“Nonlocal” Interference Effects in Frequency Domain

It is a well known fact that interference is observable as a variation of intensity only when the path difference between two arms of an interferometer is shorter than the coherence length of the light. Nevertheless, interference effects do not vanish in such case, but they manifest themselves as a modulation of the spectrum. It is also known that the photon pairs produced by spontaneous parametric down-conversion show energy correlation (entanglement). A quantum measurement on one photon of the entangled pair affects considerably the whole system due to the “collapse” of the wave function. The correlation in entangled states is purely a quantum effect. It will be shown that the interference in the frequency domain and the “nonlocality” of quantum mechanics may appear simultaneously. An experiment is proposed which should demonstrate that if a filter providing spectral selection is placed in the route of one photon of the entangled pair and the photon is detected behind it, then interference appears in the (distant) Mach-Zehnder interferometer placed in the route of the other photon of the pair even if the optical path difference through the interferometer exceeds the coherence length of the light and if the spectra of these two photons do not overlap. The effect described represents a very graphical illustration of strong frequency correlation of the considered two-photon entangled state.