Victor A. S. V. Bittencourt

The CνB energy density through the quantum measurement theory

We apply concepts from the quantum measurement theory to obtain some cosmological neutrino background (CνB) properties and discuss their relevance in defining theoretical bounds on cosmological neutrino energy density. Describing three neutrino generations as a composite quantum system through the generalized theory of quantum measurement provides us with the probabilistic correlation between observable energies and neutrino flavor eigenstates. By observing that flavor-averaged and flavor-weighted energies are the quantum observables respectively generated by selective and non-selective quantum measurement schemes, it is possible to identify the constraints on the effective mass value expression that determines the neutrino contribution to the energy density of the cosmic inventory. Our results agree with the quantum mechanics viewpoint that asserts that the cosmological neutrino energy density is obtained from a coherent sum of mass eigenstate energies, for normal and inverted mass hierarchies.

Entanglement of Dirac bi-spinor states driven by Poincaré classes of SU(2)⊗SU(2) coupling potentials

Abstract A generalized description of entanglement and quantum correlation properties constraining internal degrees of freedom of Dirac(-like) structures driven by arbitrary Poincare classes of external field potentials is proposed. The role of (pseudo)scalar, (pseudo)vector and tensor interactions in producing/destroying intrinsic quantum correlations for SU ( 2 ) ⊗ SU ( 2 ) bi-spinor structures is discussed in terms of generic coupling constants. By using a suitable ansatz to obtain the Dirac Hamiltonian eigenspinor structure of time-independent solutions of the associated Liouville equation, the quantum entanglement, via concurrence, and quantum correlations, via geometric discord, are computed for several combinations of well-defined Poincare classes of Dirac potentials. Besides its inherent formal structure, our results set up a framework which can be enlarged as to include localization effects and to map quantum correlation effects into Dirac-like systems which describe low-energy excitations of graphene and trapped ions.

SU(2)⊗SU(2) bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions

The entanglement between SU(2) SU(2) internal degrees of freedom of parity and helicity for reected and transmitted waves of Dirac-like particles scattered by a potential step along an arbitrary direction on the x y plane is quantied. Diusion ( E V ) and Klein zone (V E) energy regimes are considered. It has been shown that, for SU(2) SU(2) polarized structures of helicity eigenstates impinging the barrier, the local interaction with a step potential destroys the parity-spin separability. The framework presented here can be straightforwardly translated into a useful theoretical tool for obtaining the spin-spin entanglement in the context of enlarged scenarios of nonrelativistic 2D systems, as for instance those for describing single layer graphene, or even single trapped ions with Dirac bi-spinor mathematical structure.

Lattice-layer entanglement in Bernal-stacked bilayer graphene

The complete lattice-layer entanglement structure of Bernal stacked bilayer graphene is obtained for the quantum system described by a tight-binding Hamiltonian which includes mass and bias voltage terms. Through a suitable correspondence with the parity-spin

Schr\"odinger cat and Werner state disentanglement simulated by trapped ion systems

SU(2)\otimes SU(2)

Entanglement of Dirac bi-spinor states driven by Poincar\'e classes of

structure of a Dirac Hamiltonian, when it brings up tensor and pseudovector external field interactions, the lattice-layer degrees of freedom can be mapped into such a parity-spin two-qubit basis which supports the interpretation of the bilayer graphene eigenstates as entangled ones in a lattice-layer basis. The Dirac Hamiltonian mapping structure simply provides the tools for the manipulation of the corresponding eigenstates and eigenenergies of the Bernal-stacked graphene quantum system. The quantum correlational content is then quantified by means of quantum concurrence, in order to have the influence of mass and bias voltage terms quantified, and in order to identify the role of the trigonal warping of energy in the intrinsic entanglement. Our results show that while the mass term actively suppresses the intrinsic quantum entanglement of bilayer eigenstates, the bias voltage term spreads the entanglement in the Brillouin zone around the Dirac points. In addition, the interlayer coupling modifies the symmetry of the lattice-layer quantum concurrence around a given Dirac point. It produces some distortion on the quantum entanglement profile which follows the same pattern of the isoenergy line distortion in the Bernal-stacked bilayer graphene.

