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Europhysics Letters (EPL)

Experimental Test of Bell's Inequality for Energy and Time

Jurgen Brendel, Ernst Mohler, W. Martienssen

Published Dec 1, 1992• 238 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/20/7/001

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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.
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We perform a two-photon interference experiment in a Michelson interferometer with photon pairs produced by spontaneous parametric down-conversion. The interferometer is set to a path difference much larger than the coherence length of the light field. Application of a time-resolved coincidence detection scheme reveals two-photon interference fringes with a visibility of 87%. This high visibility clearly demonstrates the nonclassical nature of the observed interference and should allow further spin-free tests of Bell's inequalities.
Nonlocal effects in quantum mechanics associated with entangled states have been the subject of much recent interest.1,2 Franson1 suggested that one can observe a violation of Bell's inequalities for position and time by use of two spatially separated interferometers. We report on the observation of a closely related two-photon interference. A signal photon at frequency ωs and an idler photon at frequency ωi = ωp – ωs are created simultaneously, i.e., as a conjugate pair, in parametric fluorescence inside a KDP crystal from the annihilation of a single UV pump photon with frequency ωp3.
A periodically poled MgO – doped LiNbO3 (MgO:LN) non-degenerate photon pair source is utilized for spontaneous parametric down-conversion of 532 nm photons into time-energy entangled pairs of 794 and 1614 nm photons. The entangled photons are separated using previously detailed sorting optics, such that each wavelength is independently directed through one of two modified Mach-Zehnder interferometers – also known as a Franson interferometer – after which they are fiber-optically guided to high-efficiency photon detectors. Output from the detectors is sent to a high resolution time tagger, where coincidences between the entangled photons are recorded. By varying the length of the long path in one Mach-Zehnder interferometer, it is possible to observe high visibility sinusoidal fringes in the measured coincidence rates (while no variation is seen in single photon detection rates). These fringes – due to interference between the photon probability amplitudes – are indicative of a violation of the Bell inequality, and confirm inconsistencies with local hidden variable theory for the correlations of the time-energy entangled photon pairs.
We report on a two-photon interference experiment proposed by Franson [Phys. Rev. Lett. 62, 2205 (1989)], in which sinusoidal fringes with visibilities greater than 70.7%, such as those predicted by quantum mechanics, violate a Bell inequality. We observe visibility of 80.4\ifmmode\pm\else\textpm\fi{}0.6%, implying a violation of the inequality by 16 standard deviations. Here the elements of reality under consideration are energy and time rather than spin components. Any classical field models describing separate beams in a Franson interferometer are limited to visibilities less than 50%, and hence ruled out as well, without the need for any supplementary assumptions.