一种分解指数算符的简洁方法

提出一种新的分解指数算符的方法,这种方法不仅简单易懂,而且有助于找到更多的算符恒等式.     

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

We newly construct two mutually-conjugate tripartite entangled state representations,based on which we propose the formulation of three-mode entangled fractional Fourier transformation(EFFT) and derive the transformation kernel.The EFFT’s additivity property is proved and the eigenmode of EFFT is derived.As an application,we calculate the EFFT of the three-mode squeezed vacuum state.     

Preserving Coherence of Coherent State Studied via Weyl-Wigner Correspondence

By means of the Weyl correspondence and the explicit normally ordered expression of the Wigner operator we convert the time evolution equation of coherent states, governed by some Hamiltonian operators, into seeking for consistent solution of a set of evolution equtions of classical variables which can meet the requirment that an initial coherent state remains coherent all the time.     

Fractional squeezing-Hankel transform based on the induced entangled state representations

Based on the fact that the quantum mechanical version of Hankel transform kernel(the Bessel function) is just the transform between |q, r and(s, r′|, two induced entangled state representations are given, and working with them we derive fractional squeezing-Hankel transform(FrSHT) caused by the operator e~(-iα)(a_1~?a_2~?+a_1a_2)e~(-iπa_2~?a_2), which is an entangled fractional squeezing transform operator. The additive rule of the FrSHT can be explicitly proved.     

A New Kind of Integration Transformation in Phase Space Related to Two Mutually Conjugate Entangled-State Representations and Its Uses in Weyl Ordering of Operators

Based on the two mutually conjugate entangled state representations ｜ξ〉 and ｜η〉, we propose an integration transformation in ξ - η phase space ∫∫ d^2ξd^2η/π^2e^（ξ-η）（η^＊ -v^＊）-（η-v）（ξ^＊-μ^＊）F（ξ^＊,μ^＊） F（ξ, η）≡D（μ,v）, and its inverse trans- formation, which possesses some well-behaved transformation properties, such as being invertible and the Parseval theorem. This integral transformation is a convolution, where one of the factors is fixed as a special normalized exponential function. We generalize this transformation to a quantum mechanical case and apply it to studying the Weyl ordering of bipartite operators, regarding to （Q1 -Q2） （P1 - P2） ordered and simultaneously （P1 ＋ P2） （Q1＋ Q2） ordered operators.     

Optical wavelet-fractional squeezing combinatorial transform

By virtue of the method of integration within ordered product(IWOP)of operators we find the normally ordered form of the optical wavelet-fractional squeezing combinatorial transform(WFrST)operator.The way we successfully combine them to realize the integration transform kernel of WFr ST is making full use of the completeness relation of Dirac’s ket–bra representation.The WFr ST can play role in analyzing and recognizing quantum states,for instance,we apply this new transform to identify the vacuum state,the single-particle state,and their superposition state.     

From fractional Fourier transformation to quantum mechanical fractional squeezing transformation

By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α→ tanh α,sin α→ sinh α,we find the quantum mechanical fractional squeezing transformation(FrST) which satisfies additivity.By virtue of the integration technique within the ordered product of operators(IWOP) we derive the unitary operator responsible for the FrST,which is composite and is made of e~(iπa~+a/2) and exp[iα/2(a~2 +a~(+2)).The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.     

由新二项式定理导出在Schwinger玻色实现下的原子相干态的波函数

用相干态表象和有序算符内的积分技术,我们导出了一个关系到含有双变量厄米多项式的二项式定理,用它可以导出在Schwinger玻色实现下的原子相干态在纠缠态表象中的波函数,并且得到一个新的算符恒等式。