湮灭算符任意次幂本征态的Wigner函数

Wigner Functions for Eigenstates of Arbitrary Power of Annihilation Operators

用在Fock态表象下的Wigner函数重构了湮灭算符任意次幂本征态的Wigner函数.分析了这些函数在相空间中的分布规律,并据此讨论了湮灭算符任意次幂的本征态的非经典特性.结果表明,Wigner函数的分布与湮灭算符本征值的大小有关;湮灭算符1次幂的本征态(即相干态)为准经典态(其Wigner函数的取值总是非负的),而其高次幂的本征态则具有明显的非经典特性(其Wigner函数均出现了负值).

Wigner functions for the eigenstates of arbitrary power of annihilation operators were reconstructed using their expressions in Fock presentations. The distribution of the reconstructed Wigner functions in phase spaces was analyzed, based on which the nonclassical properties of these eigenstates were discussed. The results show that, the distribution of the Wigner functions for these eigenstates depend on the eigenvalues of the annihilation operators; the eignestates of the annihilation operators of the first power （i. e. , coherent states） are quasiclassical （their Wigner functions are always non-negative ）, and those of higher powers obviously exhibit nonclassical properties （their Wigner functions may become negative）.