Entanglement in three-flavor collective neutrino oscillations

Extreme conditions present in the interiors of the core-collapse supernovae make neutrino-neutrino interactions not only feasible but dominant in specific regions, leading to the nonlinear evolution of the neutrino flavor. Results obtained when such collective neutrino oscillations are treated in the mean-field approximation deviate from the results using the many-body picture because of the ignored quantum correlations. We present the first three-flavor many-body calculations of the collective neutrino oscillations. The entanglement is quantified in terms of the entanglement entropy and the components of the polarization vector. We propose a qualitative measure of entanglement in terms of flavor-lepton number conserved quantities. We find that in the cases considered in the present work, the entanglement can be underestimated in the two-flavor approximation. The dependence of the entanglement on mass ordering is also investigated. We also explore the mixing of mass eigenstates in different mass orderings.

Automated summary

The extreme conditions in core-collapse supernovae allow for dominant neutrino-neutrino interactions, leading to nonlinear evolution of neutrino flavor. Previous mean-field approximations of collective neutrino oscillations deviate from many-body calculations due to the neglect of quantum correlations. We present the first three-flavor many-body calculations of collective neutrino oscillations, quantifying entanglement using entanglement entropy and polarization vector components. We propose a qualitative measure of entanglement based on flavor-lepton number conserved quantities and find that entanglement can be underestimated in two-flavor approximation. The dependence of entanglement on mass ordering is also investigated, along with the mixing of mass eigenstates in different orderings.