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Annual Meeting Optical Society of America

Theory of phase memory in interference between two pairs of downconverted photons

Z. Y. Ou, L. J. Wang, L. Mandeļ

Published Jan 1, 1989• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1989.wq2

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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.
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.
A proposed experiment is analyzed theoretically. In the proposed experiment two coherent pump waves fall on two identical nonlinear crystals, down-converted signal and idler beams from the two crystals are mixed by two beam splitters, and the coincidence counting rate for photons leaving the beam splitters is measured. We show that this counting rate depends on the phase difference between the two coherent pump waves, and results from the interference of the vacuum with the down-converted photons. The experiment could be used to look for locality violations along the lines recently proposed by Grangier, Potasek, and Yurke [Phys. Rev. A 38, 3132 (1988)], but without the need for a coherent reference beam for homodyning.
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.
Photons emitted in the process of spontaneous parametric downconversion of pump light in a nonlinear crystal are made the basis of a new optical communication scheme, which depends on the fact that two downconverted photons are always produced simultaneously. If the pump light is modulated and the downconverted photons are transmitted in two separate beams which fall on two separate detectors, registering their simultaneous arrival allows great discrimination against background and noise to be achieved. Communication is possible with relatively few photons and even when the signal is ordinarily lost in the noise, so that the communication channel can be made virtually interception proof. The feasibility of the scheme is demonstrated by a pilot experiment.