Phase coherent resonator detection as a complete quantum measurement of the two-mode spectral quantum state of light

The introduction of phase coherence in the detection of quantum noise of light yields a pure quantum measurement of spectral modes. We theoretically show that such coherent quantum measurement performed with the technique of resonator detection (RD) is able to access any direction in the two-mode phase space of spectral sidebands under appropriate conditions, thus furnishing a complete measurement of the four-dimensional Wigner function. We obtain a realistic measurement operator for coherent RD by including the effects of imperfect resonator mode matching in our analysis. Moreover, we experimentally demonstrate the realization of phase coherent RD to characterize a two-mode displaced quantum state.