Citation
Purdue, Patricia Marie (2003) Topics in LIGORelated Physics: Interferometric Speed Meters and Tidal Work. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0YKJSW34. https://resolver.caltech.edu/CaltechTHESIS:03062014090212906
Abstract
In the quest to develop viable designs for thirdgeneration optical interferometric gravitationalwave detectors, one strategy is to monitor the relative momentum or speed of the testmass mirrors, rather than monitoring their relative position. The most straightforward design for a speedmeter interferometer that accomplishes this is described and analyzed in Chapter 2. This design (due to Braginsky, Gorodetsky, Khalili, and Thorne) is analogous to a microwavecavity speed meter conceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meter and the optical interferometric speed meter is developed and used to show (in accord with the speed being a quantum nondemolition observable) that in principle the interferometric speed meter can beat the gravitationalwave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies . However, in practice, to reach or beat the SQL, this specific speed 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 requires only a modest input power and appears to be a fully practical candidate for thirdgeneration LIGO. It can beat the SQL (the approximate sensitivity of secondgeneration LIGO interferometers) over a broad range of frequencies (~ 10 to 100 Hz in practice) by a factor h/h_{SQL} ~ √W^(SQL)_(circ)/W_{circ}. 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 (the LIGOII power). If squeezed vacuum (with a powersqueeze factor e^{2R}) is injected into the interferometer's output port, the SQL can be beat with a much reduced laser power: h/h_{SQL} ~ √W^(SQL)_(circ)/W_{circ}e^{2R}. For realistic parameters (e^{2R} ≃ 10 and W_{circ} ≃ 800 to 2000 kW), the SQL can be beat by a factor ~ 3 to 4 from 10 to 100 Hz. [However, as the power increases in these expressions, the speed meter becomes more narrow band; additional power and reoptimization of some parameters are required to maintain the wide band.] By performing frequencydependent homodyne detection on the output (with the aid of two kilometerscale filter cavities), one can markedly improve the interferometer's sensitivity at frequencies above 100 Hz.
Chapters 2 and 3 are part of an ongoing effort to develop a practical variant of an interferometric speed meter and to combine the speed meter concept with other ideas to yield a promising third generation interferometric gravitationalwave detector that entails low laser power.
Chapter 4 is a contribution to the foundations for analyzing sources of gravitational waves for LIGO. Specifically, it presents an analysis of the tidal work done on a selfgravitating body (e.g., a neutron star or black hole) in an external tidal field (e.g., that of a binary companion). The change in the massenergy of the body as a result of the tidal work, or "tidal heating," is analyzed using the LandauLifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that the work done on the body is gauge invariant, while the bodytidalfield interaction energy contained within the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtonian theory, 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 role in analyses, by others, of the dynamics and stability of the inspiraling neutronstar binaries whose gravitational waves are likely to be seen and studied by LIGO.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Physics 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Group:  TAPIR, Astronomy Department, LIGO 
Thesis Committee: 

Defense Date:  18 June 2002 
Record Number:  CaltechTHESIS:03062014090212906 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:03062014090212906 
DOI:  10.7907/0YKJSW34 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  8107 
Collection:  CaltechTHESIS 
Deposited By:  Benjamin Perez 
Deposited On:  06 Mar 2014 17:33 
Last Modified:  12 Feb 2021 00:33 
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