Nondemolition measurements in gravitational-wave experiments

In connection with the problem of raising the sensitivity of gravitational-wave experiments, a study is made of the quantum limitations that can arise when a classical force is measured by the response of a quantum oscillator. Following up work done by the groups at Caltech and Moscow, and also by Unruh, attention is drawn to a class of nondemolition measurements that are free of quantum limitations on the accuracy with which a force can be measured. It is shown that such measurements can be realized in the case of observation of operators that are quantum integrals of the motion of the investigated system. The physical reasons for the presence or absence of a quantum sensitivity limit for an arbitrary choice of an observable are elucidated; they reside in the degree of uncertainty of the initial state of the system. In the case of integrals of the motion, this uncertainty can be reduced to zero by an initial precise measurement and subsequently remains zero (quasinondemolition measurement). It is shown further that one can make a choice of observables that do not depend on the initial state of the quantum system at all but retain information about an external influence. In this case, a precise continuous measurement can be realized without special preparation of the state of the system (strictly nondemolition measurement). The general rule for the construction of such an optimal variable is identical to the recommendations of the quantum theory of filtration