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Physical Review A

Models of a two-photon Einstein-Podolsky-Rosen interference experiment

Morton H. Rubin, Yanhua H. Shih

Published Jun 1, 1992• 27 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.45.8138

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Journal of the Optical Society of America B•Oct 1, 1999•4 citations
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.
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.
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.
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.
Quantum entanglement first attracted attention as the heart of the Einstein-Podolsky-Rosen (EPR) paradox and one of the most counterintuitive phenomena in the view of classical physics [1]. Hong-Ou-Mandel (HOM) [2] and Franson interferences [3] are regarded as important evidence of the non-classical nature of photon sources. Since a two-photon interference experiment with time-energy entangled photons was proposed by J. D. Franson [2], the fourth-order interferences beyond the one-photon coherence length have attracted considerable attention as important and interesting quantum phenomena in quantum optics. Surprisingly, Franson interference has been not experimentally demonstrated by use of two-photon pairs emitted from a cascade-type atomic system with continuous wave (CW) pumping, as originally proposed by Franson.
Einstein–Podolsky–Rosen (EPR) correlations produced for two-photon entangled wave packets are analyzed by use of optical Wigner functions. In particular, type-II optical parametric downconversion systems are used, and the effects of the length of the crystal and the filter bandwidth on the Wigner functions are studied. The relation between the optical Wigner functions and the interference experiment with a beam splitter is studied. We find that, whereas in first-order correlation experiments (typified, for example, by Young’s interference experiment) the “photon interferes with itself” [ P. A. M. Dirac , The Principles of Quantum Mechanics (Clarendon, Oxford, UK, 1958), p. 9], in the EPR correlations the two-photon amplitude function interferes with itself. Such interference is analyzed by use of the optical Wigner functions.