Coherent states for four-mode systems in quantum optics

Abstract

We introduce and study the properties of a class of coherent states for the group SU(1,1)×SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We also derive a phase space representation based on pair coherent states rather than the standard harmonic-oscillator coherent states. We discuss the utility of the resulting "bi-pair coherent states" in the context of four-mode interactions in quantum optics. © 1995 The American Physical Society.