But sensing is not perfect: amplifiers introduce noise, and this makes small amplitudes
harder to measure. The amplitudes of vibration are largest in the resonance band near
, so amplifier noise limits the detector sensitivity to gravitational wave frequencies
near
. But if the noise is small, then the measurement bandwidth about
can be
much larger than the resonant bandwidth
. Typical measurement bandwidths are
10 Hz, about 104 times larger than the resonant bandwidths, and 100 Hz is not out of the
question [61].
It is not impossible to do better than the quantum limit. The uncertainty principle only sets the limit above if a measurement tries to determine the excitation energy of the bar, or equivalently the phonon number. But one is not interested in the phonon number, except in so far as it allows one to determine the original gravitational wave amplitude. It is possible to define other observables that also respond to the gravitational wave and can be measured more accurately by squeezing their uncertainty at the expense of greater errors in their conjugate observable [111]. It is not yet clear whether squeezing will be viable for bar detectors, although squeezing is now an established technique in quantum optics and will soon be implemented in interferometric detectors (see below).
Reliable gravitational wave detection, whether with bars or with other detectors, requires coincidence
observations, in which two or more detectors confirm each other’s findings. The principal bar detector
projects around the world formed the International Gravitational Event Collaboration (IGEC) [204] to
arrange for long-duration coordinated observations and joint data analysis. A report in 2003 of an analysis
of a long period of coincident observing over three years found no evidence of significant events [52]. The
ALLEGRO bar [28] at Louisiana State University made joint data-taking runs with the nearby LIGO
interferometer, setting an upper limit on the stochastic gravitational-wave background at around 900 Hz of
[17]. More recently, because funding for many of the bar detector projects has
become more restricted, only two groups continue to operate bars at present (end of 2008): the
Rome [317] and Auriga [58] groups. The latest observational results from IGEC may be found
in [56].
It is clear from the above discussion that bars have great difficulty achieving the sensitivity goal of 10–21. This limitation was apparent even in the 1970s, and that motivated a number of groups to explore the intrinsically wide-band technique of laser interferometry, leading to the projects described in Section 4.3.1 below. However, the excellent sensitivity of resonant detectors within their narrow bandwidths makes them suitable for specialized, high-frequency searches, including cross-correlation searches for stochastic backgrounds [120]. Therefore, novel and imaginative designs for resonant-mass detectors continue to be proposed. For example, it is possible to construct large spheres of a similar size (1 to 3 m diameter) to existing cylinders. This increases the mass of the detector and also improves its direction-sensing. One can in principle push to below 10–21 with spheres [118]. A spherical prototype called MiniGRAIL[260] has been operated in the Netherlands[182]. A similar prototype called the Schenberg detector[183] is being built in Brazil [23]. Nested cylinders or spheres, or masses designed to sense multiple modes of vibration may also provide a clever way to improve on bar sensitivities [88].
While these ideas have interesting potential, funding for them is at present (2008) very restricted, and the two remaining bar detectors are likely to be shut down in the near future, when the interferometers begin operating at sensitivities clearly better than 10–21.
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