Topics in LIGO-related physics: Interferometric speed meters and tidal work

In the quest to develop viable designs for third-generation interferometric gravitational-wave detectors (such as the Laser Interferometer Gravitational-Wave Observatory, LIGO), one strategy is monitoring the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. The most straightforward design for a speed-meter interferometer that accomplishes this is analyzed in Chapter 2. It is shown that in principle this design can beat the standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies. However, in practice, this specific speed meter requires exorbitantly high input light power.; Chapter 3 proposes a more sophisticated version of a speed meter. This new design requires modest input power and appears to be a fully practical candidate for third-generation detectors. It can beat the SQL over a broad range of frequencies (∼10 to 100 Hz in practice) by a factor h/h_SQL ∼ $WSQLcirc/Wc\; irc$. Here W_circ is the light power circulating in the interferometer arms and W_SQL ≃ 800 kW is the circulating power required to beat the SQL at 100 Hz. If squeezed vacuum (with a power-squeeze factor e−2 R) is injected into the interferometer's output port, the SQL can be beat with less laser power: h/h _SQL ∼ $WSQLcirc/Wc\; irce2R$. For realistic parameters (e2 R ≃ 10 and W_circ ≃ 800 kW), the SQL can be beat by a factor ∼3 from 10 to 100 Hz. By performing frequency-dependent homodyne detection on the output (using two kilometer-scale filter cavities), one can markedly improve the interferometer's sensitivity at frequencies above 100 Hz.; Chapter 4 is a contribution to the foundations for analyzing sources of gravitational waves. Specifically, it presents an analysis of the tidal work done on a self-gravitating body in an external tidal field. By examining the change in the mass-energy of the body as a result of the tidal field, it is shown that the work done is gauge invariant, while the body-tidal-field interaction energy contained within the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtonian theory, where the interaction energy depends on the localization of the gravitational energy, but the work done on the body is independent of that localization.