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Nuclear Physics B

Measuring entangled neutrino states in a toy model QFT

Hosam Mohammed, Jarah Evslin, Emilio Ciuffoli

Published Jul 9, 2020• 5 citations
Publisher

Abstract

Localized wave packet treatments of neutrino oscillations by various groups lead to mutually inconsistent predictions. The neutrino wave packet description arises as an approximate substitute for the evolution of an entangled state which is not localized. The disagreements arise from qualitative differences in the framework which are not specific to electroweak interactions, and so have analogues in simpler models. Therefore in this note we introduce a toy model which allows one to explicitly test these predictions while consistently keeping track of the entanglement of the neutrinos and the source particles. Our study is robust as we use only the Schrodinger picture evolution equations on the entangled state, which are solved explicitly without recourse to the wave packet approximation.

DOI
10.1016/j.nuclphysb.2020.115113

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Localized wave packet treatments of neutrino oscillations by various groups lead to mutually inconsistent predictions. The neutrino wave packet description arises as an approximate substitute for the evolution of an entangled state which is not localized. The disagreements arise from qualitative differences in the framework which are not specific to electroweak interactions, and so have analogues in simpler models. Therefore in this note we introduce a toy model which allows one to explicitly test these predictions while consistently keeping track of the entanglement of the neutrinos and the source particles. Our study is robust as we use only the Schrodinger picture evolution equations on the entangled state, which are solved explicitly without recourse to the wave packet approximation.
It has been claimed that wave packets must be covariant and also that decohered neutrino oscillations are always revived during measurement. These conjectures are supported by general arguments which are not specific to the electroweak theory, and so if they are true for neutrinos they will also be true for simplified models. In this paper we produce such a simplified model in which the neutrino wave function, including its entanglement with the source particle and the environment, can be calculated explicitly in quantum field theory. It exhibits neutrino oscillation, which is reduced at late times by decoherence due to interactions of the source with the environment. One simple lesson from this model is that only the difference between the environmental interactions before and after neutrino emission can reduce the amplitude of neutrino oscillations. The model will be used to test the conjectures in a companion paper.
It has been claimed that wave packets must be covariant and also that decohered neutrino oscillations are always revived during measurement. These conjectures are supported by general arguments which are not specific to the electroweak theory, and so if they are true for neutrinos they will also be true for simplified models. In this paper we produce such a simplified model in which the neutrino wave function, including its entanglement with the source particle and the environment, can be calculated explicitly in quantum field theory. It exhibits neutrino oscillation, which is reduced at late times by decoherence due to interactions of the source with the environment. One simple lesson from this model is that only the difference between the environmental interactions before and after neutrino emission can reduce the amplitude of neutrino oscillations. The model will be used to test the conjectures in a companion paper.
The initial configuration of a neutrino experiment consists of wave packets, created by the experimenter. Unmeasured final states are essentially delocalized, but it is conventional to nonetheless treat them as localized wave packets as they are in a sense measured by the environment. In this note we consider an experiment in the vacuum, and so there is no environment and the unmeasured final states are not localized. We introduce a simplified but consistent model of neutrino interactions and numerically evolve the system over a finite time using the Hamiltonian to obtain the oscillation probability. All particles involved in neutrino production or detection, localized or not, are treated and evolved consistently in quantum field theory, keeping all entanglements.
Abstract Quantum correlations provide a fertile testing ground for investigating fundamental aspects of quantum physics in various systems, especially in the case of relativistic (elementary) particle systems as neutrinos. In a recent paper, Ming et al. (Eur Phys J C 80:275, 2020), in connection with results of Daya-Bay and MINOS experiments, have studied the quantumness in neutrino oscillations in the framework of plane-wave approximation. We extend their treatment by adopting the wave packet approach that accounts for effects due to localization and decoherence. This leads to a better agreement with experimental results, in particular for the case of MINOS experiment.
I will present some of the results obtained regarding the emergence of decoherence in neutrino oscillations. In our model all the particles, including the source and detector, are treated dynamically and evolved consistently with Quantum Field Theory; decoherence can emerge naturally given the time evolution of the initial state and the final state considered. We have shown that some of the assumptions commonly used in the literature, such as the covariance of the wavepackets, are inconsistent. We found that a crucial ingredient for decoherence is the localization in space-time of the neutrino creation and detection: in Nature, such a measurement is usually carried out by environmental interactions, however it could also be approximated by considering localized wavefunctions in the final state. On the other hand, if the environmental interactions are not present (for example, if the decay happens in vacuum), the final position of the daughter particles will not be measured, i.e. they will be described by plane waves instead: in this case the neutrino is not localized either, and we don't have decoherence. A consequence of the time-evolution is that a Gaussian wavepacket will gradually spread: I will show that such an effect could in principle affect decoherence; moreover it would depend on the absolute mass scale of the neutrino, not on the Δm2\Delta m^2Δm2, which could offer a possible way to probe such a parameter by studying the neutrino oscillations.
The wave packet approach to neutrino oscillations provides an enlightening description of quantum decoherence induced, during propagation, by localization effects. Within this approach, we show that a deeper insight into the dynamical aspects of particle mixing can be obtained if one investigates the behavior of quantum correlations associated to flavor oscillations. By identifying the neutrino three-flavor modes with (suitably defined) three-qubit modes, the exploitation of tools of quantum information theory for mixed states allows a detailed analysis of the dynamical behavior of flavor entanglement during free propagation. This provides further elements leading to a more complete understanding of the phenomenon of neutrino oscillations, and a basis for possible applicative implementations. The analysis is carried out by studying the distribution of the flavor entanglement; to this aim, we perform combined investigations of the behaviors of the two-flavor concurrence and of the logarithmic negativities associated with specific bipartitions of the three flavors.