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Journal of Modern Optics

Quantum Statistics of the Optical Parametric Process for Arbitrary Initial States

Jan Peřina

Published Nov 1, 1993• 7 citations
Publisher

Abstract

Photon statistics and non-classical behaviour of light produced in the optical parametric process are studied in the approximation of small fluctuations around a stationary point. The depletion of the pump mode is included. An initial generalized superposition of a coherent state and noise as well as the influence of reservoir noise and internal losses are considered.

DOI
10.1080/09500349314552141

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Photon statistics and non-classical behaviour of light produced in the optical parametric process are studied in the approximation of small fluctuations around a stationary point. The depletion of the pump mode is included. An initial generalized superposition of a coherent state and noise as well as the influence of reservoir noise and internal losses are considered.
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.
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.