Orthonormalized eigenstates of cubic and higher powers of the annihilation operator

We have studied the orthonormalized eigenstates of the higher powers ${\mathit{a}}^{\mathit{k}}$ (k≥3) of the annihilation operator a and their properties. Our conclusions are as follows: (1) The orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ construct a complete representation with respect to α. (2) None of the orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ shows the squeezing effect in the usual sense. (3) All of the eigenstates of ${\mathit{a}}^{\mathit{k}}$ show the antibunching effect.