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Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory

Dehlinger, D, Mitchell, M W

Published May 27, 2002• 90 citations
OpenAlex

Abstract

We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein-Podolsky-Rosen ``paradox,'' we demonstrate strong polarization correlations of the entanged photons. Bell's idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of the Clauser, Horne, Shimony and Holt version of the Bell inequality finds $S = 2.307 \\pm 0.035$, in clear contradiciton of hidden variable theories. The experiments described can be performed in an afternoon.

Related papers

Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory

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We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein–Podolsky–Rosen paradox, we demonstrate strong polarization correlations of the entangled photons. Bell’s idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of the Clauser, Horne, Shimony, and Holt version of the Bell inequality finds S=2.307±0.035, in clear contradiction of hidden variable theories. The experiments described can be performed in an afternoon.

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We will describe a simple setup experiment that allows students to create polarization-entangled photons pairs. These photon pairs are in an entangled state first described in the famous 1935 article in Phys.Rev by Einstein-Podolsky-Rosen, often called E.P.R. state. Photons pairs at 810 nm are produced in two nonlinear crystals by spontaneous parametric downconversion of photons at 405 nm emitted by a violet laser diode. The polarization state of the photons pairs is easily tunable with a half-wave plate and a Babinet compensator on the laser diode beam. After having adjusted the polarization-entangled state of the photon pairs, our students can perform a test of Bell’s inequalities. They will find the amazing value for the Bell parameter between 2.3 and 2.6, depending on the quality of the adjustments of the state of polarization. The experiments described can be done in 4 or 5 hours. What is the importance of creating an entangled photons experiment for our engineering students? First of all, entanglement concept is clearly one of the most strikingly nonclassical features of quantum theory and it is playing an increasing role in present-day physics. But in this paper, we will emphasise the experimental point of view. We will try to explain why we believe that for our students this lab experiment is a unique opportunity to deal with established concepts and experimental techniques on polarization, non linear effects, phase matching, photon counting avalanche photodiodes, counting statistics, coincidences detectors. Let us recall that the first convincing experimental violations of Bell’s inequalities were performed by Alain Aspect and Philippe Grangier with pairs of entangled photons at the Institut d’Optique between 1976 and 1982. Twenty five years later, due to recent advances in laser diode technology, new techniques for generation of photon pairs and avalanche photodiodes, this experiment is now part of the experimental lab courses for our students.

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We present detailed instructions for constructing and operating an apparatus to produce and detect polarization-entangled photons. The source operates by type I spontaneous parametric downconversion in a two-crystal geometry. Photons are detected in coincidence by single-photon counting modules and show strong angular and polarization correlations. We observe more than 100 entangled photon pairs per second. A test of a Bell inequality can be performed in an afternoon.

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We present detailed instructions for constructing and operating an apparatus to produce and detect polarization-entangled photons. The source operates by type-I spontaneous parametric downconversion in a two-crystal geometry. Photons are detected in coincidence by single-photon counting modules and show strong angular and polarization correlations. We observe more than 100 entangled photon pairs per second. A test of a Bell inequality can be performed in an afternoon.

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We describe an experimental test of local realistic and nonlocal realistic theories using polarization-entangled two-photon singlet states created using a fiber-based polarization Sagnac interferometer. We show a violation of Bell's inequality in the Clauser-Horne-Shimony-Holt form by 15 standard deviations, thus excluding local hidden-variable theories, and a violation of a Leggett-type nonlocal hidden-variable inequality by more than three standard deviations, thus excluding a class of nonlocal hidden-variable theories.

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B. Betchart

The thesis documents the work done over the year to initiate an undergraduate Advanced Laboratory experiment which tests Bell's inequality.It provides reference theory for the experiment, including explanations of Bell inequalities, basics of nonlinear optics, type-I downconversion and entanglement, and polarization states of the entangled photons.A main result is the equipment and design proposal for the experiment, which will cost a total 19600, led in price by the 9000 of a four photodetector array and followed by the 5000 of a 405nm pump laser.Entangled photons are produced by pumping BBO in a two-crystal geometry.Although most of the light is transmitted, some undergoes type-I parametric downconversion.Degenerate pairs are in a tunable entangled state and can be used to show non-classical behaviour.Specifically, a violation of the CHSH Bell inequality can be observed.Usable coincidence rates of several thousand per second are expected.Experimental and data analysis methods are described as the basis of future laboratory documentation.Explanations of equipment alignment and adjustment and data collection are included, as well as derivations of relevant analyses of the experimental data.Lastly the coincidence circuit built for the experiment is reviewed.The circuit costs less than 40 to construct and demonstrates a coincidence window of between 18ns and 36ns.

