涉及双变量Hermite多项式的新二项式定理及应用  

New Generalized Binomial Theorems Involving Two-variable Hermite Polynomials Via Quantum Optics Approach and Their Applications

作　　者：孟祥国[1] MENG Xiang -guo(School of Physical Science and Information Engineerig,Shandong Provincial Key Laboratory of Optical Communication Science and Technology,Liaocheng University,Liaocheng 252059,Chin)

机构地区：[1]聊城大学物理科学与信息工程学院、山东省光通信科学与技术重点实验室,山东聊城252059

出　　处：《聊城大学学报（自然科学版）》2018年第2期66-71,86,共7页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11347026);山东省自然科学基金(ZR2016AM03、ZR2017MA011)

摘　　要：利用量子光学方法,将普通的二项式定理推广到涉及双变量Hermite多项式情况,解析推导出几个新的广义二项式定理及其推论.作为应用,解析证明多光子扣除压缩态a^mb^ne^(sa+b++ra++tb+)|00〉等价于实验上易于调控的非高斯纠缠信息源,即以双变量Hermite多项式为权重的非高斯量子态;而且发现自旋相干态的Wigner函数恰好正比于Laguerre多项式.We extend the ordinary binomial theorem to the case which involves two-variable Hermite polynomials Hl,k（x,y）in the context of quantum optics,and analytically obtain several new generalized binomial theorems and their corollaries.As their applications,we analytically prove that the multiple-photon-subtracted squeezed state a^mb^ne^（sa＋b＋＋ra＋＋tb＋）｜00〉 is equivalent to the Hermite-polynomialweighted quantum state serving as an easily controlled non-Gaussian entangled information resource,and the Wigner functions of the spin coherent states are respectively the Laguerre polynomials.

关 键 词：新二项式定理 纠缠态表象 有序算符内积分法 WIGNER函数 

分 类 号：O413.1[理学—理论物理]