New < q,n|| Representation for Studing Two-Mode Nonlinear Phase Operator

A new complete and orthonormal < q,n|| representation is constructed in which Hradil’s two-mode phase operator R exhibits its phase behavior manifestly and can be put into R = Σ^∞_q=-∞Σ^∞_n=0 ||q-1,n> < q, n||, which resembles S-G phase operator (N + l)^-1/2a = Σ^∞_n=1|n–l > < n|. The corresponding phase state is also obtained, which is quaJified to make up a phase representation.