•Jan 1, 2004•5 citations
We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein-Podolsky-Rosen ``paradox,'' we demonstrate strong polarization correlations of the entanged photons. Bell's idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of the Clauser, Horne, Shimony and Holt version of the Bell inequality finds S=2.307pm0.035S = 2.307 \\pm 0.035S=2.307pm0.035, in clear contradiciton of hidden variable theories. The experiments described can be performed in an afternoon.
We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein–Podolsky–Rosen paradox, we demonstrate strong polarization correlations of the entangled photons. Bell’s idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of the Clauser, Horne, Shimony, and Holt version of the Bell inequality finds S=2.307±0.035, in clear contradiction of hidden variable theories. The experiments described can be performed in an afternoon.
We will describe a simple setup experiment that allows students to create polarization-entangled photons pairs. These photon pairs are in an entangled state first described in the famous 1935 article in Phys.Rev by Einstein-Podolsky-Rosen, often called E.P.R. state. Photons pairs at 810 nm are produced in two nonlinear crystals by spontaneous parametric downconversion of photons at 405 nm emitted by a violet laser diode. The polarization state of the photons pairs is easily tunable with a half-wave plate and a Babinet compensator on the laser diode beam. After having adjusted the polarization-entangled state of the photon pairs, our students can perform a test of Bell’s inequalities. They will find the amazing value for the Bell parameter between 2.3 and 2.6, depending on the quality of the adjustments of the state of polarization. The experiments described can be done in 4 or 5 hours. What is the importance of creating an entangled photons experiment for our engineering students? First of all, entanglement concept is clearly one of the most strikingly nonclassical features of quantum theory and it is playing an increasing role in present-day physics. But in this paper, we will emphasise the experimental point of view. We will try to explain why we believe that for our students this lab experiment is a unique opportunity to deal with established concepts and experimental techniques on polarization, non linear effects, phase matching, photon counting avalanche photodiodes, counting statistics, coincidences detectors. Let us recall that the first convincing experimental violations of Bell’s inequalities were performed by Alain Aspect and Philippe Grangier with pairs of entangled photons at the Institut d’Optique between 1976 and 1982. Twenty five years later, due to recent advances in laser diode technology, new techniques for generation of photon pairs and avalanche photodiodes, this experiment is now part of the experimental lab courses for our students.
We describe an experimental test of local realistic and nonlocal realistic theories using polarization-entangled two-photon singlet states created using a fiber-based polarization Sagnac interferometer. We show a violation of Bell's inequality in the Clauser-Horne-Shimony-Holt form by 15 standard deviations, thus excluding local hidden-variable theories, and a violation of a Leggett-type nonlocal hidden-variable inequality by more than three standard deviations, thus excluding a class of nonlocal hidden-variable theories.
The thesis documents the work done over the year to initiate an undergraduate Advanced Laboratory experiment which tests Bell's inequality.It provides reference theory for the experiment, including explanations of Bell inequalities, basics of nonlinear optics, type-I downconversion and entanglement, and polarization states of the entangled photons.A main result is the equipment and design proposal for the experiment, which will cost a total 19600, led in price by the 9000 of a four photodetector array and followed by the 5000 of a 405nm pump laser.Entangled photons are produced by pumping BBO in a two-crystal geometry.Although most of the light is transmitted, some undergoes type-I parametric downconversion.Degenerate pairs are in a tunable entangled state and can be used to show non-classical behaviour.Specifically, a violation of the CHSH Bell inequality can be observed.Usable coincidence rates of several thousand per second are expected.Experimental and data analysis methods are described as the basis of future laboratory documentation.Explanations of equipment alignment and adjustment and data collection are included, as well as derivations of relevant analyses of the experimental data.Lastly the coincidence circuit built for the experiment is reviewed.The circuit costs less than 40 to construct and demonstrates a coincidence window of between 18ns and 36ns.