Coherence and mixedness of neutrino oscillations in a magnetic field

Abstract

The radical departure from classical physics implies quantum coherence, i.e., coherent superposition of eigenstates of Hermitian operators. In resource theory, quantum coherence is a resource for quantum operations. Typically the stochastic phenomenon induces decoherence effects. However, in the present work, we prove that nonunitary evolution leads to the generation of quantum coherence in some cases. Specifically, we consider the neutrino propagation in the dissipative environment, namely in a magnetic field with a stochastic component, and focus on neutrino flavour, spin and spin-flavour oscillations. We present exact analytical results for quantum coherence in neutrino oscillations quantified in terms of the relative entropy. Starting from an initial zero coherence state, we observe persistent oscillations of coherence during the dissipative evolution of an ultra-high energy neutrino in a random interstellar magnetic field. We found that after dissipative evolution, the initial spin-polarized state entirely “thermalizes”, and in the final steady state, the spin-up/down states have the same probabilities. On the other hand, neutrino flavour states also “thermalize”, but the populations of two flavour states do not equate to each other. The initial flavour still dominates in the final steady state.