We apply the quantum regression theorem and the input-output relation of the single-ended cavity to the linearized systems, and formulate the optical quantum nondemolition (QND) criteria. In an application, we discuss squeezing and QND nature for a crossed Kerr dispersive model.
Methods for the enhancement of optical quantum nondemolition (QND) measurements are discussed. We review the use of meter squeezing as a QND enhancement tool and present a method of QND enhancement using an electro-optic feed-forward amplifier. By applying a linearized theory it is shown that these techniques work very well together. The combined effect of these enhancement methods is modeled for two QND systems, a squeezed light beam splitter and an optical parametric amplifier. We also discuss the conflict between the normal QND criteria and QND systems that involve noiseless amplification. We use an additional parameter to quantify the problem. A method for correcting the effects of noiseless amplification is discussed and modeled. We also discuss a special case of QND that eliminates the optical interaction between the meter and signal input beams. This system is shown to be a very effective QND device.
The paper is concerned with the formulation of a continuous-time quantum-mechanical filter. In a previous paper (Ong et al., 1984), the invertibility of a quantum system coupled to a weak time-dependent classical field was studied. The physical system is modeled as an infinite-dimensional bilinear system. Necessary and sufficient conditions of invertibility were derived under the assumption that the output observable is a quantum nondemolition observable (QNDO), characterized by the classical property that its expected value is equal to its measured value. In this paper necessary and sufficient conditions are developed for an observable to qualify as a QNDO; if in addition the criteria for invertibility are met, the given observable defines a quantum nondemolition filter (QNDF). The associated filtering algorithm thus separates cleanly into the choice of output observable (a QNDO) and the choice of procedure for processing the measurement outcomes. This approach has the advantage over previous schemes that no optimization is necessary. Applications to demodulation of optical signals and to the detection and monitoring of gravitational waves are envisioned.
We analyze schemes for performing quantum nondemolition (QND) measurements in optical cavities. We consider three schemes: (1) measurement of a quadrature phase amplitude using a parametric process, (2) measurement of a quadrature phase amplitude using the optical Kerr effect in a nonlinear fiber, and (3) measurement of the photon number also using the Kerr effect in a fiber. We show that in the second scheme an enhancement of the QND effect may be obtained by making the cavity finesse for the signal larger than that for the probe.