General concepts in the theory of fluctuations and dissipation are reviewed and applied to examples in quantum optics. Brownian motion, Fokker-Planck and Langevin equations, and the Wiener-Khintchine theorem are reviewed, followed by a derivation and discussion of the fluctuation-dissipation theorem. The general problem of an oscillator coupled to a heat bath is revisited, as is the nonrelativistic theory of radiation reaction. The general ideas about fluctuations and dissipation developed in the first part of the chapter are then applied to the theory of the fundamental laser linewidth, the photon statistics of linear amplifiers and attenuators, the noise figure, amplified spontaneous emission, and the quantum theory of the beam slitter and homodyne detection.
Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier