The New Multipartite Squeezing Operator and Some of its Properties

In this paper, we introduce a pair of mutually conjugate multipartite entangled state representations for defining the squeezing operator of entangled multipartite S-n (lambda) which involves an n-mode bosonic operator realization of the SU(1,1) Lie algebra. This operator squeezes the multipartite entangled state in a natural way. We discuss the transform properties of a(j) and a(j)(dagger) under the operation of Sn (lambda) and derive the interaction Hamiltonian which can generate such an evolution. In addition, the corresponding multipartite squeezed vacuum state vertical bar lambda > is obtained. Based on this, the variances of the n-mode quadratures in vertical bar lambda > are evaluated and the violation of the Bell inequality for vertical bar lambda > is examined by using the formalism of Wigner representation.