N00N态的Wigner函数及N00N态作为输入的量子干涉

Wigner function of N00N state and quantum interference with N00N state as input

根据量子力学相干态表象下的Wigner函数公式,推导了N00N态在相空间的Wigner分布函数的解析表达式.基于相空间方法,研究N00N态作为输入的量子干涉.推导了与输入光场参数和干涉仪参数相关的输出端探测光子概率的解析表达式,并进行了数值分析.从分析结果发现,当相移参数取0和π时,输出量子态仍为N00N态.当输入2002态时,输出结果总是2002态,与相移参数无关.随着N的增加,条件概率随相位的分布峰数一般只有一个,两个,三个或四个,且峰变得更窄.这些结果可以为实验提供理论指导.

Using the formula of Wigner function in coherent representation, we have obtained the analytical expression for Wigner function of NOON state. Based on phase space method, we study the quantum interference with NOON state as input. We derive the analytical expression of conditional probability related with the input parameter N and phase parameter Ф and analyze it numerically. It is shown that, when Ф is 0 or π, the output is just NOON state. It is also shown that, for 2002 state as input, the output must be 2002 state, which is independent of phase parameters. Moreover, as the number of input photon N increases, the phase probability distributions remain to have one, two, three and four peaks and get narrower. All these results can offer theoretical reference for experiments.