Squeezed vacuum as an eigenstate of two-photon annihilation operator

We introduce the inverse annihilations and creation operators a-1 and a†-1 by their actions on the number states. We show that the squeezed vacuum exp[(1/2)ξa†2] vertical bar 0> and squeezed first number state exp[(1/2)ξa†2] vertical bar n=1> are respectively the eigenstates of the operators (a†-1 a) and (aa†-1) with eigenvalue ξ. (author). 8 refs