量子相空间分布函数与压缩相干态表示间的变换关系∗

摘要

A new operator representation, called squeezed coherent state representation, is introduced since Husimi operator has the form of squeezed coherent state. We fisrt introduce its specific integral expression. Whenκ=1, this representation is reduced to the usual P function. As an example, we calculate the squeezed coherent state representation for thermal field to illustrate a difference between P function and the squeezed coherent state representation. Especially, in order to better apply this representation to quantum optics, we reveal the integral transformations between the squeezed coherent state representation, respectively, and the following three functions: Wigner function, Q function, and Husimi function.%基于Husimi算符具有压缩相干态投影子形式，首先介绍了一个新的量子算符表示，即压缩相干态表示。当高斯展宽参数κ=1时，该函数约化为通常的P函数。作为例子，研究了热态的压缩相干态表示，通过图示说明了压缩相干态表示与P函数的区别。为更好地在量子光学问题中使用该表示，我们揭示了压缩相干态表示与Wigner函数、Q函数以及Husimi函数间的积分变换关系。