This paper gives the autocorrelation function of thermal noise when the zero point energy noise term is neglected. Such a situation applies to maser amplifiers.
Fluctuations in the amplification and absorption of waves by quantum processes are considered. Assuming for each quantum the probability (per unit time) a of producing another quantum, probability b of being absorbed, and assuming a probability c that a new quantum is introduced, a set of differential equations is obtained. By solving these equations, a complete expression for the probability of distribution of quanta is obtained, as well as expressions for the average values and fractional fluctuation. The expressions developed are applied in particular to maser-type amplifiers, and certain fluctuations in the amplification of electromagnetic waves are pointed out which are important when their quantum character becomes significant. This condition can occur in maser-type amplifiers, where thermal and extraneous noises may be very small. For such an amplifier, a is proportional to the number of excited molecules, whereas b consists of a term proportional to the number of molecules in the ground state plus terms due to certain other losses. The noise temperature of a maser-type traveling-wave amplifier is the "effective temperature" a ( a - b ) -1 h ν/ k . In superregenerative and regenerative amplifiers using resonant cavities, the noise temperature is rather similar, if losses through the input coupling hole are excluded from b . In any case, the limiting noise for an ideal amplifier corresponds to a classical noise temperature of h ν/ k .
The contribution of the saturation field to the noise figure of a three-level maser is calculated. It is shown that the effect is very small, under ordinary circumstances.Certain aspects of spontaneous-emission noise are considered. It is shown that the spontaneous-emission equivalent temperature for a free-electron vacuum-tube amplifier is one-half that of a maser.The possibility of eliminating spontaneous-emission noise is considered and it is concluded that more general quantum-mechanical amplifiers can in principle be constructed which will not have spontaneous-emission noise.