62,257 research outputs found
Quantum theory of cross-correlation heterodyne detection
Cross-correlation heterodyne detectors exhibit the potential for suppression
of the detection quantum noise below shot noise without use of optical
squeezing for capturing weak optical signals in low frequency bands. To
understand the underlying mechanism, we develop a quantum theory to describe
the noise performance of cross-correlation heterodyne detectors. By calculating
the cross spectral density (CSD) of the photocurrent fluctuations from a
cross-correlation heterodyne detector, we prove that its noise performance can
break the shot noise limit and exceed that of a regular heterodyne detector for
detection of coherent light. When the detected light signal is in a squeezed
state, we show that the corresponding CSD value is negative and discuss how a
negative CSD may be explored to improve the output signal-to-noise ratio of the
detector contaminated by classical noises through tuning the parameter of the
degree of squeezing. This work may find itself useful in space-based
gravitational wave searching and a variety of other scientific research
activities, such as observation of vacuum magnetic birefringence and
telecommunications.Comment: 2 figure
Aperture synthesis for gravitational-wave data analysis: Deterministic Sources
Gravitational wave detectors now under construction are sensitive to the
phase of the incident gravitational waves. Correspondingly, the signals from
the different detectors can be combined, in the analysis, to simulate a single
detector of greater amplitude and directional sensitivity: in short, aperture
synthesis. Here we consider the problem of aperture synthesis in the special
case of a search for a source whose waveform is known in detail: \textit{e.g.,}
compact binary inspiral. We derive the likelihood function for joint output of
several detectors as a function of the parameters that describe the signal and
find the optimal matched filter for the detection of the known signal. Our
results allow for the presence of noise that is correlated between the several
detectors. While their derivation is specialized to the case of Gaussian noise
we show that the results obtained are, in fact, appropriate in a well-defined,
information-theoretic sense even when the noise is non-Gaussian in character.
The analysis described here stands in distinction to ``coincidence
analyses'', wherein the data from each of several detectors is studied in
isolation to produce a list of candidate events, which are then compared to
search for coincidences that might indicate common origin in a gravitational
wave signal. We compare these two analyses --- optimal filtering and
coincidence --- in a series of numerical examples, showing that the optimal
filtering analysis always yields a greater detection efficiency for given false
alarm rate, even when the detector noise is strongly non-Gaussian.Comment: 39 pages, 4 figures, submitted to Phys. Rev.
The cross-correlation search for a hot spot of gravitational waves : Numerical study for point spread function
The cross-correlation search for gravitational wave, which is known as
'radiometry', has been previously applied to map of the gravitational wave
stochastic background in the sky and also to target on gravitational wave from
rotating neutron stars/pulsars. We consider the Virgo cluster where may be
appear as `hot spot' spanning few pixels in the sky in radiometry analysis. Our
results show that sufficient signal to noise ratio can be accumulated with
integration times of the order of a year. We also construct numerical
simulation of radiometry analysis, assuming current constructing/upgrading
ground-based detectors. Point spread function of the injected sources are
confirmed by numerical test. Typical resolution of radiometry analysis is a few
square degree which corresponds to several thousand pixels of sky mapping.Comment: 9 pages, 9 figures, Amaldi 9 & NRD
Constraint Likelihood analysis for a network of gravitational wave detectors
We propose a coherent method for the detection and reconstruction of
gravitational wave signals for a network of interferometric detectors. The
method is derived using the likelihood functional for unknown signal waveforms.
In the standard approach, the global maximum of the likelihood over the space
of waveforms is used as the detection statistic. We identify a problem with
this approach. In the case of an aligned pair of detectors, the detection
statistic depends on the cross-correlation between the detectors as expected,
but this dependence dissappears even for infinitesimally small misalignments.
