Dynamics of disentanglement, density matrix and coherence in neutrino oscillations

TL;DR

This paper investigates the quantum dynamics of neutrino disentanglement, propagation, and detection, highlighting conditions for coherence and potential corrections in short-baseline experiments.

Contribution

It provides a detailed analysis of how neutrino states evolve and disentangle, connecting quantum measurement processes with neutrino oscillation phenomena and proposing possible experimental corrections.

Findings

Disentanglement time scales affect coherence and detection rates.

Factorization of detection probability holds when disentanglement occurs quickly.

Coherence persists up to the inverse oscillation frequency, then oscillates due to interference.

Abstract

In charged current weak interaction processes, neutrinos are produced in an entangled state with the charged lepton. This correlated state is disentangled by the measurement of the charged lepton in a detector at the production site. We study the dynamical aspects of disentanglement, propagation and detection, in particular the conditions under which the disentangled state is a coherent superposition of mass eigenstates. The appearance and disappearance far-detection processes are described from the time evolution of this disentangled "collapsed" state. The familiar quantum mechanical interpretation and factorization of the detection rate emerges when the quantum state is disentangled on time scales \emph{much shorter} than the inverse oscillation frequency, in which case the final detection rate factorizes in terms of the usual quantum mechanical transition probability provided the final density of states is insensitive to the neutrino energy difference. We suggest \emph{possible} corrections for short-baseline experiments. If the charged lepton is unobserved, neutrino oscillations and coherence are described in terms of a reduced density matrix obtained by tracing out an un-observed charged lepton. The diagonal elements in the mass basis describe the production of mass eigenstates whereas the off diagonal ones provide a measure of coherence. It is shown that coherences are of the same order of the diagonal terms on time scales up to the inverse oscillation frequency, beyond which the coherences oscillate as a result of the interference between mass eigenstates.