Incoherence, Quantum Fluctuations, and Noise

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Abstract
An examination is made of the relationship between the uncertainty principle and minimum amplifier noise. First, the concept of coherence is discussed, and an incoherence parameter is defined in terms of the uncertainty that enters into the uncertainty principle. Harmonic oscillator states are examined for coherence. The concept of noise is then discussed and contrasted with incoherence, noise referring to behavior in time of a single system while incoherence involving comparison among members of an ensemble. It is shown, with illustrations, that the two concepts are different, and that an incoherent field of a cavity mode need not exhibit noise. In particular, the zero-point field in a lossless cavity is not noise. The superposition of many incoherent effects, however, usually leads to noise. Spontaneous emission is examined both for coherence and noise. It is shown that the spontaneous emission field of a single molecule is incoherent but does not exhibit noise; the (low order) spontaneous emission from a molecular beam, however, does constitute noise. Spontaneous emission from complex systems is also discussed. The origin of fundamental noise in an amplifier is investigated and is shown to come from spontaneous emission by the amplification mechanism. It is concluded that fundamental noise cannot be determined by a consideration of quantum fluctuations of—or by the application of the uncertainty principle to—the electromagnetic field only, as has been done in several recent articles. The physical significance of the zero-point field is analyzed, and is shown to lie in a formal contribution to spontaneous emission by the mechanism coupled to the field, provided this mechanism is treated quantum mechanically.