\mbox{SU}(2) \otimes \mbox{SU}(2)

Disentanglement and loss of quantum correlations due to one global collective noise effect are described for two-qubit Schrodinger cat and Werner states of a four level trapped ion quantum system. Once the Jaynes-Cummings ionic interactions are mapped onto a Dirac spinor structure, the elementary tools for computing quantum correlations of two-qubit ionic states are provided. With two-qubit quantum numbers related to the total angular momentum and to its projection onto the direction of an external magnetic field (which lifts the degeneracy of the ions internal levels), a complete analytical profile of entanglement for the Schrodinger cat and Werner states is obtained. Under vacuum noise (during spontaneous emission), the two-qubit entanglement in the Schrodinger cat states is shown to vanish asymptotically. Otherwise, the robustness of Werner states is concomitantly identified, with the entanglement content recovered by their noiseless-like evolution. Most importantly, our results point to a firstly reported sudden transition between classical and quantum decay regimes driven by a classical collective noise on the Schrodinger cat states, which has been quantified by the geometric discord.

coupling potentials

Abstract A generalized description of entanglement and quantum correlation properties constraining internal degrees of freedom of Dirac(-like) structures driven by arbitrary Poincare classes of external field potentials is proposed. The role of (pseudo)scalar, (pseudo)vector and tensor interactions in producing/destroying intrinsic quantum correlations for SU ( 2 ) ⊗ SU ( 2 ) bi-spinor structures is discussed in terms of generic coupling constants. By using a suitable ansatz to obtain the Dirac Hamiltonian eigenspinor structure of time-independent solutions of the associated Liouville equation, the quantum entanglement, via concurrence, and quantum correlations, via geometric discord, are computed for several combinations of well-defined Poincare classes of Dirac potentials. Besides its inherent formal structure, our results set up a framework which can be enlarged as to include localization effects and to map quantum correlation effects into Dirac-like systems which describe low-energy excitations of graphene and trapped ions.

Effects of Lorentz boosts on Dirac bispinor entanglement

In this paper we describe the transformation properties of quantum entanglement encoded in a pair of spin 1/2 particles described via Dirac bispinors. Due to the intrinsic parity-spin internal structure of the bispinors, the joint state is a four-qubit state exhibiting multipartite entanglement, and to compute global correlation properties we consider the averaged negativities over each possible bi-partition. We also consider specific bipartitions, such as the spin-spin and the particle-particle bipartitions. The particle-particle entanglement, between all degrees of freedom of one particle and all degrees of freedom of the other particle, is invariant under boosts if each particle has a definite momentum, although the spin-spin entanglement is degraded for high speed boosts. Correspondingly, the mean negativities are not invariant since the boost drives changes into correlations encoded in specific bipartitions. Finally, the results presented in the literature about spin-momentum entanglement are recovered by considering the projection of bispinorial states into positive intrinsic parity, and some striking differences between the appropriate approach for this case and the one usually treated in the literature are discussed.

Graphene lattice-layer entanglement under non-Markovian phase noise.

The evolution of single particle excitations of bilayer graphene under effects of non-Markovian noise is described with focus on the decoherence process of lattice-layer (LL) maximally entangled states. Once that the noiseless dynamics of an arbitrary initial state is identified by the correspondence between the tight-binding Hamiltonian for the AB-stacked bilayer graphene and the Dirac equation -- which includes pseudovector- and tensor-like field interactions -- the noisy environment is described as random fluctuations on bias voltage and mass terms. The inclusion of noisy dynamics reproduces the Ornstein-Uhlenbeck processes: a non-Markovian noise model with a well-defined Markovian limit. Considering that an initial amount of entanglement shall be dissipated by the noise, two profiles of dissipation are identified. On one hand, for eigenstates of the noiseless Hamiltonian, deaths and revivals of entanglement are identified along the oscillation pattern for long interaction periods. On the other hand, for departing LL Werner and Cat states, the entanglement is suppressed although, for both cases, some identified memory effects compete with the pure noise-induced decoherence in order to preserve the the overall profile of a given initial state.