Based on the technique of integration within an ordered product of nonlinear Bose operators, a new kind of nonlinear coherent entangled state, which exhibits both the property of coherent state and quantum entanglement, is constructed and its application in squeezing is discussed.
The coherent entangled state |β, x〉 is proposed in Fock space, which exhibits both the properties of the coherent and entangled states. The |β, x〉 makes up a new quantum mechanical representation, and the completeness relation of |β, x〉 is proved by virtue of the technique of integral within an ordered product of operators. The corresponding Schmidt decomposition of |β, x〉 is investigated. Furthermore, a feasible experimental scheme of |β, x〉 is presented, and generalized P-representation is constructed in the coherent entangled state |β, x〉.
A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product, which exhibits both the properties of a coherent state and an entangled state, and spans a complete and orthonormal representation. The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation. Moreover, a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters. As applications of this four-mode continuous variable coherent-entangled state, a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.
With use of the newly proposed bipartite coherent entangled state (generated by asymmetric beamsplitter) and by projecting both the classical symplectic transform and the classical dilation one in phase space onto quantum mechanical Hilbert space, we construct a six-parameter squeezing operator, which has its own squeezing property, in a natural way. The derivation is implemented on the basis of the technique of integration within an ordered product of operators and the completeness of the bipartite coherent entangled state.