In the quest to develop viable designs for third-generation optical interferometric gravitational-wavedetectors, one strategy is to monitor the relative momentum or speed of the test-mass mirrors,rather than monitoring their relative position. The most straightforward design for a speed-meterinterferometer that accomplishes this is described and analyzed in Chapter 2. This design (dueto Braginsky, Gorodetsky, Khalili, and Thorne) is analogous to a microwave-cavity speed meterconceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meterand the optical interferometric speed meter is developed and used to show (in accord with the speedbeing a quantum nondemolition observable) that in principle the interferometric speed meter canbeat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over anarbitrarily wide range of frequencies . However, in practice, to reach or beat the SQL, this specificspeed meter requires exorbitantly high input light power. The physical reason for this is explored,along with other issues such as constraints on performance due to optical dissipation.
Chapter 3 proposes a more sophisticated version of a speed meter. This new design requiresonly a modest input power and appears to be a fully practical candidate for third-generation LIGO.It can beat the SQL (the approximate sensitivity of second-generation LIGO interferometers) overa broad range of frequencies (~ 10 to 100 Hz in practice) by a factor h/hSQL ~ √W^(SQL)_(circ)/Wcirc.Here Wcirc is the light power circulating in the interferometer arms and WSQL ≃ 800 kW is thecirculating power required to beat the SQL at 100 Hz (the LIGO-II power). If squeezed vacuum(with a power-squeeze factor e-2R) is injected into the interferometer's output port, the SQL canbe beat with a much reduced laser power: h/hSQL ~ √W^(SQL)_(circ)/Wcirce-2R. For realistic parameters(e-2R ≃ 10 and Wcirc ≃ 800 to 2000 kW), the SQL can be beat by a factor ~ 3 to 4 from 10to 100 Hz. [However, as the power increases in these expressions, the speed meter becomes morenarrow band; additional power and re-optimization of some parameters are required to maintain thewide band.] By performing frequency-dependent homodyne detection on the output (with the aidof two kilometer-scale filter cavities), one can markedly improve the interferometer's sensitivity atfrequencies above 100 Hz.
Chapters 2 and 3 are part of an ongoing effort to develop a practical variant of an interferometricspeed meter and to combine the speed meter concept with other ideas to yield a promising third-generation interferometric gravitational-wave detector that entails low laser power.
Chapter 4 is a contribution to the foundations for analyzing sources of gravitational waves forLIGO. Specifically, it presents an analysis of the tidal work done on a self-gravitating body (e.g., aneutron star or black hole) in an external tidal field (e.g., that of a binary companion). The changein the mass-energy of the body as a result of the tidal work, or "tidal heating," is analyzed using theLandau-Lifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that thework done on the body is gauge invariant, while the body-tidal-field interaction energy containedwithin the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtoniantheory, where the interaction energy is shown to depend on how one localizes gravitational energy,but the work done on the body is independent of that localization. These conclusions play a rolein analyses, by others, of the dynamics and stability of the inspiraling neutron-star binaries whosegravitational waves are likely to be seen and studied by LIGO.
