Wideband Dual Sphere Detector of Gravitational Waves

Abstract

We present the concept of a sensitive and broadband resonant mass gravitational wave detector. A massive sphere is suspended inside a second hollow one. Short, high-finesse Fabry-Perot optical cavities read out the differential displacements of the two spheres as their quadrupole modes are excited. At cryogenic temperatures, one approaches the standard quantum limit for broadband operation with reasonable choices for the cavity finesses and the intracavity light power. A molybdenum detector, of overall size of 2 m, would reach spectral strain sensitivities of 2 3 10 223 Hz 21͞2 between 1000 and 3000 Hz. This stems, however, from the noise performance of the employed readout systems. A general analysis of the problem, valid for any linear detector, has been given in Ref. [2]. Secondary resonant masses are linked to the main resonant mass to efficiently couple the signal amplitude to the final readout, but then the bandwidth is limited to a fraction of the main resonator frequency. Such a coupling is poorer the smaller the total number n of resonators, and, correspondingly, the bandwidth decreases with n. To open the bandwidth, one would have to use multimode systems [3,4] with n $ 3, but, until now, only two-(mechanical) mode systems have worked their way into operating detectors, giving a fractional bandwidth Df͞f ø 0.1.However, if a single mechanical resonator were driven only by its thermal noise and by a signal force, the signal to noise ratio would be independent of frequency, and thus the band would open up provided enough signal amplitude can be coupled to the final readout. The possibilities offered nowadays by optomechanical systems are such that the interplay between the back-action of the radiation pressure and the photon counting noise in a high finesse, high power Fabry-Perot cavity would allow enough signal coupling [5] to get broadband operation at the Standard Quantum Limit (SQL) (see below).We have been attracted by the possibilities offered by optical readout systems, as vigorously developed for interferometric GW detectors, and more recently applied in connection with cryogenic bar GW detectors [6,7]. We take a Fabry-Perot optical cavity as the motion sensor. In a system under development [7], the length of the sensor cavity is compared to that of a second cavity, separately kept, which acts as a reference. We do not take into account here the noise introduced by the reference cavity, assuming for simplicity that it is negligible. With a sensor cavity length of the order of centimeters, there is no loss of signal strength for finesses F as high as the highest attainable with current technology, F 10 6 , for GW in the kHz range. So we have considerable freedom to vary the finesse and the light power P incident on the cavity, in search for optimal conditions at a chosen frequency, which do not demand unreasonable values for these parameters.Let us then turn to the primary mechanical resonator, whose motion is directly related to the incoming GW. We take into consideration both solid and hollow sp...

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