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Acta Optica Sinica

Photon statistics for two-photon processes

HE Long-qing

Published Jan 1, 1985• 0 citations
OpenAlex

Abstract

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.

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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.
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.
We derive the generating function for single molecule photon emission events within the context of the stochastically modulated optical Bloch equations. Statistical properties of single molecule photon counting experiments are deduced from a set of coupled differential equations only slightly more complicated than the Bloch equations themselves. This formulation allows for the study of photon bunching and antibunching within a single theoretical framework and provides a description of these behaviors that emphasizes the connection with single molecule experiments. Application is made to the spectroscopy of a chromophore coupled to a single two level system.
Exact solutions of the master equations which describe single-mode mmm-photon absorption and mmm-photon emission processes in a two-level atomic system are obtained using a density-matrix approach. Some aspects of the photon statistics, e.g., antibunching, are discussed.