Quantum Statistics of Homodyne and Heterodyne Detection

Abstract

There are three basic techniques that may be employed to detect optical radiation: photon detection, homodyne detection, and heterodyne detection (see Fig. 1). From the photocounting theory of Kelley and Kleiner [1], one can readily show that photon detection, in the limit of unity quantum efficiency, can be interpreted as the quantum measurement of the total photon number operator N for any quantum state of a quasi-monochromatic input field. No similar quantum description is as yet available for homodyne or heterodyne detection. In this paper, we shall derive the abstract quantum description of homodyne detection. Because heterodyne detection involves the more complicated concept of simultaneous measurement of non-commuting observables, its quantum description will only be briefly discussed.