Quantum limits on resonant-mass gravitational-radiation detectors

Abstract

The methods of quantum detection theory are applied to a resonant-mass gravitational-radiation antenna. Quantum sensitivity limits are found which depend strongly on the quantum state in which the antenna is prepared. Optimum decision strategies and their corresponding sensitivities are derived for some important initial states. The linear detection limit (${E}_{min}\ensuremath{\sim}\ensuremath{\hbar}\ensuremath{\omega}$) is shown to apply when the antenna is prepared in a coherent state. Preparation of the antenna in an excited energy eigenstate or in a state highly localized in position or momentum space leads to increased sensitivity. A set of minimum-uncertainty states for phase-sensitive detection is introduced.