QUANTUM NONDEMOLITION STROBOSCOPIC SCHEME FOR COUPLED HARMONIC-OSCILLATORS

The current generation of Weber gravitational wave antennae is a multimode system which makes use of a transducer resonant with the antenna and is expected to reach the standard quantum limit of sensitivity and possibly, by using quantum nondemolition measurement strategies, to surpass it. Quantum nondemolition measurement strategies have been studied until now only for a single harmonic oscillator. In this paper we generalize the stroboscopic quantum nondemolition strategy to coupled harmonic oscillators. We calculate the commutator of the relative displacement at different times for two and three coupled harmonic oscillators. It is shown that the commutator is time dependent in such a way as to retain values close to zero for a duration of the order of the uncoupled period of oscillations. The stability of this result with respect to frequency detunings is studied. The implications of this result for adapting the proposed quasistroboscopic quantum nondemolition schemes to coupled oscillators are also discussed.