Generalized Fresnel operators corresponding to optical Fresnel diffraction and the squeezed states  

作　　者：LI HongQi REN TingQi 

机构地区：[1]Department of Physics, Qufu Normal University, Qufu 273165, China [2]Department of Physics, Heze University, Heze 274015, China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2012年第8期1345-1350,共6页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A16);the Specialized Research Fund for the Doctoral Program of Higher Education China (Grant No.20103705110001)

摘　　要：Corresponding to optical Fresnel diffraction, we show that the exponential quadratic operator exp is actually a generalized single-mode Fresnel operator （GFO） in compact form, where [Q,P]=ih. We also demonstrate that exp{iα[（Q1＋Q2）2＋（p1-P2）2]＋iβ[（Q1-Q2）2＋（p1＋p2）2]＋iy（Q1P2＋Q2P1）} is a two-mode GFO. Their disentangling formula and normal ordering form are derived with the use of technique of integration within an ordered product （IWOP） of operators and the coherent state representation. The squeezed states generated by these two GFOs are obtained.Corresponding to optical Fresnel diffraction, we show that the exponential quadratic operator exp{ i[ P2+ Q2+ (PQ+QP)]/2} is actually a generalized single-mode Fresnel operator (GFO) in compact form, where [Q,P]=i . We also demonstrate that exp{i [(Q1+Q2)2+(P1 P2)2]+i [(Q1 Q2)2+(P1+P2)2]+i (Q1P2+Q2P1)} is a two-mode GFO. Their disentangling formula and normal ordering form are derived with the use of technique of integration within an ordered product (IWOP) of operators and the coherent state representation. The squeezed states generated by these two GFOs are obtained.

关 键 词：Fresnel diffraction single-mode Fresnel operator two-mode Fresnel operator IWOP technique 

分 类 号：O436.1[机械工程—光学工程] O431[理学—光学]