(ed.). Gravitational waves (IOP, 2001)(422s).

The physics of resonant mass detectors 37small noise in a large bandwidth (∼1000 Hz) near f 0 (note that this band ismuch larger than f Q). Today typical bandwidths of realizable amplifiersare 1 Hz, but in the very near future it is hoped to extend these to 10 Hz, andeventually to 100 Hz.• Quantum limit. According to the Heisenberg uncertainty principle, the zeropointvibrations of a bar with a frequency of 1 kHz have rms amplitude〈δl 2 〉 1 2quant =( )1Ð 2∼ 4 × 10 −21 m.2π MfThis is bigger than the expected signal, and comparable to the thermal limitover 1 ms. It represents the accuracy with which one can measure theamplitude of vibration of the bar. So as soon as current detectors improvetheir thermal limits, they will run into the quantum limit, which must beovercome before a signal at 10 −21 can be seen with such a detector. Oneway to overcome this limit is by increasing the size of the detector and evenby making it spherical. This increases its mass dramatically, pushing thequantum limit down below 10 −21 .Another way around the quantum limit is to avoid measuring δl, but insteadto measure other observables. After all, the goal is to infer the gravitationalwaveamplitude, not to measure the state of vibration of the bar. It is possibleto define a pair of conjugate observables that have the property that one ofthem can be measured arbitrarily accurately repeatedly, so that the resultinginaccuracy of knowing the conjugate variable’s value does not disturb thefirst variable’s value. Then, if the first variable responds to the gravitationalwave, the gravitational wave may be measured accurately, even though thefull state of the bar is poorly known. This method is called ‘back reactionevasion’. The theory was developed in a classic paper by Caves et al [8].However, no viable schemes to do this have been demonstrated for bardetectors so far.3.3.1 New bar detectors and their capabilitiesResonant-mass detectors are limited by properties of materials and, as we havejust explained, they have their best sensitivity in a narrow band around theirresonant frequency. However, they can usefully explore higher frequencies (above500 Hz), where the interferometer noise curves are rising (see earlier figures).From the beginning, bars were designed to detect bursts. If the burstradiation carries significant energy in the bar’s bandwidth, then the bar can dowell. Standard assumptions about gravitational collapse suggest a signal with abroad spectrum to 1 kHz or more, so that most of the sensitive bars today wouldbe suited to observe such a signal. Binary coalescence has a spectrum that peaksat low frequencies, so bars are not partiularly well suited for such signals. Onthe other hand, neutron-star and stellar-mass black-hole normal modes range in