where
h
is Planck's constant,
c
is the speed of light and
the wavelength of the laser light. In the case of systems with
cavities in the arms where the number of effective reflections is
approximately 50, fluctuations in the amplitude of the light
arise immediately after the beamsplitter where vacuum
fluctuations enter into the system. These are then enhanced by
the power build up effects of the optical cavities. In this
case
Evaluating this at 10 Hz, for powers of around
W after the beamsplitter and masses of 30 kg,
indicates an amplitude spectral density for each mass of
. Given the target sensitivity of the detector at 10 Hz in
Fig.
3
of approximately
which translates to a motion of each test mass of close to
it is clear that radiation pressure may be a significant
limitation at low frequency. Of course the effects of the
radiation pressure fluctuations can be reduced by increasing the
test masses, or by decreasing the laser power at the expense of
deproving sensitivity at higher frequencies.
It should be noted that as discussed in [33, 22, 23] and [64] for a simple Michelson system, the optimisation of laser power to minimise the combined effect photon shot noise and radiation pressure fluctuations allows one to reach exactly the sensitivity limit predicted by the Heisenberg Uncertainty Principle, in its position and momentum formulation. An extension of this analysis to a system with cavities in the arms has been carried out by one of the authors [50] with the same result and it seems likely to be true for the more complicated optical systems using power and signal recycling also.
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Gravitational Wave Detection by Interferometry (Ground
and Space)
Sheila Rowan and Jim Hough http://www.livingreviews.org/lrr-2000-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |