Comparative performance of two-, three-, and four-mode gravitational radiation detectors

The sensitivity of two-, three-, and four-mode resonant gravitational radiation detectors is calculated. We employ a detailed noise model and we show how to parametrize multimode detectors so that their performances can be directly compared. Numerical results are presented for several cases which assume experimentally realistic values for losses in the detector system. We determine the optimal configurations which minimize the noise temperature for each detector. The dependences of their noise temperatures due to variations from their optimal conditions are explored. The signal-to-noise ratios for optimally configured detectors are plotted to show their effective bandwidths. Our results show that optimally configured three- and four-mode detectors perform significantly better than two-mode detectors. Based on realistic loss estimates, current detectors operating at 4 K can be made capable of detecting gravitational pulses with $h=7\mathrm{}\times {10}^{-20\mathrm{}}$. 50-mK detectors presently under construction are capable of achieving $h=6\mathrm{}\times {10}^{-21\mathrm{}}$. From our optimization results we point out that detectors with more than four modes would be difficult to construct and would provide little additional improvement in sensitivity.