Phase and amplitude uncertainties in multimode heterodyning

Operator representations are developed for simultaneous phase and squared amplitude measurements made via optical heterodyne detection on a multimode radiation field. A high mean field uncertainty principle is proven for these measurements under the condition that the signal and image band states are independent, and the image band has zero mean. No such limitation applies when arbitrary signal/image band dependence is permitted, as is illustrated with appropriate multimode squeezed-state radiation. This work generalizes an earlier single-mode study.