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Optica Acta International Journal of Optics

Quantum Statistics of Quadratic Optical Parametric Processes with Intense Coherent or Stochastic Pumping: Photon statistics

Vlasta Peřinová, Jan Peřina

Published Jun 1, 1981• 40 citations
Publisher

Abstract

The photon statistics of quadratic parametric two-mode processes are derived starting from the results of the first part of this paper. A general theory is presented and particular processes are discussed. Assuming the initial field to be coherent, fluctuations of the pumping field are taken into account. The effects of antibunching and anticorrelation of photons on the photon distribution, its factorial moments, fluctuations in modes and their correlations for the amplification process are demonstrated and their dependence on levels of pumping field fluctuations is shown.

DOI
10.1080/716099559

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The photon statistics of quadratic parametric two-mode processes are derived starting from the results of the first part of this paper. A general theory is presented and particular processes are discussed. Assuming the initial field to be coherent, fluctuations of the pumping field are taken into account. The effects of antibunching and anticorrelation of photons on the photon distribution, its factorial moments, fluctuations in modes and their correlations for the amplification process are demonstrated and their dependence on levels of pumping field fluctuations is shown.
A unified treatment of the description of the statistical dynamical properties of two-mode quadratic optical parametric processes with intense coherent or stochastic pumping (parametric amplification, frequency conversion, second subharmonic generation, etc. as special cases are involved) including the lossy mechanism is developed. The Heisenberg-Langevin equations are derived and their solutions are used to obtain the quantum characteristic functions and the corresponding quasidistributions. The Fokker-Planck equation approach is adopted as well and the equivalence of both the approaches is explicitly found.
The quantum theory of the statistical properties and the photocount statistics of intense radiation in Raman scattering are presented making use of the coherent-state techniques. Both the Heisenberg-Langevin and Fokker-Planck equations approaches are developed. The existence of the conditional Glauber-Sudarshan quasi-distribution is also discussed. The time dependences of the photocount distribution and its factorial moments are demonstrated in the case of stimulated scattering and anticorrelation and antibunching of scattered photons are found.
The photon statistic of two-photon processes is treated for the general case of two-level systems. After generalizing the generating-function method, we derived the generating function with parameter r (atomic population ratio), its partial differential equation, and equations of factoril moments as well as equations of correlation functions. Analytical solutions were obtained for various values of r. Curves of n and g(2) versus τ and r were deduced for three kinds of initial fields. Both the effect of r on photon antibunching and characteristics photon statistics for two-photon amplifiers are discussed. The photon superbunching is proposed as one of the criteria for two-photon amplification.
A theory of a quantum amplifier based on two-photon transitions is presented. The model consists of an assemblage of atoms interacting with a single mode of the light field via two-photon absorption and emission. The treatment is quantum mechanical, and the emphasis is on the photon-statistical aspects of the problem. Difference-differential equations for the density matrix of the field mode are derived. The equations are solved for a special case. Differential equations for the expectation vaues of the number of photons and of the field amplitudes, and for their higher statistical moments, are also obtained. Approximate solutions for the average number of photons are found, and the effect of the amplification process on the statistical fluctuations of the number of photons and the field amplitudes is discussed. The results of this study suggest that such an amplifier does not have the coherence properties of a laser amplifier because it tends to increase the statistical fluctuations of the field.