ABCD rule involved in the product of general SU(1,1) squeezing operators and quantum states' Fresnel transformation

被引:8
作者
Fan, Hong-Yi [1 ]
Hu, Li-Yun [1 ]
机构
[1] Shanghai Jiao Tong Univ, Dept Phys, Shanghai 200030, Peoples R China
基金
中国国家自然科学基金;
关键词
D O I
10.1016/j.optcom.2007.11.033
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
Base on our preceding paper [H.Y. Fan, H.L. Lu, Opt. Commun. 258 (2006) 51] we find that there exists ABCD rule involved in the product of general SU(1,1) squeezing operators, which can be considered as the quantum optics countpart of the ABCD rule in classical optics. Both one- and two-mode cases are considered, especially, the ABCD theorem embodied in the Fresnel transformation of two-mode number state is exhibited. (C) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码:1629 / 1634
页数:6
相关论文
共 25 条
[1]   Could Fresnel optics be quantum mechanics in phase space? [J].
Crasser, O ;
Mack, H ;
Schleich, WP .
FLUCTUATION AND NOISE LETTERS, 2004, 4 (01) :L43-L51
[2]   'Nonclassical' states in quantum optics: a 'squeezed' review of the first 75 years [J].
Dodonov, VV .
JOURNAL OF OPTICS B-QUANTUM AND SEMICLASSICAL OPTICS, 2002, 4 (01) :R1-R33
[3]  
Erdelyi A, 1953, HIGHER TRANSCENDENTA
[4]   Entangled states, squeezed states gained via the route of developing Dirac's symbolic method and their applications [J].
Fan, HY .
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2004, 18 (10-11) :1387-1455
[5]   Operator ordering in quantum optics theory and the development of Dirac's symbolic method [J].
Fan, HY .
JOURNAL OF OPTICS B-QUANTUM AND SEMICLASSICAL OPTICS, 2003, 5 (04) :R147-R163
[6]   EIGENVECTORS OF 2 PARTICLES RELATIVE POSITION AND TOTAL MOMENTUM [J].
FAN, HY ;
KLAUDER, JR .
PHYSICAL REVIEW A, 1994, 49 (02) :704-707
[7]  
FAN HY, 1995, PHYS REV A, V51, P3343, DOI 10.1103/PhysRevA.51.3343
[8]   HERMITE POLYNOMIAL STATES IN 2-MODE FOCK SPACE [J].
FAN, HY ;
YE, X .
PHYSICS LETTERS A, 1993, 175 (06) :387-390
[9]   Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations [J].
Fan, HY ;
Lu, HL ;
Fan, Y .
ANNALS OF PHYSICS, 2006, 321 (02) :480-494
[10]   2-mode Fresnel operator and entangled Fresnel transform [J].
Fan, HY ;
Lu, HL .
PHYSICS LETTERS A, 2005, 334 (2-3) :132-139