Barut-Girardello coherent states for and and their macroscopic superpositions

Abstract

The Barut-Girardello (BG) coherent states (CS) representation is extended to the noncompact algebras and in (reducible) quadratic boson realizations. The BG CS take the form of multimode ordinary Schr?dinger cat states. Macroscopic superpositions of CS ( canonical CS, n = 1, 2, ...) are pointed out which are overcomplete in the N-mode Hilbert space and the relation between the canonical CS and the BG-type CS representations is established. The sets of and BG CS and their discrete superpositions contain many states studied in quantum optics (even and odd N-mode CS, pair CS) and provide an approach to quadrature squeezing, alternative to that of intelligent states. New subsets of weakly and strongly nonclassical states are pointed out and their statistical properties (first- and second-order squeezing, photon number distributions) are discussed. For specific values of the angle parameters and small amplitude of the canonical CS components, these states approach multimode Fock states with one, two or three bosons/photons. It is shown that eigenstates of a squared non-Hermitian operator (generalized cat states) can exhibit squeezing of the quadratures of A.