Cooper-pair number–phase Wigner function for the bosonic operator Josephson model

On the basis of Feynman's explanation about Cooper pair that “a bound pair act as a Bose particle” and the bosonic operator Hamiltonian of Josephson junction [H.-Y. Fan, Phys. Lett. A 289 (2001) 172] as well as the entangled state representation we introduce characteristic function and Wigner function in the sense of Cooper-pair number–phase. We employ the correlated-amplitude–number state representation to present it. The Cooper-pair number distribution and phase distribution are the marginal distributions of this Wigner distribution, respectively.