介观LC回路数-相量子化和Josephson结的Cooper对数-相量子化

Number-phase quantization scheme for LC circuit and Josephson junction's Cooper pairs

传统的介观LC回路的量子化是将电量q和电感与电流的乘积L×I分别作为量子力学中的坐标算符Q和动量算符P来处理;本文采取另外一种量子化的观点,即将电量q(q=en)中的n作为荷数算符,并建立电流和相算符θ之间对应关系,就能实现介观LC回路的数-相范畴的量子化,并得到以数-相算符表示的Hamiltonian;通过引进纠缠态表象,对超导Josephson结也可以实现Cooper对数-相量子化,并给出了相应的物理解释。

Traditionally, the quantization scheme for a mesoscopic LC circuit lies in that electric charge q and electric current L × I are respectively quantized as the coordinate operator Q and momentum operator P. A new quantization scheme is proposed in which number n of the electric charge q（q = en） is quantized as the charge number operator and the relation between electric current and phase operator θ can be derived, in this way the quantization of mesoscopic LC circuit in the context of number-phase is realized and the corresponding Hamiltonian is obtained. The results show that the Cooper pair number-phase-difference quantization scheme is also available for Josephson junction after introducing the entangled state representation.