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Journal of the Optical Society of America B

Fourth-order interference in parametric downconversion

John G. Rarity, P. R. Tapster

Published Jun 1, 1989• 91 citations
Publisher

Abstract

A two-photon state can be selected by coincidence detection of photon pairs created in parametric downconversion. We demonstrate a reduction in the coincidence-count rate when pairs of photons are combined in a beam splitter. This reduction occurs only when photon wave functions overlap and can permit accurate (subpicosecond) relative timing measurements. We relate the width of the coincidence reduction to the bandwidth of the downconverted light and thence to the detailed phase-matching conditions in the parametric downconversion crystal. We also demonstrate that the loss of coincidences is associated with an increased probability of detection of photon pairs in each output of the beam splitter.

DOI
10.1364/josab.6.001221

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A two-photon state can be selected by coincidence detection of photon pairs created in parametric downconversion. We demonstrate a reduction in the coincidence-count rate when pairs of photons are combined in a beam splitter. This reduction occurs only when photon wave functions overlap and can permit accurate (subpicosecond) relative timing measurements. We relate the width of the coincidence reduction to the bandwidth of the downconverted light and thence to the detailed phase-matching conditions in the parametric downconversion crystal. We also demonstrate that the loss of coincidences is associated with an increased probability of detection of photon pairs in each output of the beam splitter.
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We study the Hong-Ou-Mandel interferometer in the regime of spontaneous parametric down-conversion with high pump beam power at the crystal. In this regime one and two photons from a pump pulsed laser beam generate one and two pairs of photons, respectively. These photons are then directed to the beam splitter of the interferometer and detected at its exit in coincidence. An interesting phenomenon is observed: The reduction of the visibility of the Hong-Ou-Mandel coincidence peak (or dip) with the increase of pump power. We study the relation between the visibility of the fourth-order interference pattern and the power of the pumping laser beam for type I and type II phase-matching crystals. Our theoretical calculations are in good agreement with the experimental results.
In the process of parametric downconversion in a nonlinear crystal, incident photons split up into two lower frequency photons that emerge in different directions. Because the downconverted photons appear simultaneously, an optical communication channel based on transmission and simultaneous detection of these photon pairs should be able to achieve great discrimination against background. Indeed, it should be able to operate even in conditions in which the light signal would otherwise be lost in the noise. Such a communication channel requires relatively few photons per second and could be almost interception proof. The feasibility of the idea has been explored experimentally, and the results involving photoelectric coincidence counting measurements are presented.
An analysis is presented of the interference between two photon pairs produced in the process of downconversion from two identical crystals, which are then mixed by beam splitters. Because the downconverted photons are entangled with the vacuum, they carry information about the phase of the pump field. As a result the two-photon detection probability is shown to depend on the phase of the pump, even when the resolving time of the detector electronics is far longer than the coherence time of the light.
Angle-separated pair photons emitted in spontaneous parametric fluorescence are superimposed at a beamsplitter and detected by coincidence techniques. The coincidence disappears when the photon path lengths to the beamsplitter are equal to within their inverse bandwidth due to fourth-order interference. The photon bandwidth is set by wide apertures placed to satisfy phase-matching conditions at the nonlinear crystal. The resulting broadband photons are short (39-fs full width at half maximum) and show an oscillatory tail resulting from the hard-edge apertures. Two-color photons are created by blocking the central portion of the apertures leading to strong oscillations of the coincidence rate as a function of path-length difference. Both effects are predicted by the theory of fourth-order interference coupled with the detailed phase-matching conditions in the nonlinear crystal used as a source. The two colors overlap at different positions on the beamsplitter. We show how this could be used as a test of local realistic theories by formulating a Bell inequality based on relative phases between the colors.