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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Mapping and violating Bell inequality with entangled photons

David Guzmán, Leonardo J. Uribe, Alejandra Valencia, Ferney J. Rodríguez, Luis Quiroga

Published Oct 8, 2015• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2223197

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•Jun 28, 2023•0 citations
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.
Abstract In this paper, we report an experimental activity suitable for undergraduate students that makes them question their ideas about locality and realism. The experiment here reported complements previous educational approaches to Bell inequalities, since the usually called S function, that quantifies correlations, is mapped by measuring it for different detection angles. The students themselves worked in a pre-aligned setup that allowed them to test and violate the Clauser–Horne–Shimony–Holt–Bell inequality for two distant photons entangled in polarization.
Conventional tests of Bell’s inequality rely on entangled photon pairs. Here, we replace entangled pairs with two independent photons of orthogonal polarization, and demonstrate that Bell’s inequality is still violated. Given the inherent local realism of independent photons, this experiment proves that Bell’s inequality cannot falsify the local realism of photons. We thus conjecture that the violation of Bell’s inequality by entangled photon pairs originates from their orthogonal polarizations, rather than the breakdown of local realism. To interpret this unexpected violation with independent photons, we further substitute the two photons with two monochromatic light beams, and calculate the transmittance correlation through polarizers via Malus’s law and Karl Pearson’s correlation formula. We show that this correlation also defies Bell’s inequality. Retracing the derivation of Bell’s inequality reveals its validity is restricted to binary events, which accounts for the observed violation with light beams. Finally, we propose a thought experiment involving gradual attenuation of light intensity down to the single-photon regime, and hypothesize that single-photon transmission through a polarizer does not constitute a binary event. This hypothesis provides a unified interpretation for both our experimental findings and all canonical Bell inequality tests reported to date.
Teaching quantum mechanics is challenging, not least because the theory often conflicts with our classical worldview. Quantum correlations in particular are notoriously counter-intuitive. Their non-classical behavior is typically revealed through Bell-type inequalities. Among these, Wigner's Inequality constitutes a particularly accessible test, as it relies on minimal set-theoretic assumptions. In this pedagogical paper, we derive Wigner's Inequality, describe a quantum-optical setup to experimentally violate it, and provide access to the raw data, enabling students and instructors to perform their own analyses. Our measured data shows clear violations of Wigner's Inequality, directly illustrating the non-classical nature of quantum correlations. By connecting theory, experiment, and data analysis, this paper equips educators with a resource for engaging students in authentic scientific practice and developing a deeper understanding of quantum systems.
In a local realist model, physical properties are defined prior to and independent of measurement and no physical influence can propagate faster than the speed of light. Proper experimental violation of a Bell inequality would show that the world cannot be described with such a model. Experiments intended to demonstrate a violation usually require additional assumptions that make them vulnerable to a number of ``loopholes.'' In both pulsed and continuously pumped photonic experiments, an experimenter needs to identify which detected photons belong to the same pair, giving rise to the coincidence-time loophole. Here, via two different methods, we derive Clauser-Horne- and Eberhard-type inequalities that are not only free of the fair-sampling assumption (thus not being vulnerable to the detection loophole), but also free of the fair-coincidence assumption (thus not being vulnerable to the coincidence-time loophole). Both approaches can be used for pulsed as well as for continuously pumped experiments. Moreover, as they can also be applied to already existing experimental data, we finally show that a recent experiment [Giustina et al., Nature (London) 497, 227 (2013)] violated local realism without requiring the fair-coincidence assumption.
The growth of quantum technologies is attracting the interest of many students eager to learn concepts such as quantum entanglement or quantum superposition. However, the non-intuitive nature of these concepts poses a challenge to understanding them. Here, we present an entangled photon system which can perform a Bell test, i.e. the CHSH inequality, and can obtain the complete tomography of the two-photon state. The proposed setup is versatile, cost-effective and allows for multiple classroom operating modes. We present two variants, both facilitating the measurement of Bell inequalities and quantum state tomography. Experimental results showcase successful manipulation of the quantum state of the photons, achieving high-fidelity entangled states and significant violations of Bell's inequalities. Our setup's simplicity and affordability enhances accessibility for less specialized laboratories, allowing students to familiarize themselves with quantum physics concepts.
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.