量子光学中的双模幺正相位算符及其经典对应  

Two-mode Unitary Phase Operator in Quantum Optics and Its Classical Correspondence

作　　者：展德会 范洪义[2] ZHAN De-hui;FAN Hong-yi(College of Mechanic and Electronic Engineering,Wuyi University,Wuyishan 354300,China;Department of Material Science and Engineering,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]武夷学院机电工程学院,福建武夷山354300 [2]中国科学技术大学材料科学与工程系,安徽合肥230026

出　　处：《量子光学学报》2021年第4期267-270,共4页Journal of Quantum Optics

基　　金：武夷学院引进人才科研启动经费(YJ201808)。

摘　　要：众所周知,传统定义的单模相位算符不是幺正算符。我们选择另一种定义相算符的途径,鉴于相位的测量总是相对的,就像势能的测量是相对于零势能位置一样,所以我们在双模空间中引入相位算符。具体做法是在纠缠态表象的基础上提出幺正的双模相位算符,它的本征值就是经典位相。在此理论框架内,相角对应的正则共轭算符是光子数差算符。并且给出了数差-相测不准关系以及此相位算符的Weyl-Wigner经典对应,发现它是双变数相空间(q1,p1;q2,p2)中的相exp[iargtan(p1+p1)/(q1-q1)]。Since the traditional definition of single-mode phase operator is not unitary,we attempt to identify a new definition.In view of the phase measurement is always relative to another reference phase,like the potential energy is always relative to zero-point position,we select to introduce phase operator in two-mode Fock space,which is the concrete way to propose a unitary two-mode phase operator operating on the two-mode entangled state representation.Its eigenvalue is just classical phase,and whose phase angle is the conjugate to photon-difference operator.We also present the number-difference-phase uncertainty relationship as well as Weyl-Wigner classical correspondence of the phase operator,which is the phase exp[i arg tan (p1+p1)/(q1-q1)]in the two variable-pair coordinate-momentum space(q1,p1;q2,p2).

关 键 词：双模幺正相位算符 有序算符内的积分技术 数差-相测不准关系 Weyl-Wigner经典对应 

分 类 号：O431[机械工程—光学工程]