We solve the problem by applying constraints on thelikelihood functional and
obtain a new class of statistics. The resulting method can be applied to the
data from a network consisting of any number of detectors with arbitrary
detector orientations. The method allows us reconstruction of the source
coordinates and the waveforms of two polarization components of a gravitational
wave. We study the performance of the method with numerical simulation and find
the reconstruction of the source coordinates to be more accurate than in the
standard approach.Comment: 13 pages, 6 figure
Continuous quantum measurement with independent detector cross-correlations
We investigate the advantages of using two independent, linear detectors for
continuous quantum measurement. For single-shot quantum measurement, the
measurement is maximally efficient if the detectors are twins. For weak
continuous measurement, cross-correlations allow a violation of the
Korotkov-Averin bound for the detector's signal-to-noise ratio. A vanishing
noise background provides a nontrivial test of ideal independent quantum
detectors. We further investigate the correlations of non-commuting operators,
and consider possible deviations from the independent detector model for
mesoscopic conductors coupled by the screened Coulomb interaction.Comment: 4 pages, 2 figure
Detection methods for non-Gaussian gravitational wave stochastic backgrounds
We address the issue of finding an optimal detection method for a
discontinuous or intermittent gravitational wave stochastic background. Such a
signal might sound something like popcorn popping. We derive an appropriate
version of the maximum likelihood detection statistic, and compare its
performance to that of the standard cross-correlation statistic both
analytically and with Monte Carlo simulations. The maximum likelihood statistic
performs better than the cross-correlation statistic when the background is
sufficiently non-Gaussian. For both ground and space based detectors, this
results in a gain factor, ranging roughly from 1 to 3, in the minimum
gravitational-wave energy density necessary for detection, depending on the
duty cycle of the background. Our analysis is exploratory, as we assume that
the time structure of the events cannot be resolved, and we assume white,
Gaussian noise in two collocated, aligned detectors. Before this detection
method can be used in practice with real detector data, further work is
required to generalize our analysis to accommodate separated, misaligned
detectors with realistic, colored, non-Gaussian noise.Comment: 25 pages, 12 figures, submitted to physical review D, added revisions
in response to reviewers comment
Subtraction-noise projection in gravitational-wave detector networks
In this paper, we present a successful implementation of a subtraction-noise
projection method into a simple, simulated data analysis pipeline of a
gravitational-wave search. We investigate the problem to reveal a weak
stochastic background signal which is covered by a strong foreground of
compact-binary coalescences. The foreground which is estimated by matched
filters, has to be subtracted from the data. Even an optimal analysis of
foreground signals will leave subtraction noise due to estimation errors of
template parameters which may corrupt the measurement of the background signal.
The subtraction noise can be removed by a noise projection. We apply our
analysis pipeline to the proposed future-generation space-borne Big Bang
Observer (BBO) mission which seeks for a stochastic background of primordial
GWs in the frequency range Hz covered by a foreground of
black-hole and neutron-star binaries. Our analysis is based on a simulation
code which provides a dynamical model of a time-delay interferometer (TDI)
network. It generates the data as time series and incorporates the analysis
pipeline together with the noise projection. Our results confirm previous ad
hoc predictions which say that BBO will be sensitive to backgrounds with
fractional energy densities below Comment: 54 pages, 15 figure
Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise I: Frequentist analyses
Gravitational wave detectors will need optimal signal-processing algorithms
to extract weak signals from the detector noise. Most algorithms designed to
date are based on the unrealistic assumption that the detector noise may be
modeled as a stationary Gaussian process. However most experiments exhibit a
non-Gaussian ``tail'' in the probability distribution. This ``excess'' of large
signals can be a troublesome source of false alarms. This article derives an
optimal (in the Neyman-Pearson sense, for weak signals) signal processing
strategy when the detector noise is non-Gaussian and exhibits tail terms. This
strategy is robust, meaning that it is close to optimal for Gaussian noise but
far less sensitive than conventional methods to the excess large events that
form the tail of the distribution. The method is analyzed for two different
signal analysis problems: (i) a known waveform (e.g., a binary inspiral chirp)
and (ii) a stochastic background, which requires a multi-detector signal
processing algorithm. The methods should be easy to implement: they amount to
truncation or clipping of sample values which lie in the outlier part of the
probability distribution.Comment: RevTeX 4, 17 pages, 8 figures, typos corrected from first version
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