Spatially Separated Two Color Photons in Fourth Order Interference

Abstract

Non-degenerate parametric downconversion is often thought of as a process where single pump photons are downconverted to pairs of longer wavelength photons that are emitted simultaneously in directions satisfying the phase matching conditions and energy conservation. The coincidence properties of these photon pairs were first studied in the early 1970’s1 and results of these (and later) photon counting coincidence experiments support a simplistic ‘fuzzy ball’ picture of the photon pairs. The limitations of this picture are clearly illustrated by more recent theory and experiments2-7 studying the effect of recombining pair photons at a beamsplitter. As discrete photons have random relative phase we do not expect to see classical second order interference effects in such experiments. In the simplistic picture each photon (of a pair) would independently choose a random output direction from the beamsplitter with consequent halving of the coincidence rate (for a 50/50 beamsplitter). When the path lengths between the pair photon source and the beamsplitter are not equal this is in fact the case. However at zero path length difference the coincidence rate reduces to near zero due to fourth order (involving four fields) interference at the beamsplitter. The range of path length differences over which this reduction can be seen is related by Fourier transform to the pair-photon bandwidth. Other workers use interference filters to limit this bandwidth4,7 while in this work the pair photon bandwidth is primarily limited by apertures combined with the detailed phase matching conditions in the non-linear crystal used as a source. Well away from degeneracy these conditions lead to a multicolor cone of downconverted light produced around the pump beam direction. Using symmetrically placed horizontal slit apertures we select broadband photon pairs and the coincidence rate plotted against path length difference shows a reduction with side oscillations characteristic of a sine function (see figure 4).