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Journal of Physics Conference Series

Parametric amplification and up-conversion of optical image in coupled nonlinear optical processes

E. V. Makeev, A. S. Chirkin

Published Apr 1, 2006• 2 citations
Publisher

Abstract

We develop quantum theory of process of the parametric optical image amplification at high-frequency pumping which is accompanied by up - conversion one. Such interactions can be implemented by two coupled three-frequency optical processes. The theory developed takes into account the diffraction effect and the difference of group velocities of interacting waves. The expressions for mean photon numbers and noise figures of the interacting waves are obtained and the dependence of these parameters on the interaction length are examined.

DOI
10.1088/1742-6596/36/1/018

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A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.
Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.
The teleportation of entangled optical images is for the first time considered. The scheme offered is based on process of four-partite state generation in coupled parametric interactions realizing in an aperiodic nonlinear photonic crystal. The coupled nonlinear optical process consists of one parametric down-conversion process which is followed by two up-conversion ones. We study nonclassical properties of the generated fields by analyzing the EPR correlations for different pairs of modes and carry out the comparison of the EPR correlations of the input and images output images and also calculate fidelity of the teleportation exploiting the covariance matrices of the images. We take into account the difference of spatial frequency bandwidths of the entangled images and fields generated in the coupled process. It has been established that under certain parameters of the scheme one can be obtain rather high fidelity of the teleportation and good preservation of the quantum correlations of the input images for all details of the images.
Quasi-phase-matched consecutive three-frequency interactions between waves with nonmultiple frequencies are considered. The quantum theory of parametric amplification is developed in the approximation of an undepleted low-frequency pump field in the Heisenberg representation. It is shown that, with a certain choice of quasi-phase-matching orders, the regime of exponential increase in the mean number of photons of interacting waves can be realized. In this case, the photon statistics of generated waves is super-Poissonian one. The correlation of fluctuations of numbers of photons with different frequencies is also considered.