Emaranhamento intrínseco em sistemas tipo-Dirac

Abstract

Dirac equation is supported by a $SU(2) \otimes SU(2)$ group structure, such that its solutions describe two discrete degrees of freedom, intrinsic parity and spin, which in general are entangled. In this work we will characterize such spin-parity under a general perspective as well as from the point of view of two Dirac-like systems: a four level trapped ion, in the context of the quantum simulation of Dirac equation with external fields, and for the bilayer graphene. We will derive a method for the construction of the eigenstates of the Dirac Hamiltonian including constant external potentials. We will then study the non-local character of mixed bispinor states in connection with CP transformations, verifying that the spin-parity entanglement is invariant under such transformations. Additionally, we will investigate how Lorentz boosts affect the entanglement encoded in two bispinorial particles. In this last case, entanglement is not in general invariant for antisymmetric states, although the entanglement on chiral projections exhibit invariance properties. In the second part of the work, we will describe how the spin-parity entanglement is translated to the Dirac-like systems considered. For the bilayer graphene, for example, the $SU(2)\otimes SU(2)$ structure of Dirac equation is reflected onto entanglement between lattice and layer quantum numbers. We will describe the evolution of arbitrary states of such systems and we will consider the inclusion of global and local noise effects on the Dirac-like dynamics, through Kraus operators, related to random fluctuations of the system parameters. For both systems the noise degraded the entanglement associated with the $SU(2) \otimes SU(2)$ structure. Our results and the formalism here develop are a support for the description of intrinsic correlations in Dirac-like systems, specially for graphene, which can be further develop for implementation of quantum algorithms.