Spontaneous Emission Noise in Quantum Electronics

Abstract

On this auspicious occasion I thought it might be a good idea to revisit the question of spontaneous emission noise in quantum electronics and photonics. Low noise was one of the important attributes originally ascribed to masers, and so it was important to understand the effects of spontaneous emission noise in maser amplifiers and oscillators. One of the first papers to discuss the problem in detail was the well-known 1957 paper by Shimoda, Takahashi, and Townes, entitled “Fluctuations in Amplification of Quanta with Application to Maser Amplifiers” [1]. This paper, which calculated energy fluctuations, is still referenced in works on photonic communications. Another important early discussion, also in 1957, was by R. V. Pound in a paper entitled “Spontaneous Emission and the Noise Figure of Maser Amplifiers” [2]. This paper extended the Nyquist-Johnson formulation of thermal noise in electric circuits to encompass the case of negative resistances and negative temperatures such as are encountered in maser amplifiers. It demonstrated that all such noise can be identified as spontaneous emission noise. Many other papers have been written on the subject, but the fundamental nature of spontaneous emission noise and how it can most easily be treated to solve real-world problems does not seem even now to be well understood by many people. The challenge is to discuss the subject in simple and yet rigorous ways. This turned out to be more than I could manage properly before the aforementioned auspicious occasion was past, but here is a beginning. I claim little originality here, perhaps just a fresh look. My discussion does not involve any of the details of the matter-radiation interaction, but they are not really needed. The only things that are required to establish the necessary fundamentals of this problem are the fluctuation-dissipation theorem, and Planck’s law of radiative thermal equilibrium.