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Optica Acta International Journal of Optics

On the Photon Statistics and Squeezing in the Scattering between Relativistic Electrons and Interfering Electromagnetic Fields

Vlasta Peřinová, Jan Peřina, A. Lukš, C. Sibilia, M. Bertolotti

Published Jul 1, 1984• 6 citations
Publisher

Abstract

Conditions are found under which photon antibunching, subpoissonian behaviour and squeezing are possible in interfering radiation fields interacting with electron beams. Using an equation of motion for moments derived from the generalized Fokker-Planck equation, it is shown that these fully quantum phenomena can occur in a high-gain limit of stimulated scattering under particular conditions.

DOI
10.1080/713821573

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Physical Review A•Jul 1, 1985•25 citations
Conditions are found under which photon antibunching, subpoissonian behaviour and squeezing are possible in interfering radiation fields interacting with electron beams. Using an equation of motion for moments derived from the generalized Fokker-Planck equation, it is shown that these fully quantum phenomena can occur in a high-gain limit of stimulated scattering under particular conditions.
The quantum statistical properties of independent light beams are considered, forming interference fringes, which are in interaction with a particle (electron) beam treated as a two-level system. Using the master equation and the generalized Fokker-Planck equation techniques, the photocount statistics are derived and it is demonstrated that the whole, initially coherent, radiation field remains coherent for all times while single modes exhibit two-peak bistable behaviour, varying their photon statistics from Poisson statistics to some intermediate statistics for coherent and chaotic radiation.
The stimulated Compton scattering of photons between two oppositely propagating coherent lights by a relativistic electron moving along the same line is studied analytically. The system is described in a moving frame so that the electron becomes nonrelativistic and the frequencies of the two lights coincide. Except for the replacement of the static wiggler by a propagating light, our system is essentially the same as a free-electron laser working in the Compton regime and described in the usual Bambini-Renieri frame. The Q representation of two-mode coherent states is adopted to describe the radiation fields, and the electron states are expressed in terms of plane waves. A perturbative solution, with the quantum recoil of the electron as the perturbation parameter, of the time evolution of the system is carried out far beyond the first order. It demonstrates that two nonclassical effects, i.e., squeezing and photon antibunching, occur as results of the scattering. It also confirms once more the fact that quantum recoils play the exclusive role in generating such nonclassical photon states. A very important improvement in the present treatment is that the electron part of the density matrix is traced out before the calculation of the squeezing effect. As a result, it is found that there is no squeezing if the initial state is a vacuum. This is, perhaps, a significant new discovery. Many-electron effects are ignored in the present study.
A theory is developed for the interaction of coherent electromagnetic (EM) radiation with a free electron gas and for the influence of the plasma on the photon statistics of the radiation field. Two important possibilities for generating squeezed states are shown: Squeezed states can be generated by the interaction of a one-mode laser with a plasma in a cavity; squeezed states can be generated by transmitting coherent radiation through the plasma. The maximal squeezing of the radiation obtained in the latter case is equal to the reciprocal of the dielectric constant of the plasma. Inside the plasma the EM field is represented by quasiphotons. Their dispersion relations are derived by using Bogoliubov transformations together with a self-consistency requirement for the motion of the electrons interacting with these quasiphotons. The squeezing processes are found to be strong when the frequency of the radiation is a little above the plasma frequency. By adding a constant magnetic field in the direction of propagation of the EM wave different amounts of squeezing are obtained for right- and left-circularly polarized EM waves.