T. Vo | Searcharxiv

arXiv2021

LIGOs Quantum Response to Squeezed States

Gravitational Wave interferometers achieve their profound sensitivity by combining a Michelson interferometer with optical cavities, suspended masses, and now, squeezed quantum states of light. These states modify the measurement process of the LIGO, VIRGO and GEO600 interferometers to reduce the quantum noise that masks astrophysical signals; thus, improvements to squeezing are essential to further expand our gravitational view of the universe. Further reducing quantum noise will require both lowering decoherence from losses as well more sophisticated manipulations to counter the quantum back-action from radiation pressure. Both tasks require fully understanding the physical interactions between squeezed light and the many components of km-scale interferometers. To this end, data from both LIGO observatories in observing run three are expressed using frequency-dependent metrics to analyze each detector's quantum response to squeezed states. The response metrics are derived and used to concisely describe physical mechanisms behind squeezing's simultaneous interaction with transverse-mode selective optical cavities and the quantum radiation pressure noise of suspended mirrors. These metrics and related analysis are broadly applicable for cavity-enhanced optomechanics experiments that incorporate external squeezing, and -- for the first time -- give physical descriptions of every feature so far observed in the quantum noise of the LIGO detectors.

physics.ins-det↗

arXiv2015

From Canards of Folded Singularities to Torus Canards in a Forced van der Pol Equation

We study canard solutions of the forced van der Pol (fvdP) equation in the relaxation limit for low-, intermediate-, and high-frequency periodic forcing. A central numerical observation is that there are two branches of canards in parameter space which extend across all positive forcing frequencies. For low-frequency forcing, we demonstrate the existence of primary maximal canards induced by folded saddle-nodes of type I, and establish explicit formulas for the parameter values at which the primary maximal canards and their folds exist. We then turn to the intermediate- and high-frequency forcing regimes, and show that the fvdP equation possesses torus canards instead. These torus canards consist of long segments near families of attracting and repelling limit cycles of the fast system, in alternation. We also derive explicit formulas for the parameter values at which the maximal torus canards and their folds exist. Primary maximal canards and maximal torus canards correspond geometrically to the situation in which the persistent manifolds near the family of attracting limit cycles coincide to all orders with the persistent manifolds that lie near the family of repelling limit cycles. The formulas derived for the folds of maximal canards in all three frequency regimes turn out to be representations of a single formula in the appropriate parameter regimes, and this unification confirms our numerical observation. In addition, we study the secondary canards induced by the folded singularities in the low-frequency regime and find that their fold curves turn around in the intermediate-frequency regime. We identify the mechanism responsible for this turning. Finally, we show that the fvdP equation is a normal form for a class of single-frequency periodically-driven slow/fast systems with two fast variables and one slow variable which possess a nondegenerate fold of limit cycles.

math.DS↗