Quantum transitions and quantum entanglement from Dirac-like dynamics simulated by trapped ions

Quantum transition probabilities and quantum entanglement for two-qubit states of a four level trapped ion quantum system are computed for time-evolving ionic states driven by Jaynes-Cummings Hamiltonians with interactions mapped onto a \mbox{SU}(2)\otimes \mbox{SU}(2) group structure. Using the correspondence of the method of simulating a $3+1$ dimensional Dirac-like Hamiltonian for bi-spinor particles into a single trapped ion, one preliminarily obtains the analytical tools for describing ionic state transition probabilities as a typical quantum oscillation feature. For Dirac-like structures driven by generalized Poincar\'e classes of coupling potentials, one also identifies the \mbox{SU}(2)\otimes \mbox{SU}(2) internal degrees of freedom corresponding to intrinsic parity and spin polarization as an adaptive platform for computing the quantum entanglement between the internal quantum subsystems which define two-qubit ionic states. The obtained quantum correlational content is then translated into the quantum entanglement of two-qubit ionic states with quantum numbers related to the total angular momentum and to its projection onto the direction of the trapping magnetic field. Experimentally, the controllable parameters simulated by ion traps can be mapped into a Dirac-like system in the presence of an electrostatic field which, in this case, is associated to ionic carrier interactions. Besides exhibiting a complete analytical profile for ionic quantum transitions and quantum entanglement, our results indicate that carrier interactions actively drive an overall suppression of the quantum entanglement.Comment: 27 pags, 5 fig

Maximal correlation between flavor entanglement and oscillation damping due to localization effects

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 signatures exhibited by flavor transition probabilities as an effective averaging of the oscillating terms are then explained as owing to loss of entanglement between mass modes involved in the relativistic propagation.Comment: 13 pages, 03 figure

Chiral oscillations in three-flavor neutrino mixing

Massive particles whose dynamics are described by the free Dirac equation can oscillate between left and right-handed chiral states, undergoing chiral oscillations. The phenomenon is prominent for non-relativistic particles, and can yield a depletion on the expected measured flux of cosmic neutrinos and a modification of quantum correlations encoded in lepton-antineutrino pairs. In this context, the interplay between chiral and flavor oscillations plays an important role in the description of neutrino flavor dynamics. In this paper, we extend previous results and obtain flavor oscillation formulas including chiral oscillations for N flavor mixing. We consider the general case of mixing that can distinguish between left and right-handed states and derive the flavor oscillation probabilities for Dirac and Majorana neutrinos within the bispinor formalism. We show that, for three flavors, oscillation probabilities between chiral left and right-handed flavor states allows for distinguishing between Dirac and Majorana neutrinos in the presence of additional CP-violation Majorana phases. To summarize, our work addresses to phenomenologically accessible chiral oscillation effects on non-relativistic neutrino dynamics and on quantum correlations encoded in flavor states

Chiral oscillations in the non-relativistic regime

Massive Dirac particles are a superposition of left and right chiral components. Since chirality is not a conserved quantity, the free Dirac Hamiltonian evolution induces chiral quantum oscillations, a phenomenon related to the \textit{Zitterbewegung}, the trembling motion of free propagating particles. While not observable for particles in relativistic dynamical regimes, chiral oscillations become relevant when the particle's rest energy is comparable to its momentum. In this paper, we quantify the effect of chiral oscillations on the non-relativistic evolution of a particle state described as a Dirac bispinor and specialize our results to describe the interplay between chiral and flavor oscillations of non-relativistic neutrinos: we compute the time-averaged survival probability and observe an energy-dependent depletion of the quantity when compared to the standard oscillation formula. In the non-relativistic regime, this depletion due to chiral oscillations can be as large as 40$\%$. Finally, we discuss the relevance of chiral oscillations in upcoming experiments which will probe the cosmic neutrino background.Comment: 14 pages, 3 figure

Lepton-Antineutrino Entanglement and Chiral Oscillations

Dirac bispinors belong to an irreducible representation of the complete Lorentz group, which includes parity as a symmetry yielding two intrinsic discrete degrees of freedom: chirality and spin. For massive particles, chirality is not dynamically conserved, which leads to chiral oscillations. In this contribution, we describe the effects of this intrinsic structure of Dirac bispinors on the quantum entanglement encoded in a lepton-antineutrino pair. We consider that the pair is generated through weak interactions, which are intrinsically chiral, such that in the initial state the lepton and the antineutrino have definite chirality but their spins are entangled. We show that chiral oscillations induce spin entanglement oscillations and redistribute the spin entanglement to chirality-spin correlations. Such a phenomenon is prominent if the momentum of the lepton is comparable with or smaller than its mass. We further show that a Bell-like spin observable exhibits the same behavior of the spin entanglement. Such correlations do not require the knowledge of the full density matrix. Our results show novel effects of the intrinsic bispinor structure and can be used as a basis for designing experiments to probe chiral oscillations via spin correlation measurements