Effects of Electron Shot Noise and Quantum Field Fluctuations on the Photon Statistics of the Coherent Spontaneous Harmonic Radiation

We present a theoretical analysis of the statistical fluctuations in the coherent spontaneous harmonic radiation (CSHR) generated by a free electron laser (FEL) under the conditions applicable in a previously published experiment [1] where sub-Poisson optical fluctuations were observed. The numerical analyses presented here document the conclusion that the emission of CSHR can serve as a useful test bed for analyses of the nonclassical aspects of electron beam formation and radiation. Two possible explanations for the observed fluctuations in the CSHR are investigated as limiting physical mechanisms: the fluctuations in the number density of the radiating electrons, the so-called "shot noise," and the quantum fluctuations in the radiation field. When the uncertainties in the radiation field are considered as the only noise source as in the "quasi-classical" analysis, the statistical fluctuations in the CSHR would result in Poisson statistics. On the other hand, when the electron shot noise is regarded as the only noise contribution as assumed by the shot-noise model, we find numerically and analytically that the fluctuations, as characterized by the Fano factor, would be much smaller than those due to the quantum uncertainties in the radiation field in the "quasi-classical" analysis. The experimentally observed fluctuations are larger than those due to shot noise, but smaller than those due to quantum fluctuations in the field. Hence, neither the classical shot-noise model nor the quasi-classical analysis can explain the experimental results. Given the results presented in this report, it is clear that attention must be given to the other phenomena-including the quantum fluctuations in the electromagnetic field and the nonclassical electron correlation, which contributed to the observed laser fluctuations.