Topics in LIGO-Related Physics: Interferometric Speed Meters and Tidal Work
<p>In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors, 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...
| Summary: | <p>In the quest to develop viable designs for third-generation optical interferometric gravitational-wave
detectors, 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-meter
interferometer that accomplishes this is described and analyzed in Chapter 2. This design (due
to Braginsky, Gorodetsky, Khalili, and Thorne) is analogous to a microwave-cavity 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 gravitational-wave 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.</p>
<p>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 third-generation LIGO.
It can beat the SQL (the approximate sensitivity of second-generation LIGO interferometers) over
a broad range of frequencies (~ 10 to 100 Hz in practice) by a factor h/h<sub>SQL</sub> ~ √W^(SQL)_(circ)/W<sub>circ</sub>.
Here W<sub>circ</sub> is the light power circulating in the interferometer arms and W<sub>SQL</sub> ≃ 800 kW is the
circulating power required to beat the SQL at 100 Hz (the LIGO-II power). If squeezed vacuum
(with a power-squeeze factor e<sup>-2R</sup>) is injected into the interferometer's output port, the SQL can
be beat with a much reduced laser power: h/h<sub>SQL</sub> ~ √W^(SQL)_(circ)/W<sub>circ</sub>e<sup>-2R</sup>. For realistic parameters
(e<sup>-2R</sup> ≃ 10 and W<sub>circ</sub> ≃ 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 re-optimization of some parameters are required to maintain the
wide band.] By performing frequency-dependent homodyne detection on the output (with the aid
of two kilometer-scale filter cavities), one can markedly improve the interferometer's sensitivity at
frequencies above 100 Hz.</p>
<p>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 gravitational-wave detector that entails low laser power.</p>
<p>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 self-gravitating 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 mass-energy of the body as a result of the tidal work, or "tidal heating," is analyzed using the
Landau-Lifshitz 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 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 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 neutron-star binaries whose
gravitational waves are likely to be seen and studied by LIGO.</p> |
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