Quantum Theory of Optical Homodyne and Heterodyne Detection
Matthew J. Collett, R. Loudon, Crispin W. Gardiner · Journal of Modern Optics · 1987
The theory of balanced homodyne and heterodyne detection is developed for inputs in which the signal field is in an arbitrary quantum state and the local-oscillator field is in a highly excited coherent state. Exact expressions are derived for the photocount moment-generating functions in the special case of a coherent signal. For more general signals, the first two moments of the photocount probability distribution are determined. The moments are evaluated for the examples of a coherent signal with a chaotic noise component, and for squeezed light derived from a degenerate and from a non-degenerate parametric amplifier. The corresponding moments for direct detection are obtained so that comparisons can be made. The Kelley-Kleiner photocount distribution formula is adapted to balanced detection schemes. Light beams are characterized throughout by their energy fluxes, and the theory accordingly describes steady-state experiments.