Using the newly constructed bipartite coherent entangled state, we derive the corresponding squeezing operators, which have their own squeezing properties, in a natural way. The derivation is based on the method of integration within an ordered product of operators and the completeness relation of the bipartite coherent entangled state.
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.
The coherent-intermediate-entangled state |α, x ⟩ λ,ν is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The |α, x ⟩ λ,ν makes up a new quantum mechanical representation, and the completeness relation of |α, x ⟩ λ,ν is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state |α, x ⟩ λ,ν and the Schmidt decomposition of |α, x ⟩ λ,ν is investigated.
We show that the best way to study the relationship between quantum entanglement and quantum squeezing for the multimode case is through constructing the new n -pair entangled state representation . The explicit form of the 2 n -mode squeezing operator which squeezes the n -pair entangled state can be directly derived via the transition from to where M is an n × n complex matrix, and the technique of integration within an ordered product of operators. We also analyze the squeezing properties of the 2 n -mode squeezed state for M being Hermitian, and obtain the variances of the 2 n -mode quadrature operators in the 2 n -mode squeezed vacuum state with a concise result; the condition for reaching the minimum of the uncertainty relationship is also investigated.
For two unequal-mass particles, we construct the entangled state representation and then derive the corresponding squeezing operator. This squeezing operator has a natural realization in the entangled state representation, which exhibits the intrinsic relation between squeezing and quantum entanglement. This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings. The maximum squeezing occurs when the two particles possess equal mass. When the two particles' mass difference becomes large, the component of the two single-mode squeezings becomes dominant.