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Physical Review A

Reply to ‘‘Comment on ‘Einstein-Podolsky-Rosen state for space-time variables in a two-photon interference experiment’ ’’

Yanhua H. Shih, A. V. Sergeinko, Morton H. Rubin

Published Nov 1, 1993• 0 citations
Publisher

Abstract

The assertion of Kwait, Steinberg, and Chiao [preceding Comment, Phys. Rev. A 48, 3999 (1993)] that alignment problems and the size of the beam-defining irises explain the decrease in the visibility in two-photon interference experiments is examined. We argue that these effects can explain the reason that the visibility does not attain its maximum theoretical value, but that it fails to explain the decrease in the visibility with the path differences in the interferometers. We conclude that one explanation of this effect is the breakdown of perfect frequency phase matching in parametric down-conversion.

DOI
10.1103/physreva.48.4001

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The assertion of Kwait, Steinberg, and Chiao [preceding Comment, Phys. Rev. A 48, 3999 (1993)] that alignment problems and the size of the beam-defining irises explain the decrease in the visibility in two-photon interference experiments is examined. We argue that these effects can explain the reason that the visibility does not attain its maximum theoretical value, but that it fails to explain the decrease in the visibility with the path differences in the interferometers. We conclude that one explanation of this effect is the breakdown of perfect frequency phase matching in parametric down-conversion.
A recent article by Shih, Sergienko, and Rubin [Phys. Rev. A 47, 1288 (1993)] reports a two-photon interference effect in which fringes with a visibility of 59% were observed; for an ideal system, quantum mechanics predicts perfect visibility interference. In explanation of this discrepancy, the authors conclude that the reduced visibility is due to ``nonperfect phase matching of the down-conversion,'' the parent process of the correlated photon pairs. They imply that the nonperfect phase matching stems from the finite size of their down-conversion crystal. We argue that the crystal length was not a limiting factor in their measurement, citing three similar experiments which achieved higher visibilities [Kwiat, Steinberg, and Chiao, Phys. Rev. A 47, R2472 (1993); Brendel, Mohler, and Martienssen, Phys. Rev. Lett. 66, 1142 (1991); Europhys. Lett. 20, 575 (1992)].
A pair of correlated photons generated from parametric down conversion was sent to two independent Michelson interferometers. Second order interference was studied by means of a coincidence measurement between the outputs of two interferometers. The reported experiment and analysis studied this second order interference phenomena from the point of view of Einstein-Podolsky-Rosen paradox. The experiment was done in two steps. The first step of the experiment used 50 psec and 3 nsec coincidence time windows simultaneously. The 50 psec window was able to distinguish a 1.5 cm optical path difference in the interferometers. The interference visibility was measured to be 38 percent and 21 percent for the 50 psec time window and 22 percent and 7 percent for the 3 nsec time window, when the optical path difference of the interferometers were 2 cm and 4 cm, respectively. By comparing the visibilities between these two windows, the experiment showed the non-classical effect which resulted from an E.P.R. state. The second step of the experiment used a 20 psec coincidence time window, which was able to distinguish a 6 mm optical path difference in the interferometers. The interference visibilities were measured to be 59 percent for an optical path difference of 7 mm. This is the first observation of visibility greater than 50 percent for a two interferometer E.P.R. experiment which demonstrates nonclassical correlation of space-time variables.
A pair of correlated photons generated from parametric down-conversion was sent to two independent Michelson interferometers. Second-order interference was studied by means of a coincidence measurement between the outputs of two interferometers. The reported experiment and analysis studied this second-order interference phenomenon from the point of view of the Einstein-Podolsky-Rosen (EPR) paradox. The experiment was done in two steps. The first step of the experiment used 50-psec and 3-nsec coincidence time windows simultaneously. The 50-psec window was able to distinguish a 1.5-cm optical path difference in the interferometers. The interference visibility was measured to be 38% and 21% for the 50-psec time window and 22% and 7% for the 3-nsec time window, when the optical path differences of the interferometers were 2 cm and 4 cm, respectively. By comparing the visibilities between these two windows, the experiment showed the nonclassical effect which resulted from an EPR state. The second step of the experiment used a 20-psec coincidence time window, which was able to distinguish a 6-mm optical path difference in the interferometers. The interference visibilities were measured to be 59% for an optical path difference of 7 mm. This is an observation of visibility greater than 50% for a two-interferometer EPR experiment which demonstrates nonclassical correlation of space-time variables.
After a very brief review of the historical Einstein, Podolsky, and Rosen (EPR) experiments, a new two-photon interference type EPR experiment is reported. A two-photon state was generated by optical parametric down conversion. Pairs of light quanta with degenerate frequency but divergent directions of propagation were sent to two independent Michelson interferometers. First and second order interference effectors were studied. Different than other reports, we observed that the second order interference visibility vanished when the optical path difference of the interferometers were much less than the coherence length of the pumping laser beam. However, we also observed that the second order interference behaved differently depending on whether the interferometers were set at equal or different optical path differences.
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.