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 Poincaré 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 Poincaré 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.

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

“…For instance, trapped ion interacting Hamiltonians once mapped onto the structure of the Dirac equation can straightforwardly reproduce typical quantum effects of relativistic nature, such as the zitterbewegung/trembling motion [6], the Klein paradox [7], or even the spinor-motion correlation inherent to the tachyonic dynamics [13]. Moreover, quantum correlations between SU(2) ⊗ SU(2) internal degrees of freedom of intrinsic parity and spin polarization of Dirac particles [14,15] (corresponding to SU(2) ⊗ SU(2) bi-spinors) can work as an efficient quantifier of two-qubit entanglement of trapped ion structures.…”

“…(3) can be reproduced by a suitable trapped ion setup [11] such that its eigenstates are given in terms of a superposition of four internal ionic states, which spans the four dimensional Hilbert space associated to the Dirac bi-spinor discrete degrees of freedom. By suitably mapping the ionic state basis onto the complete set of four eigenstates of (3) [15], the dynamics of the ionic states can be entirely described by the Dirac SU(2) ⊗ SU(2) structure. Then, the transition probabilities between the different internal ionic levels (once driven by the Dirac-like dynamics), and the entanglement/separability between states with different angular momenta can be straightforwardly computed, as well as their origins can be identified in terms of Dirac-like observables related to the encoded quantum concurrence between spin polarization and intrinsic parity.…”

“…In particular, the inclusion of additional Dirac-like global potentials driven by (pseudo)scalar, (pseudo)vector and (pseudo)tensor interactions can also create novel patterns of intrinsic SU(2) ⊗ SU(2) quantum correlations as well as destroy the separability of an eventual free particle state [15].…”

“…Considering that the Dirac Hamiltonian may be written in terms of the direct product of two-qubit operators [14,15], the SU(2)⊗SU(2) group structure (c. f. the Appendix) involving such spin-parity internal degrees of freedom exhibits an energy spectrum associated to twoqubit quantum correlated states [14]. In particular, the inclusion of additional Dirac-like global potentials driven by (pseudo)scalar, (pseudo)vector and (pseudo)tensor interactions can also create novel patterns of intrinsic SU(2) ⊗ SU(2) quantum correlations as well as destroy the separability of an eventual free particle state [15].…”

“…The complete overview of the entanglement driven by Poincaré classes of SU(2) ⊗ SU (2) coupling potentials [15] can be specialized for more feasible ionic systems as, for instance, those ones that simulate the behavior of the electric dipole moment of a spin one-half particle in an electromagnetic field [11,21]. In this case, the Hamiltonian for a neutral Dirac particle with momentum p and mass m non-minimally coupled to external electric and magnetic fields, E and B, is given bŷ…”