Quantum Statistics of Masers and Attenuators

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Abstract
We have studied the statistical properties of a single mode of a radiation field in interaction with a very large number of material quantum systems. The quantum systems are assumed to be in internal thermal equilibrium at some positive or negative temperature. Under appropriate conditions we find linear solutions to Heisenberg's equations of motion for the field. We then make use of the quantum characteristic function to evaluate the statistical properties of the field during the interaction. A general conclusion which may be drawn is as follows. If at some initial instant the field can be resolved into the sum of the Gaussian zero-point field and an independent "input" field, then at later times the total field may be resolved into the sum of three independent fields; the unaltered zero-point field, the amplified or attenuated input field, and a Gaussian thermal or spontaneous emission field.