Complementarity Analysis of Interference between Frequency-Displaced Photonic Wave-Packets

The complementarity relation between the visibility and the spectral distinguishability of frequency-displaced photonic wave-packets in a Hong-Ou-Mandel interferometer is studied. An experimental definition of $K$, the distinguishability parameter, is proposed and tested for the $K^2+\mathcal{V}^2\leq 1$ complementarity inequality when a consistent visibility parameter is defined. The results show that the spectral distinguishability is, indeed, complementary to the visibility and that the quantum aspect of the two-photon interference phenomenon can be examined by employing weak-coherent states.