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Experimentell undersökning av Bells olikhet för att utvärdera möjligheten att skapa en fysiklaboration

Oscar Alkeskog, Melwin Andersson, Josef Jörgensen, Linnea Landstedt, Fredrik Sitje

Published Jun 28, 2023• 0 citations
OpenAlex

Abstract

This report investigates wether it is feasible for undergraduate students to conduct an experiment that violates Bell’s inequality using polarization of entangled photons created in BBO-crystals, within a time frame of up to three days. For this, we conducted the experiment ourselves by drawing inspiration from other setups. This study covers the historical buildup and theory from the EPR-Paradox to the experiments that refuted Bell’s inequality.We also lay out the fundamentals of spontaneous parametric down-conversion. In addition, this study gives detailed instructions on how to set up the experiment. Our results show that with a significance level of p = 2 ・ 10−5 that Bell’s inequality (S < 2) was violated by measuring an S-value of 2,1577 ± 0,0379. From our method analysis we conclude that it is unlikely that undergraduate physics students can conduct the entire experiment within three days. However, we suggest two alternative laborations based on partially assembled setups. Either the students could optimize the quantum state of the incoming photons or they could align the laser and optical components. Another possibility is to give a demonstration or conduct a signal processing (coincidence) laboration using a fully assembled setup.

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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 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.

•May 27, 2002•90 citations
This report investigates wether it is feasible for undergraduate students to conduct an experiment that violates Bell’s inequality using polarization of entangled photons created in BBO-crystals, within a time frame of up to three days. For this, we conducted the experiment ourselves by drawing inspiration from other setups. This study covers the historical buildup and theory from the EPR-Paradox to the experiments that refuted Bell’s inequality.We also lay out the fundamentals of spontaneous parametric down-conversion. In addition, this study gives detailed instructions on how to set up the experiment. Our results show that with a significance level of p = 2 ・ 10−5 that Bell’s inequality (S < 2) was violated by measuring an S-value of 2,1577 ± 0,0379. From our method analysis we conclude that it is unlikely that undergraduate physics students can conduct the entire experiment within three days. However, we suggest two alternative laborations based on partially assembled setups. Either the students could optimize the quantum state of the incoming photons or they could align the laser and optical components. Another possibility is to give a demonstration or conduct a signal processing (coincidence) laboration using a fully assembled setup.
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.
In 1964, J. Bell introduced an inequality that stated a mathematical bound for any physical system that holds both locality and realism; if we violate this inequality, it is clear that we have to reconsider the previous statement. In our work, we report an experimental activity with photons suitable for undergraduate students that makes them question these naïve ideas of nature’s behavior. With a pre-aligned setup, our students tested and violated Bell’s inequality in a two-hour laboratory session, using two distant photons entangled in polarization. In addition, complementing an educational approach to this phenomenon, the usually called S function, that quantifies correlations, was mapped using different detection angles in one of the two locations. In particular, a more complete picture of the S function, allow us to identify the initial state of light. We show in this work that it is possible for undergraduate students to question some of our common sense ideas of nature using experiments with photons.
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 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 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.