奇偶对相干态的维格纳函数和层析图函数

Wigner Functions and Tomogram Functions of Even and Odd Pair Coherent States

利用纠缠态η〉表象下的维格纳算符,重构了奇偶对相干态的维格纳函数。根据维格纳函数在相空间中随变量ρ和γ的变化规律,讨论了奇偶对相干态的非经典性质和量子干涉效应。研究发现,奇偶对相干态总呈现非经典性质,并且当q取奇数时,奇偶对相干态更容易出现非经典性质。奇偶对相干态的量子干涉效应的显著程度与q取值有关,但对于q的同一取值,奇对相干态的量子干涉效应更为显著。利用纠缠态η〉表象下的维格纳算符Δ1,2(ρ,γ)和纠缠态η,1τ,2τ〉的投影算符之间满足的拉东变换,获得了奇偶对相干态的量子层析图函数。

With the entangled state│η〉 representation of the Wigner operator, Wigner functions for even and odd pair coherent states （EOPCs） are reconstructed. In terms of variations of Wigner functions with the parameters and r in the phase space, nonclassical properties and quantum interference effects of EOPCSs are discussed. It is found that EOPCSs always exhibit nonclassical properties, especially when q is odd. Quantum interference effects of EOPCSs depend on the value of q, but for a fixed q quantum interference effects of the odd pair coherent state are more prominent. Based on the Radon transform between the entangled state │η〉 representation and the project operator of the entangled state│η,τ1,τ2〉, the quantum tomogram functions for the EOPCSs are obtained.