992 research outputs found
Sequential nonideal measurements of quantum oscillators: Statistical characterization with and without environmental coupling
A one-dimensional quantum oscillator is monitored by taking repeated position
measurements. As a first con- tribution, it is shown that, under a quantum
nondemolition measurement scheme applied to a system initially at the ground
state, (i) the observed sequence of measurements (quantum tracks) corresponding
to a single experiment converges to a limit point, and that (ii) the limit
point is random over the ensemble of the experiments, being distributed as a
zero-mean Gaussian random variable with a variance at most equal to the
ground-state variance. As a second contribution, the richer scenario where the
oscillator is coupled with a frozen (i.e., at the ground state) ensemble of
independent quantum oscillators is considered. A sharply different behavior
emerges: under the same measurement scheme, here we observe that the
measurement sequences are essentially divergent. Such a rigorous statistical
analysis of the sequential measurement process might be useful for
characterizing the main quantities that are currently used for inference,
manipulation, and monitoring of many quantum systems. Several interesting
properties of the quantum tracks evolution, as well as of the associated
(quantum) threshold crossing times, are discussed and the dependence upon the
main system parameters (e.g., the choice of the measurement sampling time, the
degree of interaction with the environment, the measurement device accuracy) is
elucidated. At a more fundamental level, it is seen that, as an application of
basic quantum mechanics principles, a sharp difference exists between the
intrinsic randomness unavoidably present in any quantum system, and the
extrinsic randomness arising from the environmental coupling, i.e., the
randomness induced by an external source of disturbance.Comment: pages 16 Figures
Noise Estimate of Pendular Fabry-Perot through Reflectivity Change
A key issue in developing pendular Fabry-Perot interferometers as very
accurate displacement measurement devices, is the noise level. The Fabry-Perot
pendulums are the most promising device to detect gravitational waves, and
therefore the background and the internal noise should be accurately measured
and reduced. In fact terminal masses generates additional internal noise mainly
due to thermal fluctuations and vibrations. We propose to exploit the
reflectivity change, that occurs in some special points, to monitor the
pendulums free oscillations and possibly estimate the noise level. We find that
in spite of long transients, it is an effective method for noise estimate. We
also prove that to only retain the sequence of escapes, rather than the whole
time dependent dynamics, entails the main characteristics of the phenomenon.
Escape times could also be relevant for future gravitational wave detector
developments.Comment: PREPRINT Metrology for Aerospace (MetroAeroSpace), 2014 IEEE
Publication Year: 2014, Page(s): 468 - 47
Parameterizing Quasiperiodicity: Generalized Poisson Summation and Its Application to Modified-Fibonacci Antenna Arrays
The fairly recent discovery of "quasicrystals", whose X-ray diffraction
patterns reveal certain peculiar features which do not conform with spatial
periodicity, has motivated studies of the wave-dynamical implications of
"aperiodic order". Within the context of the radiation properties of antenna
arrays, an instructive novel (canonical) example of wave interactions with
quasiperiodic order is illustrated here for one-dimensional (1-D) array
configurations based on the "modified-Fibonacci" sequence, with utilization of
a two-scale generalization of the standard Poisson summation formula for
periodic arrays. This allows for a "quasi-Floquet" analytic parameterization of
the radiated field, which provides instructive insights into some of the basic
wave mechanisms associated with quasiperiodic order, highlighting similarities
and differences with the periodic case. Examples are shown for quasiperiodic
infinite and spatially-truncated arrays, with brief discussion of computational
issues and potential applications.Comment: 29 pages, 10 figures. To be published in IEEE Trans. Antennas
Propagat., vol. 53, No. 6, June 200
Perspectives on Beam-Shaping Optimization for Thermal-Noise Reduction in Advanced Gravitational-Wave Interferometric Detectors: Bounds, Profiles, and Critical Parameters
Suitable shaping (in particular, flattening and broadening) of the laser beam
has recently been proposed as an effective device to reduce internal (mirror)
thermal noise in advanced gravitational wave interferometric detectors. Based
on some recently published analytic approximations (valid in the
infinite-test-mass limit) for the Brownian and thermoelastic mirror noises in
the presence of arbitrary-shaped beams, this paper addresses certain
preliminary issues related to the optimal beam-shaping problem. In particular,
with specific reference to the Laser Interferometer Gravitational-wave
