Two-mode coherent states for SU(1,1)circle times SU(1,1) - art. no. 033812

摘要

We study two types of coherent states for two-mode realizations of the direct product group SU(1,1)xSU(1,1) [which is locally isomorphic to SO(2,2)] constructed from the coupling of two single-mode realizations of SU(1,1). The basis states for the relevant representations of SU(1,1)xSU(1,1) are constructed from the SU(1,1) Clebsch-Gordon coefficients. From these, Perelomov and Barut-Giradello coherent stares ale constructed. Various properties of the states are discussed, and methods for generating them are proposed. Some of the states can be generated by the operation of beam splitters with two-mode squeezed vacuum states or pair coherent states as inputs. We show that a competitive two-channel two-photon process gives rise to states of the Barut-Girardello type as the steady-state solutions of the associated master equation for appropriate initial conditions. [References: 43]