Generation of orthonormalized eigenstates of the operatorak(fork≥3) from coherent states and their higher-order squeezing

In this paper, we study first the connection of the k orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ with coherent states, then, according to the higher-order squeezing defined by Zhang et al. [Phys. Lett. A 150, 27 (1990)], study the properties of the higher-order squeezing of k orthonormalized eigenstates. Our results show that the k orthonormalized eigenstates can be represented as a linear superposition of k coherent states, and that all of them are minimum uncertainty states of the operators ${\mathit{Z}}_1$(N) and ${\mathit{Z}}_2$(N) (N=mk, m=1,2,3, . . .) for even and odd k, and all of them have the Nth-order squeezing [N=(m+1/2)k, m=0,1,2, . . .] for even k.