Gain, Loss and the Shot-Noise Rule

Abstract

In this tutorial, a classical Langevin equation, a classical Markov equation, and a quantum Langevin equation are used to model the amplification and attenuation of an optical signal. Equations are derived for the photon-number moments (mean and variance). All three approaches produce the same moment equations. In the first approach, the moments of the noise sources must be specified (using physical insight), whereas in the second and third approaches, they are determined self-consistently and satisfy the shot-noise rule: The number variance is driven at a rate that equals the sum of the moduli of the rates in the mean equation.