Quantum correlations in neutrino oscillations in curved spacetime

Gravity induced neutrino-antineutrino oscillations are studied in the context of one- and two-flavor scenarios. This allows one to investigate the particle-antiparticle correlations in two and four level systems, respectively. Flavor entropy is used to probe the entanglement in the system. The well known witnesses of nonclassicality such as Mermin and Svetlichny inequalities are investigated. Since the extent of neutrino-antineutrino oscillation is governed by the strength of the gravitational field, the behavior of nonclassicality shows interesting features as one varies the strength of the gravitational field. Specifically, the suppression of the entanglement with the increase of the gravitational field is observed which is witnessed in the form of decrease in the flavor entropy of the system. The features of the Mermin and the Svetlichny inequalities allow one to make statements about the degeneracy of neutrino mass eigenstates.

Figure 1

Gravitational “Zeeman-splitting”: Weak gravitational effect, as given by Eq. (3), is considered for the ease of demonstration.

Figure 2

Neutrino-antineutrino oscillations in (a) one-flavor, and (b) two-flavor scenarios.

Figure 3

Fixed flavor case: (a) Survival probability, and (b) von Neumann entropy, as functions of gravitational potential and distance traveled by neutrino/antineutrino, for the massive states ${\nu }_1\leftrightarrow {\nu }_2$ corresponding to neutrino-antineutrino oscillation. The various parameters used are: $m=5\times {10}^{-3}\mathrm{eV}$, $|\overrightarrow{B^g}|\sim {10}^{-2}\mathrm{eV}$.

Figure 4

Left panel: The variation of von Neumann entropy for 2-flavor neutrino-antineutrino oscillation with respect to the distance ($L$) traveled by neutrinos and the gravitational potential ($B_0^g$). Right panel: The contributions to flavor entropy from neutrino-neutrino oscillations depicted by blue (plane) surface and neutrino-antineutrino oscillations shown by pink (meshed) surface, with the magnitude of $\mathcal{S}$ enhanced 10 times in the later case.

Figure 5

(a) Mermin $M_4$ and (b) Svetlichny $S_4$ parameters with respect to the distance ($L$) traveled by neutrinos with $B_0^g=5\times {10}^{-2}$. Black lines correspond to the classical bounds of these parameters.