Impossibility of naively generalizing squeezed coherent states
Robert A. FisherChemistry Division, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545Michael Martin NietoChemistry Division, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545Vernon D. SandbergChemistry Division, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545
1984en
ABI
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 ($k\ensuremath{-}1$).
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