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Physical Review Letters

Experimental violation of Bell’s inequality based on phase and momentum

John Rarity, P. R. Tapster

Published May 21, 1990• 611 citations
Publisher

Abstract

Two-color photon pairs are selected by two double apertures placed to satisfy the phase-matching conditions at a down-conversion crystal. The different wavelengths are superposed at spatially separated points on a beamsplitter and coincident two-photon detections are measured. On adjusting phase plates in the beams before the beamsplitter an apparent nonlocal fourth-order interference effect is seen which violates Bell's inequality by several standard deviations.

DOI
10.1103/physrevlett.64.2495

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Two-color photon pairs are selected by two double apertures placed to satisfy the phase-matching conditions at a down-conversion crystal. The different wavelengths are superposed at spatially separated points on a beamsplitter and coincident two-photon detections are measured. On adjusting phase plates in the beams before the beamsplitter an apparent nonlocal fourth-order interference effect is seen which violates Bell's inequality by several standard deviations.
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.
An interference experiment with photon pairs produced by degenerate parametric fluorescence is performed. The pairs are split and directed to two spatially separated Michelson interferometers. The interferometers are set to path differences which cause time delays far exceeding the coherence time of the light. We investigate photon coincidences between the output arms of the interferometers and observe nonlocal fourth-order interferences in the absence of second-order interferences. Maximum visibilities up to 86% are obtained, leading to a violation of Bell's inequality for energy and time by several standard deviations.
Quantum mechanical models of beam splitters1 predict interesting fourth-order interference effects when nonclassical light is used. If indistinguishable one-photon states are simultaneously input into each port of a 50/50 beam splitter, the theory predicts that each output will contain either two photons or none. A naive (particle) theory would predict a mixture of two’s and one’s. The required |1,1〉 photon state can be selected in nondegenerate parametric downconversion experiments by photon-counting coincidence detection. The disappearance of this coincidence after a beam splitter has recently been studied,1-2 and the range of path length differences over which the effect can be seen is related by Fourier transform to the photon bandwidth. In our work the bandwidth is not limited by external filters, and we have developed a theory which relates the measured photon length to the geometry of the apparatus and the detailed phase matching conditions at the parametric crystal. This theory of phase matching viewed through a beam splitter produces some unexpected results when the beam splitter is tilted and when large aperture detectors are considered.
Coincidence detections are measured between the output ports of a beam splitter whose input is an orthogonally polarized two-photon state produced in type-II spontaneous parametric down-conversion. When the delays between the two optical paths leading to each detector are varied by two spatially separated Pockel cells, a two-photon interference effect is seen that highlights a simultaneous entanglement in both spin and space-time variables. In contrast to all previous experimental tests of Bell's in- equalities, which have utilized states entangled with respect to only one type of observable, the double entanglement realized here allows the demonstration of two different types of Bell inequality violations in one experimental setup.
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.