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A Test of Bell's Inequality for the Undergraduate Laboratory

B. Betchart

Published Jan 1, 2004• 5 citations
OpenAlex

Abstract

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.

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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.
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.
Optimization of a Pulsed Source of Entangled Photons for the Violation of the CHSH Inequality This thesis focuses on my work carried out in the Quantum Communications laboratory with the Quantum Future research group of the Department of Information Engeneering, in which I worked on the creation and optimization of a pulsed source of polarization entangled photons. The main focus in the laboratory was to optimize the experimental setup to prove the entangled nature of the photons produced. This was done by violating the Bell inequality in the form presented by Clauser, Horne, Shimony and Holt (CHSH) in 1969. The present work's objective is to provide an overview of all the crucial physical phenomena exploited in the experiment to obtain the wanted results. In section 1 a presentation of the phenomenon of entanglement and of Bell's argument proving the incapability to describe its properties with a both real and local theory is given, along with the derivation of the ``CHSH inequality and the possibility to violate it with polarization entangled photons. Sections 2 and 3 focus on the properties of the Gaussian beam used in the experiment and its source: the mode-locked Mira laser. A brief discussion about mode-locked lasers and their properties is provided. In section 4 the nonlinear optical phenomena of second harmonic generation and spontaneous parametric down conversion are discussed, the former from a classical standpoint and the latter with a few quantum mechanical considerations. Section 5 focuses on polarization optics and the both classical and quantum mechanical formalism of the Jones vectors. A discussion of the effects of the birefringent devices used in the experiment on the photons' state is provided. Finally, sections 6 and 7 display a complete overview of the experimental setup and the results obtained for the violation of the inequality. A systematic explanation of the experimental optimization procedure is provided in section 6 as it may be useful for the future experimenters, since it proved to be tricky. Throughout all the work, various characteristics of the devices used in the experimental setup are given, hopefully making the most important and peculiar aspects of the experiment clear.
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.