Entanglement and correlations in fast collective neutrino flavor oscillations

TL;DR

This paper investigates the full many-body quantum dynamics of fast collective neutrino flavor oscillations, revealing different regimes of stability, the role of entanglement, and connecting fast modes to slow bipolar oscillations.

Contribution

It provides a detailed analysis of many-body effects, entanglement, and phase transitions in fast neutrino oscillations beyond mean-field approximations.

Findings

Identification of three dynamical regimes: stable, marginally unstable, and unstable configurations.

Evidence linking fast collective modes to the same phase transition as slow bipolar oscillations.

Development of a semi-classical approximation capturing entanglement entropy dynamics.

Abstract

Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings like supernovae and neutron star binary merger remnants, which are characterized by large neutrino densities. In these settings, simulations in the mean-field approximation show that neutrino-neutrino interactions can overtake vacuum oscillations and give rise to fast collective flavor evolution on time-scales $t\propto\mu^{-1}$, with $\mu$ proportional to the local neutrino density. In this work, we study the full out-of-equilibrium flavor dynamics in simple multi-angle geometries displaying fast oscillations in the mean field linear stability analysis. Focusing on simple initial conditions, we analyze the production of pair correlations and entanglement in the complete many-body-dynamics as a function of the number $N$ of neutrinos in the system, for up to thousands of neutrinos. Similarly to simpler geometries with only two neutrino beams, we identify three regimes: stable configurations with vanishing flavor oscillations, marginally unstable configurations with evolution occurring on long time scales $\tau\approx\mu^{-1}\sqrt{N}$, and unstable configurations showing flavor evolution on short time scales $\tau\approx\mu^{-1}\log(N)$. We present evidence that these fast collective modes are generated by the same dynamical phase transition which leads to the slow bipolar oscillations, establishing a connection between these two phenomena and explaining the difference in their time scales. We conclude by discussing a semi-classical approximation which reproduces the entanglement entropy at short to medium time scales and can be potentially useful in situations with more complicated geometries where classical simulation methods starts to become inefficient.