Four-mode coherent entangled state as an entanglement of two bipartite coherent entangled states

摘要

By introducing a four-mode unitary operator U = exp[-i lambda(X1P2 + X2P3 + X3P4 + X4P1)], we show how a four-mode coherent entangled state can be generated by entangling a two bipartite coherent entangled state. The corresponding squeezed vacuum state U vertical bar 0000 > in four-mode Fock space is derived by virtue of the technique of integration within ordered production of operators, which exhibits the standard squeezing for the four-mode quadratures. A new ideal quantum mechanical representation vertical bar alpha, beta, gamma > is constructed from U vertical bar 0000 > in the limit of infinite squeezing, which possesses the properties of both coherent and entangled states. The entanglement involved in vertical bar alpha, beta, gamma > is explained. A scheme for generating vertical bar alpha, beta, gamma > is presented.