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Register a new userA field-theoretical approach to entanglement in neutrino mixing and oscillations
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The phenomena of particle mixing and flavor oscillations in elementary particle physics can be addressed by the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we show that such a description can be extended to the domain of quantum field theory, where we uncover a fine structure of quantum correlations associated with multi-mode, multi-particle entanglement. By means of an entanglement measure based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the states of flavor neutrinos and anti-neutrinos. Remarkably, we show that the entanglement is connected with experimentally measurable quantities, i.e. the variances of the lepton numbers and charges.
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We report on recent results about entanglement in the context of particle mixing and oscillations. We study in detail single-particle entanglement arising in two-flavor neutrino mixing. The analysis is performed first in the context of Quantum Mechanics, and then for the case of Quantum Field Theory.
Neutrino mixing and oscillations in quantum field theory framework had been studied before, which shew that the Fock space of flavor states is unitarily inequivalent to that of mass states (inequivalent vacua model). A paradox emerges when we use these neutrino weak states to calculate the amplitude of $W$ boson decay. The branching ratio of W(+) -> e(+) + nu_mu to W(+) -> e(+) + nu_e is approximately at the order of O({m_i^2}/{k^2}). The existence of flavor changing currents contradicts to the Hamiltonian we started from, and the usual knowledge about weak processes. Also, negative energy neutrinos (or violating the principle of energy conservation) appear in this framework. We discuss possible reasons for the appearance of this paradox.
We propose a covariant scheme for measuring entanglement on general hypersurfaces in relativistic quantum field theory. For that, we introduce an auxiliary relativistic field, the discretizer, that by locally interacting with the field along a hypersurface, fully swaps the fields and discretizers states. It is shown, that the discretizer can be used to effectively cut-off the fields infinities, in a covariant fashion, and without having to introduce a spatial lattice. This, in turn, provides us an efficient way to evaluate entanglement between arbitrary regions on any hypersurface. As examples, we study the entanglement between complementary and separated regions in 1+1 dimensions, for flat hypersurfaces in Minkowski space, for curved hypersurfaces in Milne space, and for regions on hypersurfaces approaching null-surfaces. Our results show that the entanglement between regions on arbitrary hypersurfaces in 1+1 dimensions depends only on the space-time endpoints of the regions, and not on the shape of the interior. Our results corroborate and extend previous results for flat hypersurfaces.
We consider a class of models for the relativistic covariant wave packets which can be used as asymptotically free in and out states in the quantum field theoretical formalisms for description of the neutrino flavor oscillation phenomenon. We demonstrate that the new asymmetric wave packet (AWP) is an appropriate alternative for the more convenient symmetric wave packets, like the so-called relativistic Gaussian packet (RGP) widely used in the QFT-based approaches to neutrino oscillations. We show that RGP is not a particular case of AWP, although many properties of these models are almost identical in the quasistable regime. We discuss some features of AWP distinguishing it from RGP.
We investigate the importance of going beyond the mean-field approximation in the dynamics of collective neutrino oscillations. To expand our understanding of the coherent neutrino oscillation problem, we apply concepts from many-body physics and quantum information theory. Specifically, we use measures of nontrivial correlations (otherwise known as entanglement) between the constituent neutrinos of the many-body system, such as the entanglement entropy and the Bloch vector of the reduced density matrix. The relevance of going beyond the mean field is demonstrated by comparisons between the evolution of the neutrino state in the many-body picture vs the mean-field limit, for different initial conditions.
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