Topics of LIGO physics: Quantum noise in advanced interferometers and template banks for compact-binary inspirals.

摘要

This thesis deals with the planning for advanced interferometeric gravitational-wave detectors, as well as the detection of inspiral waves using first-generation interferometers.; In Chapters 2–4 (in collaboration with Alessandra Buonanno), the signal recycling interferometer proposed for LIGO-II is studied in the two-photon formalism. This study reveals the optical spring effect, which allows the interferometer to beat the standard quantum limit, while in the same time introduces a dynamical instability. A classical control system is designed to suppress this instability. In Chapter 5 (in collaboration with Alessandra Buonanno and Nergis Mavalvala), the quantum noise in heterodyne readout schemes for advanced interferometers is studied. In Chapter 6 (in collaboration with Patricia Purdue), a QND Speed-Meter interferometer with Michelson topology is proposed, analyzed and shown to be a promising candidate for third-generation interferometers (LIGO-III or EURO). This design requires adding a kilometer-scale cavity into the interferometer. In Chapter 7, Sagnac interferometers are analyzed and shown to exhibit a similar broadband QND performance without the need of additional cavity—as expected since these interferometers are sensitive only to time-dependent mirror displacement, and are automatic speed meters.; In Chapter 8 (in collaboration with Alessandra Buonanno and Michele Vallisneri), the Post-Newtonian (PN) breakdown at late-stage inspirals of non-spinning binary black holes (with 5 $M\odot$ m₁, m₂ 20 $M\odot$) is studied. We propose the use of Detection Template Families (DTFs)—extensions of ordinary PN templates that can mimic all different PN waveforms and hence are plausible to catch the real waveform, yet do not provide straightforward parameter estimation.; In Chapter 9 (in collaboration with Alessandra Buonanno and Michele Vallisneri), binaries carrying spins are studied using an adiabatic PN model. Based on features of the precession dynamics, we construct a DTF, using a modified Apostolatos' ansatz, that can mimic the modulated waveforms reasonably well, while keeping a small number of parameters to be searched over one by one, with the rest searched over automatically. We also propose a (computationally) plausible way of searching over the entire physical parameter space of neutron-star-black-hole binaries.