New Three-Mode Einstein-Podolsky-Rosen Entangled State Representation and Its Application in Squeezing Theory

By extending the Einstein-Podolsky-Rosen bipartite entanglement to the tripartite case, we construct the common eigenvector of the tripartite center-of-mass coordinate and two mass-weighted relative momenta, which is a new entangled state of continuum variables. The classical dilation transform of variables in such a state induces a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.