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Physical Review A

Comment on ‘‘Photon antibunching in a free-electron laser’’

G. Dattoli, Juan Carlos Gallardo, Alberto Renieri, A. Torre

Published Nov 1, 1985• 2 citations
Publisher

Abstract

In a recent paper of Lee [Phys. Rev. A 31, 1213 (1985)], it was stated that the photon-number distribution in a free-electron laser is always sub-Poissonian. This statement is clearly in contradiction with well-known published results. We show that in the recoilless approximation the photon statistics is Poissonian. However, for electron recoil different from zero, the photon-number distribution presents bunching (antibunching) for positive (negative) detuning parameter.

DOI
10.1103/physreva.32.3134

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In a recent paper of Lee [Phys. Rev. A 31, 1213 (1985)], it was stated that the photon-number distribution in a free-electron laser is always sub-Poissonian. This statement is clearly in contradiction with well-known published results. We show that in the recoilless approximation the photon statistics is Poissonian. However, for electron recoil different from zero, the photon-number distribution presents bunching (antibunching) for positive (negative) detuning parameter.
A perturbative solution to the difference-differential equation describing the time evolution of a free-electron laser based on the Bambini-Renieri Hamiltonian is obtained. This solution indicates that the photon number distribution is always sub-Poissonian as long as the perturbation approximation is valid. This photon antibunching becomes much more prominent as more photons are emitted; so it can enhance the coherent properties of the free-electron-laser radiation in a way that is very welcome.
A great deal of effort has been devoted during the last decade to the theory of nonclassical states of the radiation field. From a practical point of view some of the most interesting predictions of these theories concern the generation of light with sub-Poissonian photon counting statistics for which Such light is evidently less noisy than laser radiation with obvious implications for the improved performance of optical systems. When the temporal autocorrelation function of the photon counts increases as the delay time increases from zero the light is also said to be antibunched.
Photon anti-bunching, measured via the Hanbury-Brown-Twiss experiment, is one of the key signatures of quantum light and is tied to sub-Poissonian photon number statistics. Recently, it has been reported that photon anti-bunching or conditional sub-Poissonian photon number statistics can be obtained via second-order interference of mutually incoherent weak lasers and heralding based on photon counting [Phys. Rev. A92, 033855 (2015)10.1103/PhysRevA.92.033855; Opt. Express24, 19574 (2016)10.1364/OE.24.019574; https://arxiv.org/abs/1601.08161]. Here, we report theoretical analysis on the limits of manipulating conditional photon statistics via interference of weak lasers. It is shown that conditional photon number statistics can become super-Poissonian in such a scheme. We, however, demonstrate explicitly that it cannot become sub-Poissonian, i.e., photon anti-bunching cannot be obtained in such a scheme. We point out that incorrect results can be obtained if one does not properly account for seemingly negligible higher-order photon number expansions of the coherent state.