Quantum nondemolition measurements via quadratic coupling

Abstract

We consider making quantum nondemolition measurements on a harmonic oscillator by coupling it to an oscillator readout system using a four-wave-mixing interaction. The quantum nondemolition variable of interest appears as a nonlinear function of the number operator. It has the form ${\hat{D}}_1\mathrm{}\left(t\right)=cos\left(\chi a^{†}at\right)$. A sequence of measurements of this operator may be made with completely predictable results. The possible use of this system to detect gravitational radiation is suggested.