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arXiv:1705.08601 · The European Physical Journal C

Testing violation of the Leggett–Garg-type inequality in neutrino oscillations of the Daya Bay experiment

Qiang Fu, Xurong Chen

Published Nov 1, 2017• 40 citations
arXivHTMLPDF

Abstract

The Leggett–Garg inequality (LGI), derived under the assumption of realism, acts as the temporal Bell inequality. It is studied in electromagnetic and strong interaction like photonics, superconducting qubits and nuclear spin. The weak interaction two-state oscillations of neutrinos affirmed the violation of Leggett–Garg-type inequalities (LGtI). We make an empirical test for the deviation of experimental results with the classical limits by analyzing the survival probability data of reactor neutrinos at a distinct range of baseline dividing energies, as an analog to a single neutrino detected at different times. A study of the updated data of the Daya Bay experiment unambiguously depicts an obvious cluster of data over the classical bound of LGtI and shows a $$6.1\sigma $$ significance of the violation of them.

DOI
10.1140/epjc/s10052-017-5371-y

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The Leggett–Garg inequality (LGI), derived under the assumption of realism, acts as the temporal Bell inequality. It is studied in electromagnetic and strong interaction like photonics, superconducting qubits and nuclear spin. The weak interaction two-state oscillations of neutrinos affirmed the violation of Leggett–Garg-type inequalities (LGtI). We make an empirical test for the deviation of experimental results with the classical limits by analyzing the survival probability data of reactor neutrinos at a distinct range of baseline dividing energies, as an analog to a single neutrino detected at different times. A study of the updated data of the Daya Bay experiment unambiguously depicts an obvious cluster of data over the classical bound of LGtI and shows a 6.1σ6.1\sigma 6.1σ significance of the violation of them.
Abstract Leggett–Garg inequality (LGI) is a time analogue of Bell’s inequality that concerns measurements performed on a system at different times. Violation to LGI indicates quantum coherence. We present a Leggett–Garg-type inequality compatible with more general neutrino oscillation frameworks, allowing the effects of decoherence to be taken into consideration. The inequality is applied to test coherence for data from Daya Bay, MINOS, and KamLAND experiments, and their results are compared to theoretical predictions to investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations of over 10σ10\sigma 10σ 10σ , and of over 90 %\%% % of theoretical predictions, while the KamLAND data exhibit violation of 1.9σ1.9\sigma 1.9σ 1.9σ , being of 58 %\%% % of the theoretical prediction. The present work is the first to have considered the energy uncertainties in neutrino coherence tests.
The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than 6σ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.
The Leggett-Garg inequality (LGI) as a temporal analog of Bell's inequality, derived using the notion of realism, is studied in a hitherto unexplored context involving weak-interaction-induced two-state oscillations of decaying neutral kaons and neutrinos. The maximum violation of the LGI obtained from the relevant quantum mechanical results is significantly higher for oscillating neutrinos compared to that for kaons. Interestingly, the effect of CP noninvariance for the kaon oscillation is to enhance this violation, while, for neutrinos, the violation is sensitive to the value of mixing parameter.
We revisit the study of the violation of the Leggett-Garg inequality in neutrino oscillation data as a mean to test some of the fundamental aspects of quantum mechanics. In particular, we consider the results of the Daya Bay and RENO reactor experiments, and the MINOS and NOvA accelerator experiments. We find that DB and MINOS exhibit a strong manifestation of Leggett-Garg violation, whereas for RENO and NOvA data, the indication is weaker. Considering the particular baselines and energy ranges explored by each experiment, our results demonstrate that the Leggett-Garg violation is more evident for smaller baseline-to-energy ratios in all the data sets studied, a relevant aspect to consider when looking for evidence of quantum mechanical decoherence in neutrino oscillations.
This project examines the quantum mechanical nature of neutrino oscillations through the Leggett-Garg Inequality (LGI), a test for temporal correlations that distinguishes quantum mechanics from classical hidden-variable theories. Using data from the MINOS experiment, which measures neutrino survival probabilities across a 735 km baseline, two methods were employed to calculate LGI violations: a conventional approach and an overlap method. While both are valid, the overlap method is theoretically more accurate as it incorporates uncertainties in energy. The conventional method identified 80 triplets with 62 LGI violations, while the overlap method identified 780 triplets with an average of 528 LGI violations. These results demonstrate significant LGI violations, affirming quantum coherence in neutrino oscillations and challenging classical macrorealism. This study advances our understanding of quantum behavior in macroscopic systems, offering robust evidence for the quantum mechanical framework of neutrino physics.
The Leggett-Garg inequality (LGI), an analogue of Bellś inequality involving correlations of measurements of one observable on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. In this work, we investigate its implications in the context of neutrino flavour (νeL↔νμLν_{e}^{L}\leftrightarrowν_μ^{L}νeL​↔νμL​) and spin (νeL↔νeRν_{e}^{L}\leftrightarrowν_{e}^{R}νeL​↔νeR​) oscillations in the presence of a constant transverse magnetic field. For systems with strong magnetic fields, we show that, for both cases, there are length regions ΔLΔLΔL where the LGI is violated, as quantified by the correlator functions K3K_{3}K3​ and K4K_{4}K4​.