SQUEEZED STATES, METAPLECTIC GROUP, AND OPERATOR MOBIUS TRANSFORMATIONS

We present an analysis, based on the metaplectic group Mp(2), of the r ecently introduced single-mode inverse creation and annihilation opera tors and of the associated eigenstates of different two-photon annihil ation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle rela tion to the two unitary irreducible representations of Mp(2) is brough t out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demo nstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both an alytically and numerically.