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arXiv:physics/0506212 · Journal of Optics B Quantum and Semiclassical Optics

Four-photon interference: a realizable experiment to demonstrate violation of EPR postulates for perfect correlations

P. Hariharan, Joseph Samuel, Supurna Sinha

Published Jan 1, 1999• 2 citations
arXivHTMLPDF

Abstract

Bell's theorem reveals contradictions between the predictions of quantum mechanics and the EPR postulates for a pair of particles only in situations involving imperfect statistical correlations. However, with three or more particles, contradictions emerge even for perfect correlations. We describe an experiment which can be realized in the laboratory, using four-photon entangled states generated by parametric down-conversion, to demonstrate this contradiction at the level of perfect correlations.

DOI
10.1088/1464-4266/1/2/002

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Bell's theorem reveals contradictions between the predictions of quantum mechanics and the EPR postulates for a pair of particles only in situations involving imperfect statistical correlations. However, with three or more particles, contradictions emerge even for perfect correlations. We describe an experiment which can be realized in the laboratory, using four-photon entangled states generated by parametric down-conversion, to demonstrate this contradiction at the level of perfect correlations.
It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the EPR program contradicts quantum mechanics even for the cases of perfect correlations. By perfect correlations is meant arrangements by which the result of the measurement on one particle can be predicted with certainty given the outcomes of measurements on the other particles of the system. This incompatibility with quantum mechanics is stronger than the one previously revealed for two-particle systems by Bell’s inequality, where no contradiction arises at the level of perfect correlations. Both spin-correlation and multiparticle interferometry examples are given of suitable three- and four-particle arrangements, both at the gedanken and at the real experiment level.
Simultaneous entanglement in spin and space-time of a two-photon quantum state generated in type-2 spontaneous parametric down-conversion is demonstrated by the observation of quantum interference with 98% visibility in a simple beam-splitter (Hanburry Brown-Twiss) anticorrelation experiment. The nonlocal cancellation of two-photon probability amplitudes as a result of this double entanglement allows us to demonstrate two different types of Bell's inequality violations in one experimental setup.
We present an overview of the method for generating entangled photon pairs via spontaneous parametric down conversion and the experimental method of detecting entangled states or Bell-states with the use of photon statistics, the two key systems required to realize quantum state teleportation and other related experiments. As a proof of the quantum nature of teleportation we performed an entanglement swapping experiment, where the teleported state itself was entangled. The experiment clearly showed that the entanglement survived the teleportation, as the quantum correlations of the teleported photon violated Bell's inequality.
This chapter describes three experiments to test and demonstrate the principles of quantum mechanics using correlated photons. These include the demonstration that the photon exists; production and measurement of entangled states of photons, including a measurement of a violation of a Bell inequality; and the interference of a single photon with itself and the quantum eraser. The experiments are presented in order of difficulty. In a birefringent medium, spontaneous parametric down-conversion occurs due to the interaction of the light and the medium. The analysis given can be generalized to show that the down-converted photons are created in planes other than the horizontal plane. All the down-converted photons of a given wavelength form a cone about the pump-beam axis, but photons in each pair follow, by conservation of momentum, correlated paths in the cone. The down-converted photons are created in a cone about the pump-beam direction. The experiment uses the horizontal slice of the down-conversion cone that contains the pump beam.
Simultaneous entanglement in spin and space-time of a two-photon quantum state generated in type-II spontaneous parametric down-conversion is demonstrated by the observation of quantum interference with 98% visibility in simple beam-splitter (Hanburry Brown-Twiss) anticorrelation and quantum beating experiments. The cancellation of two-photon probability amplitudes as a result of this double entanglement allow us to demonstrate two different types of Bell's inequality violations in one experimental setup.