Two Flavour Neutrino Oscillation in Matter and Quantum Entanglement
Bipin Singh Koranga, Baktiar Wasir Farooq
TL;DR
This paper investigates quantum entanglement in two-flavor neutrino oscillations propagating through matter by applying Von Neumann entropy to quantify entanglement between flavour modes. It articulates the vacuum and matter oscillation formalisms, introducing matter-modified mixing and mass-squared differences with $A=2\sqrt{2}G_{F}N_{e}E$ and $\Delta_{21}^{m}$, and derives the corresponding oscillation probability $P_{e\mu}^{m}$. Entanglement entropy is computed from the reduced density matrix as $S(\rho)=-\mathrm{Tr}(\rho\log\rho)$, yielding the matter form $S^{matter}(\rho) = -P_{Survival}^{matter}\log P_{Survival}^{matter} - P_{Oscillation}^{matter}\log P_{Oscillation}^{matter}$. Numerical results for representative matter density and mixing parameters indicate that matter effects typically enhance entanglement and modify the $L/E$ dependence of the entanglement, highlighting a link between matter-modified flavor dynamics and quantum correlations.
Abstract
In this article, we investigate the entanglement entropy for neutrino oscillations when neutrino propogate in matter, utilising Von Neumann entropy. We discuss two flavour neutrino oscillation in vaccum and matter. We demonstrate statistically that, depending on the length of oscillation for each energy, the entanglement entropy for the succeeding periods of the two-flavor neutrino oscillations in matter.