Impossibility of naively generalizing squeezed coherent states

Abstract

Pertinent properties of the unitary operators that create coherent states and squeezed coherent states are discussed. We show that certain generalizations of squeezed coherent states do not exist. This is accomplished by demonstrating that for the generalized squeeze operators ${U}_{k}=\mathrm{exp}(i{A}_{k})=\mathrm{exp}[{z}_{k}{({a}^{\ifmmode\dagger\else\textdagger\fi{}})}^{k}+i{h}_{k\ensuremath{-}1}\ensuremath{-}{({z}_{k})}^{*}{a}^{k}]$, $〈0|{U}_{k}|0〉$ diverges, $k>2$. This implies that $|0〉$ is not an analytic vector of ${A}_{k}$ for all $k>2$, where ${h}_{k\ensuremath{-}1}$ is a Hermitian polynomial in $a$ and ${a}^{\ifmmode\dagger\else\textdagger\fi{}}$ up to powers of ($k\ensuremath{-}1$).