Classical and Quantized Fields in Optical Parametric Interactions

M. A. Jafarizadeh, Ali Adibi, Abasalt Rostami

K. Dechoum, Trevor W. Marshall, Emilio Santos

We study spontaneous parametric processes starting from the quantized field equations in the Heisenberg picture using the common approximation of treating the laser pump as classical. After a (standard) linearization procedure we pass to the Wigner representation and the process becomes formally equivalent to the parametric interaction of two incoming zero-point modes with a pumping laser wave coupled by an optically nonlinear medium. Then the treatment of parametric down conversion and parametric up conversion are described by the Maxwell equations and look like a parametric amplification of the vacuum field. The fourth-order correlation function between the signal and idler fields is obtained in a form that makes for easy comparison with experimental results.

Rakesh Kumar

J Leach, C Elliot Strimbu, Perry R. Rice

We investigate intensity cross-correlation functions for two cavity QED systems. These are a driven optical cavity containing a single two-level atom interacting with a single mode of the cavity field with quantized centre of mass motion, and a two-level atom in an optical parametric oscillator. We find analytic results in the weak driving field limit using quantum trajectory theory. We find large violations of inequalities that must be satisfied by classical fields. One of these inequalities is well known, g (2) ij (τ) ≤ √g (2) jj (0)g (2) jj (0), where i and j denote two modes of the field. We also derive a new inequality that cross-correlations must satisfy, |g (2) ij (τ) - 1| 2 ≤ |(g (2) ii (0) - 1)(g (2) jj (0) - 1)|. Large violations of classical inequalities and asymmetrical behaviour in delay time τ are found in complimentary regimes for the cavity QED system with quantized centre of mass motion. They always exist for the two-level atom inside an optical parametric oscillator.

Joseph Akeyo Omolo

This book provides exact analytical solutions to some of the most challenging and exciting problems in quantum optics, ranging from the theory of multi-level atom-radiation field interaction to multi-photon parametric processes in non-linear quantum optics. The problems are generally reduced to two-state dynamics for which detailed reader-friendly solution procedures displaying every important mathematical step are presented. The exact discrete and equivalent continuous variable time evolution operators generate explicitly specified time evolving spin / helicity coherent state vectors and Schroedinger wave functions describing the general quantum states of light, including dissipative dynamics. Photon polarization state dynamics under semi-classical and fully quantized parametric interactions is clearly presented. All the results in fully quantized parametric processes in non-linear quantum optics are new and are appearing for the first time in the literature. The book is particularly useful for graduate level teaching and as a resource text for research in linear and non-linear quantum optics.

Andrei I. Maimistov, Ashat M. Basharov