Ultimate sensitivity limit of a resonant gravitational wave antenna using a linear motion detector

The sensitivity of a resonant-mass gravitational radiation antenna coupled to a motion detector with given noise properties is calculated in detail. It is shown that the quantum-mechanical limit of linear amplifier performance implies an important restriction on the sensitivity for any system using a linear motion detector. For a signal frequency ${\omega }_a$, this fundamental limit requires that the gravitational radiation pulse be capable of driving the antenna from rest to an energy level exceeding $2\hslash {\omega }_a$.