摘要We analyse the optical four-wave mixing operator S and relate it to the two-mode Fresnel operator. It is shown that the direct product of the two-mode Fresnel operator and the single-mode Fresnel operator has a natural representation on the basis of a three-mode entangled state, which is constructed by S and a beam splitter transform.
Abstract：We analyse the optical four-wave mixing operator S and relate it to the two-mode Fresnel operator. It is shown that the direct product of the two-mode Fresnel operator and the single-mode Fresnel operator has a natural representation on the basis of a three-mode entangled state, which is constructed by S and a beam splitter transform.
[1] Scully M O and Zubairy M S 2000 Quantum Optics(London: Cambridge University) p 471 [2] Loudon R and Knight P L 1987 J. Mod. Opt. 34709 [3] Fan H Y and Lu H L 2005 Phys. Lett. A 334 132 [4] Fan H Y and Jiang N Q 2005 Physics Scripta 71277 [5] Ma S J and Hu L Y 2008 Commun. Theor. Phys. 50489 [6] Klauder J R and Skargerstam B S 1985 Coherent States(Singapore: World Scientific) [7] Fan H Y 2003 J. Phys. B: Quantum Semiclass 5 1 W\"{unsche A 1999 J. Phys. B: Quantum Semiclass 1 11 [8] Fan H Y, Lu H L and Fan Y 2006 Ann. Phys. 321480 [9] Ma S J and Hu L Y 2008 Commun. Theor. Phys. 491295 [10] Fan H Y and Hu L Y 2008 Chin. Phys. B 17 1640
2009, Vol. 26 
