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Optica Acta International Journal of Optics

Quantum Statistics of Scattering between Relativistic Electrons and Interfering Laser Fields in the Zero-gain Approximation

Vlasta Peřinová, Jan Peřina, A. Lukš

Published Sep 1, 1985• 2 citations
Publisher

Abstract

The quantum-statistical properties are examined for two independent laser beams, forming interference fringes, which are in interaction with a particle (electron) beam treated as a ‘two-step’ reservoir system. Using the master equation and generalized Fokker-Planck equation techniques, the photon statistics are derived in closed form. Anticorrelation effects are found, indicating competition between modes, but no sub-poissonian or squeezing effects are possible.

DOI
10.1080/713821841

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The quantum-statistical properties are examined for two independent laser beams, forming interference fringes, which are in interaction with a particle (electron) beam treated as a ‘two-step’ reservoir system. Using the master equation and generalized Fokker-Planck equation techniques, the photon statistics are derived in closed form. Anticorrelation effects are found, indicating competition between modes, but no sub-poissonian or squeezing effects are possible.
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.
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A unified approach to the quantum statistics of single-mode linear processes described by the general Fokker-Planck equation and the generalized initial superposition of coherent and chaotic fields is developed to reveal the common traits in the mathematical models of several quantum optical systems. Processes such as the degenerate parametric amplification and the harmonic oscillator eventually coupled to the thermal or rigged reservoir are involved as special cases. A sufficient condition for the validity of the master equation is formulated as its being formally independent of possible reservoirs. The dependence of non-classical phenomena such as the sub-Poisson photon statistics and squeezing on the drift and diffusion coefficients is discussed.
Starting from the master equation for density operator of the atoms and the field mode and applying the operator method of adiabatic elimination of the atomio variables developed by Haake and Lewenstein, we derived the Fokker-Planck Equation for Wigner function of the lightfield and its steady-state solution. With a Gaussian approximation to the solution, analytical and numerical results on the photon statistics for various pumping strengths are obtained. Comparisons with previous works are made.
The conditions are examined under which interference effects should be observable in the superposition of two light beams derived from independent sources. The quantum-mechanical description of these effects differs from the classical description principally in that it is necessarily based on expectation values of the light intensity at one or more space-time points. It is shown that pure states of the radiation field which are not energy states give rise to interference effects, but in that case the two beams cannot meaningfully be described as statistically independent. For a realistic description mixed states have to be introduced, when the expectation value of the intensity gives no indication of interference effects. On the other hand, the intensity correlation at two space-time points is a periodic function of the separation of the points and indicates the presence of transient interference effects. The effects become readily observable only when the average photon occupation number of each cell of phase space is appreciably greater than 1, and this explains why laser beams were needed for the experimental observations. It is pointed out that, even in these experiments, each photon may be regarded as interfering only with itself.