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Journal of Modern Optics

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

Vlasta Peřinová, Jan Peřina

Published Jun 1, 1981• 7 citations
Publisher
DOI
10.1080/716099557

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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 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.
Abstract A study of ‘high temperature’ entangled states in a system of two parametrically coupled quantum oscillators placed into independent thermal baths is performed taking into account partially coherent parametric pump. Processes in an open system are considered based on the Heisenberg–Langevin formalism. We obtain a closed system of equations for the averaged quadratic correlation functions in quantum stochastic problem as a result of Markov processes approximation. On the basis of numerical calculations the dynamics of the logarithmic negativity, which is the measure of entanglement in the system, is investigated. It is shown that the partial coherence of the parametric pump makes the lifetime of the entangled states finite. The threshold characteristics of the formation and existence of these states are specified.