Effects of mode degeneracy in the LIGO Livingston Observatory recycling cavity

We analyze the electromagnetic fields in a Pound-Drever-Hall locked, marginally unstable, Fabry-Perot cavity as a function of small changes in the cavity length during resonance. More specifically, we compare the results of a detailed numerical model with the behavior of the recycling cavity of the Laser Interferometer Gravitational-wave Observatory (LIGO) detector that is located in Livingston, Louisiana. In the interferometer's normal mode of operation, the recycling cavity is stabilized by inducing a thermal lens in the cavity mirrors with an external CO2 laser. During the study described here, this thermal compensation system was not operating, causing the cavity to be marginally optically unstable and cavity modes to become degenerate. In contrast to stable optical cavities, the modal content of the resonating beam in the uncompensated recycling cavity is significantly altered by very small cavity length changes. This modifies the error signals used to control the cavity length in such a way that the zero crossing point is no longer the point of maximum power in the cavity nor is it the point where the input beam mode in the cavity is maximized.Comment: Eight pages in two-column format. Six color figures. To be published JOSA

The Evolution of Neural Network-Based Chart Patterns: A Preliminary Study

A neural network-based chart pattern represents adaptive parametric features, including non-linear transformations, and a template that can be applied in the feature space. The search of neural network-based chart patterns has been unexplored despite its potential expressiveness. In this paper, we formulate a general chart pattern search problem to enable cross-representational quantitative comparison of various search schemes. We suggest a HyperNEAT framework applying state-of-the-art deep neural network techniques to find attractive neural network-based chart patterns; These techniques enable a fast evaluation and search of robust patterns, as well as bringing a performance gain. The proposed framework successfully found attractive patterns on the Korean stock market. We compared newly found patterns with those found by different search schemes, showing the proposed approach has potential.Comment: 8 pages, In proceedings of Genetic and Evolutionary Computation Conference (GECCO 2017), Berlin, German

Model of Thermal Wavefront Distortion in Interferometric Gravitational-Wave Detectors I: Thermal Focusing

We develop a steady-state analytical and numerical model of the optical response of power-recycled Fabry-Perot Michelson laser gravitational-wave detectors to thermal focusing in optical substrates. We assume that the thermal distortions are small enough that we can represent the unperturbed intracavity field anywhere in the detector as a linear combination of basis functions related to the eigenmodes of one of the Fabry-Perot arm cavities, and we take great care to preserve numerically the nearly ideal longitudinal phase resonance conditions that would otherwise be provided by an external servo-locking control system. We have included the effects of nonlinear thermal focusing due to power absorption in both the substrates and coatings of the mirrors and beamsplitter, the effects of a finite mismatch between the curvatures of the laser wavefront and the mirror surface, and the diffraction by the mirror aperture at each instance of reflection and transmission. We demonstrate a detailed numerical example of this model using the MATLAB program Melody for the initial LIGO detector in the Hermite-Gauss basis, and compare the resulting computations of intracavity fields in two special cases with those of a fast Fourier transform field propagation model. Additional systematic perturbations (e.g., mirror tilt, thermoelastic surface deformations, and other optical imperfections) can be included easily by incorporating the appropriate operators into the transfer matrices describing reflection and transmission for the mirrors and beamsplitter.Comment: 24 pages, 22 figures. Submitted to JOSA

Kaon decay interferometry as meson dynamics probes

We discuss the time dependent interferences between $K_L$ and $K_S$ in the decays in $3\pi$ and $\pi\pi\gamma$, to be studied at interferometry machines such as the $\phi$-factory and LEAR. We emphasize the possibilities and the advantages of using interferences, in comparison with width measurements, to obtain information both on $CP$ conserving and $CP$ violating amplitudes. Comparison with present data and suggestions for future experiments are made.Comment: 15 pages, in RevTex, Report INFNNA-IV-93-31, UTS-DFT-93-2

Freezing In with Lepton Flavored Fermions

Dark, chiral fermions carrying lepton flavor quantum numbers are natural candidates for freeze-in. Small couplings with the Standard Model fermions of the order of lepton Yukawas are `automatic' in the limit of Minimal Flavor Violation. In the absence of total lepton number violating interactions, particles with certain representations under the flavor group remain absolutely stable. For masses in the GeV-TeV range, the simplest model with three flavors, leads to signals at future direct detection experiments like DARWIN. Interestingly, freeze-in with a smaller flavor group such as $SU(2)$ is already being probed by XENON1T.Comment: v1: 22 pages, 4 figures. Comments welcom

Kaon physics with a high-intensity proton driver

We study opportunities for future high-precision experiments in kaon physics using a high-intensity proton driver, which could be part of the front-end of a muon storage ring complex. We discuss in particular the rare decays $K_L\to\pi^0\nu\bar\nu$, $K^+\to\pi^+\nu\bar\nu$, $K_L\to\pi^0e^+e^-$, and lepton-flavour violating modes such as $K_L\to\mu e$ and $K\to\pi\mu e$. The outstanding physics potential and long-term interest of these modes is emphasized. We review status and prospects of current and planned experiments for the processes under consideration, and indicate possible improvements and strategies towards achieving the necessary higher sensitivity. Finally, we outline the machine requirements needed to perform these high-precision kaon experiments in the context of a muon storage ring facility.Comment: 26 pages, 12 figures; report of the kaon physics working group for the ECFA studies on neutrino factory and muon storage rings at CERN, G. Buchalla (convener); references update

Coating thermal noise for arbitrary shaped beams

Advanced LIGO's sensitivity will be limited by coating noise. Though this noise depends on beam shape, and though nongaussian beams are being seriously considered for advanced LIGO, no published analysis exists to compare the quantitative thermal noise improvement alternate beams offer. In this paper, we derive and discuss a simple integral which completely characterizes the dependence of coating thermal noise on shape. The derivation used applies equally well, with minor modifications, to all other forms of thermal noise in the low-frequency limit.Comment: 3 pages. Originally performed in August 2004. Submitted to CQG. (v2) : Corrections from referee and other

Supersymmetric Dissipative Quantum Mechanics from Superstrings

Following the approach of Callan and Thorlacius applied to the superstring, we derive a supersymmetric extension of the non-local dissipative action of Caldeira and Leggett. The dissipative term turns out to be invariant under a group of superconformal transformations. When added to the usual kinetic term, it provides an example of supersymmetric dissipative quantum mechanics. As a by-product of our analysis, an intriguing connection to the homeotic/hybrid fermion model, proposed for CPT violation in neutrinos, appears.Comment: Latex, 16 page

The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers

In second-generation, ground-based interferometric gravitational-wave detectors such as Advanced LIGO, the dominant noise at frequencies $f \sim 40$ Hz to $\sim 200$ Hz is expected to be due to thermal fluctuations in the mirrors' substrates and coatings which induce random fluctuations in the shape of the mirror face. The laser-light beam averages over these fluctuations; the larger the beam and the flatter its light-power distribution, the better the averaging and the lower the resulting thermal noise. In semi-infinite mirrors, scaling laws for the influence of beam shape on the four dominant types of thermal noise (coating Brownian, coating thermoelastic, substrate Brownian, and substrate thermoelastic) have been suggested by various researchers and derived with varying degrees of rigour. Because these scaling laws are important tools for current research on optimizing the beam shape, it is important to firm up our understanding of them. This paper (1) gives a summary of the prior work and of gaps in the prior analyses, (2) gives a unified and rigorous derivation of all four scaling laws, and (3) explores, relying on work by J. Agresti, deviations from the scaling laws due to finite mirror size.Comment: 25 pages, 10 figures, submitted to Class. Quantum Gra