Noise in homodyne and heterodyne detection

Quantum-mechanical calculations of the mean-square fluctuation spectra in optical homodyning and heterodyning are made for arbitrary input and local-oscillator quantum states. In addition to the unavoidable quantum fluctua-tions, it is shown that excess noise from the local oscillator always affects homodyning and, when it is broadband, also heterodyning. Both the quantum and the excess noise of the local oscillator can be eliminated by coherent subtraction of the two outputs of a 50-50 beam splitter. This result also demonstrates the fact that the basic quan-tum noise in homodyning and heterodyning is signal quantum fluctuation, not local-oscillator shot noise. Quantum noise in optical heterodyning and homodyn-ing is usually analyzed under the assumption that the photodetector output is conditionally Poisson'- 4 (con-ditioned on the input signal). This quantum noise is frequently supposed to arise from local-oscillator (LO) shot noise. However, in a fully quantum-mechanical analysis, Yuen and Shapiro5-7 have shown that it ac-tually arises from the signal quantum fluctuation; in particular, homodyning and heterodyning are realiza