Role of non-gaussian quantum fluctuations in neutrino entanglement

Abstract

The flavor evolution of neutrinos in environments with large neutrino number densities is an open problem at the nexus of astrophysics and neutrino flavor physics. Among the many unanswered questions pertaining to this problem, it remains to be determined whether neutrino-neutrino coherent scattering can give rise to nontrivial quantum entanglement among neutrinos, and whether this can affect the flavor evolution in a meaningful way. To gain further insight into this question, here we study a simple system of two interacting neutrino beams, and obtain the exact phase-space explored by this system using the Husimi quasi-probability distribution. We observe that the entanglement induced by the coupling leads to strong delocalization in phase-space with largely non-Gaussian quantum fluctuations. The link between the neutrino entanglement and quantum fluctuations is illustrated using the one-and two-neutrino entropy. In addition, we propose an approximate phasespace method to describe the interacting neutrinos problem, where the exact evolution is replaced by a set of independent mean-field evolutions with a statistical sampling of the initial conditions. The phase-space approach provides a simple and accurate method to describe the gross features of the neutrino entanglement problem. Applications are shown using time-independent and timedependent Hamiltonians in the non-adiabatic regime.

Neutrino Fast Flavor Instability in three dimensions for a Neutron Star Merger

“…If we ignore higher-order correlations by employing a mean-field approximation, we can construct dynamical quantities which only encode flavor coherence. (For investigations of the appropriateness of the mean field approximation see [47][48][49][50][51][52]). These quantities are the neutrino generalized density matrices, and which characterize the phase-space density for neutrinos and antineutrinos at time t, 3-position x, and 3-momentum p. When integrated over phase space, their diagonal components represent the number of neutrinos of a given flavor while the off-diagonal components give a measure of the coherence between two flavors.…”

Multi-Neutrino Entanglement and Correlations in Dense Neutrino Systems

“…Coherent evolution of lepton flavors, that depends on self-interactions between neutrinos induced by weak interactions [6][7][8][9][10], plays an important role. First studies of the quantum correlations in coherent evolution of dense neutrino systems, beyond meanfield descriptions, are providing important insights into such dynamics [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. So far, they have focused on entanglement witnesses involving two neutrinos, such as entanglement entropy, negativity and concurrence [15][16][17][18][19][21][22][23][24][25][26].…”