Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

Abstract

We establish a new three-mode entangled state representation ∣ β,ζ 〉θ of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare ∣ β,ζ 〉θ. Based on ∣ β,ζ 〉θ a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.