Orthonormalized Eigenstates of Operator a k and Their Squeezing Properties

Abstract

The orthonormalized eigenstates of the higher powers, a ^k (k  3), of the annihilation operator a were obtained. We discuss the mathematical properties and the squeezing properties of the orthonormalized eigenstates of a ^k. We prove that these orthonormalized eigenstates of a ^k construct a complete representation, that none of them have the squeezed effect in the usual sense, and that higher-order squeezing can be found.