Time evolution, squeezing and entanglement for an optical frequency up-conversion with a driving term

Abstract

By using the Lewis–Riesenfeld quantum invariant theory, an explicit analytical solution for the time evolution operator of the frequency up-conversion system with a driving term is obtained. It is then used to investigate mainly the influence of the driving term, frequency detuning, and the initial states on the quantum statistical properties of the output-coupled fields. It is found that the time evolution for the general up-conversion system can efficiently convert a low-frequency squeezed light into a high-frequency squeezed light, in the case of zero-detuning, but the squeezed effect of the output fields is independent of the driving term. It is also shown that there is an entanglement between the signal and idler output photons for the general up-conversion system.

Keywords:

• time evolution
• Lewis–Riesenfeld invariant theory
• squeezing
• entanglement
• frequency up-conversion

Acknowledgements

This work was supported by the Natural Science Foundation of Hunan Province of China under Grant No. 07JJ3123, the Science and Technology Program of Hunan Province of China under Grant No. 2009FJ3072, the Scientific Research Fund of Hunan Provincial Education Department of China under Grant No. 06B004, and the Construct Program of the Key Discipline in Changsha University of Science and Technology.