Two-mode phase operator and phase state studied in number-difference orthonormal representation

We study the properties of two-mode phase operator root(a dagger + b)/(a b dagger) and the phase state by constructing the number-difference orthono rmal state \q, r]. We prove that \q, r] constitutes a complete and orthonor mal representation (number-difference representation). We show that two-mod e phase operator root(a dagger + b)/(a + b dagger) exhibits its phase behav ior explicitly in the number-difference representation, which resembles the single-mode phase operator e(i Psi) = (1/root a dagger a + 1)a. The corres ponding phase state is also studied.