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Annual Meeting Optical Society of America

An energy–time Bell inequality in two-photon interferometry

Paul G. Kwiat, Aephraim M. Steinberg, R. Y. Chiao

Published Jan 1, 1992• 0 citations
Publisher

Abstract

We have performed an EPR-type experiment first proposed by Franson,1 resulting in two-particle interference that is both nonclassical and nonlocal. We used photon pairs produced in an entangled state of energy via spontaneous down-conversion. Each photon enters an unbalanced interferometer, and we detect singles and coincidence rates at the output ports. If the long- and short-arm path-length difference is much greater than the photons’ coherence lengths, no fringes are seen in singles as the arm lengths are varied. Yet when the difference between the path-length differences of the two interferometers is less than these coherence lengths, fringes are observed in coincidence, resulting from an interference of the (indistinguishable) “long–long” and “short–short" coincidence possibilities. If the electronic resolution is sufficient to eliminate the background of "short–long" and "long–short” coincidences, the visibility may be as high as 100%.2 For V > 71%, with certain reasonable auxiliary assumptions, Bell’s inequalities can be violated. The interpretation is that no local, realistic model can yield the observed results. The use of this type of entangled state is significant because it is much closer to the original EPR paradox than the spin-singlet case commonly considered.

DOI
10.1364/oam.1992.muu5

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We have performed an EPR-type experiment first proposed by Franson,1 resulting in two-particle interference that is both nonclassical and nonlocal. We used photon pairs produced in an entangled state of energy via spontaneous down-conversion. Each photon enters an unbalanced interferometer, and we detect singles and coincidence rates at the output ports. If the long- and short-arm path-length difference is much greater than the photons’ coherence lengths, no fringes are seen in singles as the arm lengths are varied. Yet when the difference between the path-length differences of the two interferometers is less than these coherence lengths, fringes are observed in coincidence, resulting from an interference of the (indistinguishable) “long–long” and “short–short" coincidence possibilities. If the electronic resolution is sufficient to eliminate the background of "short–long" and "long–short” coincidences, the visibility may be as high as 100%.2 For V > 71%, with certain reasonable auxiliary assumptions, Bell’s inequalities can be violated. The interpretation is that no local, realistic model can yield the observed results. The use of this type of entangled state is significant because it is much closer to the original EPR paradox than the spin-singlet case commonly considered.
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 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.
The energy-time uncertainty principle is on a different footing than the momentum position uncertainty principle: in contrast to position, time is a c-number parameter, and not an operator. As Aharonov and Bohm have pointed out, this leads to different interpretations of the two uncertainty principles. In particular, one must distinguish between an inner and an outer time in the definition of the spread in time, delta t. It is the inner time which enters the energy-time uncertainty principle. We have checked this by means of a correlated two-photon light source in which the individual energies of the two photons are broad in spectra, but in which their sum is sharp. In other words, the pair of photons is in an entangled state of energy. By passing one member of the photon pair through a filter with width delta E, it is observed that the other member's wave packet collapses upon coincidence detection to a duration delta t, such that delta E(delta t) is approximately equal to planks constant/2 pi, where this duration delta t is an inner time, in the sense of Aharonov and Bohm. We have measured delta t by means of a Michelson interferometer by monitoring the visibility of the fringes seen in coincidence detection. This is a nonlocal effect, in the sense that the two photons are far away from each other when the collapse occurs. We have excluded classical-wave explanations of this effect by means of triple coincidence measurements in conjunction with a beam splitter which follows the Michelson interferometer. Since Bell's inequalities are known to be violated, we believe that it is also incorrect to interpret this experimental outcome as if energy were a local hidden variable, i.e., as if each photon, viewed as a particle, possessed some definite but unknown energy before its detection.
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.
Models of a two-photon interference experiment proposed by Franson to study the Einstein-Podolsky-Rosen (EPR) effect are presented. The experiment considers a pair of photons correlated in time and in frequency, each of which is passed through an interferometer. When the path difference through the two interferometers is set so there is no first-order interference, Franson showed that second-order interference between the two photons could occur with 100% visibility. In this paper both quantum and classical models are considered and the importance of the coincidence time window and the effect of the frequency correlation are shown. Calculations are presented for all settings of the interferometers. The EPR effect arises from entangled states; a brief discussion is given of the nature of the entangled state for this type of experiment.
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.