Observatory (LIGO) experiment, absolute and realistic lower-bounds for the
various thermal noise constituents are obtained and compared with the current
status (Gaussian beams) and trends ("mesa" beams), indicating fairly ample
margins for further reduction. In this framework, the effective dimension of
the related optimization problem, and its relationship to the critical design
parameters are identified, physical-feasibility and model-consistency issues
are considered, and possible additional requirements and/or prior information
exploitable to drive the subsequent optimization process are highlighted.Comment: 12 pages, 9 figures, 2 table
Neural Network Aided Glitch-Burst Discrimination and Glitch Classification
We investigate the potential of neural-network based classifiers for
discriminating gravitational wave bursts (GWBs) of a given canonical family
(e.g. core-collapse supernova waveforms) from typical transient instrumental
artifacts (glitches), in the data of a single detector. The further
classification of glitches into typical sets is explored.In order to provide a
proof of concept,we use the core-collapse supernova waveform catalog produced
by H. Dimmelmeier and co-Workers, and the data base of glitches observed in
laser interferometer gravitational wave observatory (LIGO) data maintained by
P. Saulson and co-Workers to construct datasets of (windowed) transient
waveforms (glitches and bursts) in additive (Gaussian and compound-Gaussian)
noise with different signal-tonoise ratios (SNR). Principal component analysis
(PCA) is next implemented for reducing data dimensionality, yielding results
consistent with, and extending those in the literature. Then, a multilayer
perceptron is trained by a backpropagation algorithm (MLP-BP) on a data subset,
and used to classify the transients as glitch or burst. A Self-Organizing Map
(SOM) architecture is finally used to classify the glitches. The glitch/burst
discrimination and glitch classification abilities are gauged in terms of the
related truth tables. Preliminary results suggest that the approach is
effective and robust throughout the SNR range of practical interest.
Perspective applications pertain both to distributed (network, multisensor)
detection of GWBs, where someintelligenceat the single node level can be
introduced, and instrument diagnostics/optimization, where spurious transients
can be identified, classified and hopefully traced back to their entry point
On the Analytic Structure of a Family of Hyperboloidal Beams of Potential Interest for Advanced LIGO
For the baseline design of the advanced Laser Interferometer
Gravitational-wave Observatory (LIGO), use of optical cavities with
non-spherical mirrors supporting flat-top ("mesa") beams, potentially capable
of mitigating the thermal noise of the mirrors, has recently drawn a
considerable attention. To reduce the severe tilt-instability problems
affecting the originally conceived nearly-flat, "Mexican-hat-shaped" mirror
configuration, K. S. Thorne proposed a nearly-concentric mirror configuration
capable of producing the same mesa beam profile on the mirror surfaces.
Subsequently, Bondarescu and Thorne introduced a generalized construction that
leads to a one-parameter family of "hyperboloidal" beams which allows
continuous spanning from the nearly-flat to the nearly-concentric mesa beam
configurations. This paper is concerned with a study of the analytic structure
of the above family of hyperboloidal beams. Capitalizing on certain results
from the applied optics literature on flat-top beams, a physically-insightful
and computationally-effective representation is derived in terms of
rapidly-converging Gauss-Laguerre expansions. Moreover, the functional relation
between two generic hyperboloidal beams is investigated. This leads to a
generalization (involving fractional Fourier transform operators of complex
order) of some recently discovered duality relations between the nearly-flat
and nearly-concentric mesa configurations. Possible implications and
perspectives for the advanced LIGO optical cavity design are discussed.Comment: 9 pages, 6 figures, typos corrected, Eqs. (24) and (26) change
Directive Emission from Defect-Free Dodecagonal Photonic Quasicrystals: A Leaky-Wave Characterization
In this paper, we study the radiation from embedded sources in
two-dimensional finite-size "photonic-quasicrystal" (PQC) slabs made of
dielectric rods arranged according to a 12-fold symmetric aperiodic tiling. The
results from our investigation, based on rigorous full-wave simulations, show
the possibility of achieving broadside radiation at multiple frequencies, with
high-directivity (e.g., 15 dB) and low-sidelobes (e.g., -12 dB). We also show
that leaky waves are supported by a PQC slab, and that the beamwidth is
directly proportional to the leaky-wave attenuation constant, which provides a
physically-incisive interpretation of the observed radiation characteristics.Comment: 7 pages, 7 figures; slight change in the title, major revision in the
text and figures. Accepted for publication in Phys. Rev.
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