Frequency and phase relations of entangled photons observed by a two-photon interference experiment

An entangled photon experiment has been performed with a large variation of the temperature of the nonlinear crystal generating the entangled pair by spontaneous downconversion. The photon pairs are separated by a nonpolarizing beamsplitter, and the polarization modes are mixed by half-wave plates. The correlation function of the coincidences is studied as a function of the temperature. In the presence of a narrow interference filter, we observe that the correlation changes between -1 and +1 about seven times within a temperature interval of about 30 degrees C. We show that the common simplified single-mode pair representation of entangled photons is insufficient to describe the results, but that the biphoton description that includes frequency and phase details gives a close to perfect fit with experimental data for two different choices of interference filters. We explain the main ideas of the underlying physics, and we give an interpretation of the two-photon amplitude, which provides an intuitive understanding of the effect of changing the temperature and inserting interference filters.