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Physics Letters A

Quantum non-demolition observables for a weber-type gravitational wave antenna coupled to a resonant transducer

Roberto Onofrio

Published Jan 1, 1987• 9 citations
Publisher
DOI
10.1016/0375-9601(87)90253-2

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A review of current efforts to approach and to surpass the fundamental limit in the sensitivity of the Weber type gravitational wave antennae is reported. Applications of quantum non-demolition techniques to the concrete example of an antenna resonant with the transducer are discussed in detail. Analogies and differences from the framework of the squeezed states in quantum optics are discussed.

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Quantum nondemolition stroboscopic scheme for coupled harmonic oscillators

Roberto Onofrio, Alessandro Rioli

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.

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Continuous Non-Demolition Observation, Quantum Filtering and Optimal Estimation

Belavkin, V P

A quantum stochastic model for an open dynamical system (quantum receiver) and output multi-channel of observation with an additive nonvacuum quantum noise is given. A quantum stochastic Master equation for the corresponding instrument is derived and quantum stochastic filtering equations both for the Heisenberg operators and the reduced density matrix of the system under the nondemolition observation are found. Thus the dynamical problem of quantum filtering is generalized for a noncommutative output process, and a quantum stochastic model and optimal filtering equation for the dynamical estimation of an input Markovian process is found. The results are illustrated on an example of optimal estimation of an input Gaussian diffusion signal, an unknown gravitational force say in a quantum optical or Weber's antenna for detection and filtering a gravitational waves.

•Sep 29, 2005•23 citations
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.
A quantum stochastic model for an open dynamical system (quantum receiver) and output multi-channel of observation with an additive nonvacuum quantum noise is given. A quantum stochastic Master equation for the corresponding instrument is derived and quantum stochastic filtering equations both for the Heisenberg operators and the reduced density matrix of the system under the nondemolition observation are found. Thus the dynamical problem of quantum filtering is generalized for a noncommutative output process, and a quantum stochastic model and optimal filtering equation for the dynamical estimation of an input Markovian process is found. The results are illustrated on an example of optimal estimation of an input Gaussian diffusion signal, an unknown gravitational force say in a quantum optical or Weber's antenna for detection and filtering a gravitational waves.