The dynamics of neutrino mixing and oscillations are studied directly in finite real time in a model that effectively describes charged current weak interactions. Finite time corrections to the S-matrix result for the appearance and disappearance probabilities are obtained. It is observed that these effects may be of the same order of the S-matrix result in long-baseline appearance experiments. We argue that fundamentally, the S-matrix is ill-suited to describe long-baseline events due to the fact that the neutrino is produced in an entangled state with the charged lepton, which can be disentangled by the measurement of the charged lepton near the production site. The appearance and disappearance far-detection process is described from the time evolution of this disentangled "collapsed" state, allowing us to establish the conditions under which factorization of detection rates emerges in long-baseline experiments. We also study the time evolution of the reduced density matrix and show explicitly how oscillations are manifest in the off-diagonal terms, i.e., coherences, as a result of a finite time analysis. Lastly, we study a model for the "GSI anomaly" obtaining the time evolution of the population of parent and daughter particles directly in real time. We confirm that the decay rate of parent and growth rate of daughters do NOT feature oscillatory behavior from interference of mass eigenstates.
The apparent symmetry between energy and momentum found in all covariant descriptions of neutrino oscillations is destroyed in the neutrino detector, a quantum mechanical system described by a density matrix diagonal in energy but not in momentum. The off diagonal matrix elements between states of different momenta and the same energy produce the coherence and interference between mass eigenstates having the same energy and different momenta that produce oscillations.
The definition of `lepton flavour eigenstates' introduced in a recent paper hep-ph/0302045 is in disagreement with the Standard Model prediction for the structure of the leptonic charged current and implies the absence of neutrino oscillations following pion decay, in contradiction to experimental data
The temporal and spatial coherence widths of the microscopic process by which a neutrino is detected are incorporated in the quantum mechanical wave packet treatment of neutrino oscillations, confirming the observation of Kiers, Nussinov and Weiss that an accurate measurement of the energies of the particles participating in the detection process can increase the coherence length. However, the wave packet treatment presented here shows that the coherence length has an upper bound, determined by the neutrino energy and the mass-squared difference, beyond which the coherence of the oscillation p…
General arguments in favor of the necessity of a wave packet description of neutrino oscillations are presented, drawing from analogies with other wave phenomena. We present a wave packet description of neutrino oscillations in stationary beams using the density matrix formalism. Recent claims of the necessity of an equal energy of different massive neutrinos are refuted.
The radical departure from classical physics implies quantum coherence, i.e., coherent superposition of eigenstates of Hermitian operators with a discrete spectrum. 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 flavor, …
In this paper, we consider the quantum correlations, coherence and entanglement, in neutrino oscillation. We find that the $l_{1}$-norm as a coherence measure is equal to sum of the three possible concurrences for measuring the entanglement among different flavor modes which were calculated in the paper by (M. Blasone et al., Europhys. Lett., {\bf 112}, 20007). Our result shows that the origin of the flavor entanglement in neutrino oscillation is the same as that of quantum coherence. Furthermore, in the wave packet framework, the variation of $l_{1}$-norm is investigated by varying the wave p…
We present a prescription for consistently constructing non-Fock coherent flavour neutrino states within the framework of the seesaw mechanism, and establish that the physical vacuum of massive neutrinos is a condensate of Standard Model massless neutrino states. The coherent states, involving a finite number of massive states, are derived by constructing their creation operator. Such a construction is the key requirement so that the oscillations of particles indeed occur. We comment on the inherent non-unitarity of the oscillation probability induced by the requirement of coherence.
We study two-flavor neutrino oscillations in a homogeneous and isotropic ensemble under the influence of neutrino-neutrino interactions. For any density there exist forms of collective oscillations that show self-maintained coherence. They can be classified by a number N of linearly independent functions that describe all neutrino modes as linear superpositions. What is more, the dynamics is equivalent to another ensemble with the same effective density, consisting of N modes with discrete energies E_i with i=1, ..., N. We use this equivalence to derive the analytic solution for two-mode (bimo…
We investigate and quantify various measures of bipartite and tripartite entanglement in the context of two and three flavor neutrino oscillations. The bipartite entanglement is analogous to the entanglement swapping resulting from a beam splitter in quantum optics. For the three neutrino systems various measures of tripartite entanglement are explored. The significant result is that a monogamy inequality in terms of negativity leads to a residual entanglement, implying true tripartite entanglement in the three neutrino system. This leads us to an analogy of the three neutrino state with a gen…
We study the effect of coherent and incoherent broadening on neutrino oscillations both in vacuum and in the presence of matter (the MSW effect). We show under very general assumptions that it is not possible to distinguish experimentally neutrinos produced in some region of space as wave packets from those produced in the same region of space as plane waves with the same energy distribution.
Leggett-Garg Inequality~(LGI) is a time analogue of Bell's inequality that concerns measurements performed on a system at different times. Violation to LGI indicates quantum coherence. We present a Leggett-Garg-type inequality compatible with more general neutrino oscillation frameworks, allowing the effects of decoherence to be taken into consideration. The inequality is applied to test coherence for data from Daya Bay, MINOS, and KamLAND experiments, and their results are compared to theoretical predictions to investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations of …
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.
We study the propagation coherence for neutrino oscillations in media with different density profiles. For each profile, we find the dependence of the coherence length, $L_{coh}$, on neutrino energy and address the issue of correspondence of results in the distance and energy-momentum representations. The key new feature in matter is existence of energy ranges with enhanced coherence around the energies $E_0$ of "infinite coherence" at which $L_{coh} \rightarrow \infty$. In the configuration space, the infinite coherence corresponds to equality of the (effective) group velocities of the eigens…
The quantum field theoretical description of coherence in the oscillations of particles, especially neutrinos, is a standing problem in particle physics. In this talk, several inconsistencies of the standard approach to particle oscillations will be explained, and how they are resolved in a process-independent manner, by a novel approach inspired by the Bardeen--Cooper--Schrieffer theory of superconductivity and the Nambu--Jona-Lasinio model. The formalism leads to corrections to the neutrino oscillation probability originally written by Pontecorvo and Gribov, however the standard probability …
Localization effects and quantum decoherence driven by the mass-eigenstate wave packet propagation are shown to support a statistical correlation between quantum entanglement and damped oscillations in the scenario of three-flavor quantum mixing for neutrinos. Once the mass-eigenstates that support flavor oscillations are identified as three-{\em qubit} modes, a decoherence scale can be extracted from correlation quantifiers, namely the entanglement of formation and the logarithmic negativity. Such a decoherence scale is compared with the coherence length of damped oscillations. Damping signat…
In this paper, we investigate the quantum coherence for two flavor neutrinos propagating in a Schwarzschild metric. In fact, this issue is explored both qualitatively via calculating the parameter $K_{3}$ in Leggett-Garg inequality (LGI) and also quantitatively by evaluating the $l_{1}$-norm, ${\cal C}(ρ)$. Using the weak field approximations, we show that the gravitational effects decrease the maximum value of $K_{3}$ for some intervals of energy such a way that there is no violation, while it leaves the maximum amount of the quantum coherence, ${\cal C}(ρ)$ unchanged.
