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

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.