyze single-molecule (SM) data obtained in Forster resonance energy transfer (FRET) or fluorescence polarization experiments. By taking explicitly background and shot noise contributions into account, PDA accurately predicts the shape of one-dimensional histograms of various parameters, such as FRET efficiency or fluorescence anisotropy. In order to describe complex experimental SM-FRET or polarization data obtained for systems consisting of multiple non-interconverting fluorescent states, several extensions to the PDA theory are presented. Effects of brightness variations and multiple-molecule events are considered independently of the detection volume parameters by using only the overall experimental signal intensity distribution. The extended PDA theory can now be applied to analyze any mixture, by using any a priori model or a model-free deconvolution approach based on the maximum entropy method (MEM). The accuracy of the analysis and the number of free parameters are limited only by data quality. Correction of the PDA model function for the presence of multiple-molecule events allows one to measure at high SM concentrations to avoid artifacts due to a very long measurement time. Tools such as MEM and combined mean donor fluorescence lifetime analysis have been developed to distinguish whether extra broadening of PDA histograms could be attributed to structural heterogeneities or dye artifacts. In this way, an ultimate resolution in FRET experiments in the range of a few Angstrom is achieved which allows for molecular Angstrom optics distinguishing between a set of fixed distances and a distribution of distances. The extended theory is verified by analyzing simulations and experimental data.