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Physical Review Letters

Observation of Spatial Quantum Beating with Separated Photodetectors

Z. Y. Ou, L. Mandeļ

Published Jul 4, 1988• 229 citations
Publisher

Abstract

When signal and idler photons produced in the process of parametric down-conversion are mixed together, and directed to two photodetectors that respond to nonoverlapping optical frequencies centered at ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$, it is found that the joint probability of two-photon detection exhibits a modulation of the form $cos({\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2})\ensuremath{\tau}$, where $c\ensuremath{\tau}$ is the path difference. The experimental results are well described by a simple quantum-mechanical analysis.

DOI
10.1103/physrevlett.61.54

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Theory of two-photon Interference in downconversion

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When signal and idler photons produced in the process of parametric down-conversion are mixed together, and directed to two photodetectors that respond to nonoverlapping optical frequencies centered at \ensuremathω1{\ensuremath{\omega}}_{1}\ensuremathω1​ and \ensuremathω2{\ensuremath{\omega}}_{2}\ensuremathω2​, it is found that the joint probability of two-photon detection exhibits a modulation of the form cos(\ensuremathω1\ensuremath−\ensuremathω2)\ensuremathτcos({\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2})\ensuremath{\tau}cos(\ensuremathω1​\ensuremath−\ensuremathω2​)\ensuremathτ, where c\ensuremathτc\ensuremath{\tau}c\ensuremathτ is the path difference. The experimental results are well described by a simple quantum-mechanical analysis.
An experiment has been performed in which signal and idler photons produced in the process of parametric downconversion are mixed at a beam splitter, and the mixed beam splitter outputs are directed to two photodetectors feeding a coincidence counter. Two optical filters with passbands centered at frequencies ω1, and ω2 are inserted just before the detectors. When the two-photon coincidence rate is measured as a function of the time delay δτ introduced between the two photons, it is found that the rate exhibits a cosine variation with δτ at the difference frequency |ω1− ω2|. The experimental results are consistent with a quantum analysis of the experiment but not with a classical treatment. We have observed a beat note with a period of 37 fs, which is several orders of magnitude shorter than the resolving time of the photodetectors. In principle a beat note should be observable at optical frequencies with this technique.
A theoretical study is made of the process in which incident pump photons that interact with a nonlinear medium (such as a crystal lacking inversion symmetry) are spontaneously split into lower-frequency signal and idler photons. The down-converted fields are quantized and described by a continuum of modes, a subset of which interacts with each photodetector. It is shown that when two ideal photodetectors are appropriately located so that they receive the conjugate signal and idler photons, then the joint probability of two-photon detection by the two detectors can equal the single-photon detection probability. The time correlation between the two detected photons is shown to be limited either by the resolving time of the detectors, or by the bandwidth of the down-converted light, and to be independent of the coherence time of the pump field or of the length of the nonlinear medium. These conclusions are compared with the results of recent experiments.
매개하향변환과정에서 동시에 발생한 서로 다른 진동수의 광자쌍을 이용한 4차 간섭실험에서 비고전적인 맥놀이 효과를 측정하였다. 각진동수가 각각 ω1\omega1ω1 과 ω2\omega2ω2 인 광자쌍을 빔분할기에서 중첩시키고, 빔분할기의 두 출구에 놓인 두 검출기로 동시계수 할 때, 두 광자가 빔분할기에 도달하는 시간 간격에 따라 cos( ω1\omega1ω1 - ω2\omega2ω2 )의 함수로 동시계수의 변화를 나타내었다. 두 광자의 파장 차이가 41㎚일 때 측정된 맥놀이 진동수 ( ω1\omega1ω1 - ω2\omega2ω2 )/2 π\piπ 는 0.29 ×1014{\times}10^{14}×1014 ㎐이었고, 진동수 차이에 해당하는 두 광자의 시간간격은 34.82fs로 측정되었다. One of the nonclassical effects in two-photon interference experiments, spatial quantum beating, is observed in fourth-order interference with pairs of photons produced by a spontaneous parametric down-conversion process. When photon pairs in different frequencies ω1\omega1ω1 and ω2\omega2ω2 are mixed together, and directed to two detectors, the coincidence counts exhibit a cosine modulation with difference frequency | ω1\omega1ω1 - ω2\omega2ω2 |. The measured coincidence counts turned out to have an interference pattern with periodicity of 10.45 ㎛ in position or 34.82fs in time delay, which corresponds to the period 2 π\piπ /| ω1\omega1ω1 - ω2\omega2ω2 | for the beat frequency of 0.29 ×1014{\times}10^{14}×1014 Hz.
A theoretical treatment is given of the situation in which two photons produced in the parametric frequency splitting of light in a nonlinear medium are allowed to interfere. It is shown that there is no interference pattern in the usual sense of quantities that are of the second order in the field, but that fourth-order interference effects are present. These could be demonstrated by placing two photodetectors at positions x,x′ in the interference plane and measuring the joint probability of two detections as a function of x – x′. The probability is predicted to exhibit a cosine modulation with separation x – x′ of close to 100% visibility, even when the integration time in the experiment greatly exceeds the reciprocal bandwidth of the accepted photons. As a result two photons cannot be detected at two points separated by a distance corresponding to an odd number of half-interference fringes. This is an interference effect that violates the laws of classical probability.