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

Abstract

The entanglement between $SU(2)\otimes SU(2)$ internal degrees of freedom of parity and helicity for reflected and transmitted waves of Dirac-like particles scattered by a potential step along an arbitrary direction on the $x-y$ plane is quantified. Diffusion ($E\ge V$) and Klein zone ($V\ge E$) energy regimes are considered. It has been shown that, for $SU(2)\otimes SU(2)$ polarized structures of helicity eigenstates impinging the barrier, the local interaction with a {\em step} potential destroys the {\em parity-spin} separability. The framework presented here can be straightforwardly translated into a useful theoretical tool for obtaining the {\em 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.

arXiv comment20 pages, 5 figures

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Cited by in corpus (9)

• Lattice-layer entanglement in Bernal-stacked bilayer graphene
• Entanglement of Dirac bi-spinor states driven by Poincaré classes of $\mbox{SU}(2) \otimes \mbox{SU}(2)$ coupling potentials
• Quantum transitions and quantum entanglement from Dirac-like dynamics simulated by trapped ions
• Graphene lattice-layer entanglement under non-Markovian phase noise
• Effects of Lorentz boosts on Dirac bispinor entanglement
• Schrödinger cat and Werner state disentanglement simulated by trapped ion systems
• Goos-H{ä}nchen Shift for Relativistic Particles Based on Dirac's Equation
• CP symmetry and thermal effects on Dirac bi-spinor spin-parity local correlations
• Dirac bi-spinor entanglement under local noise and its simulation by Jaynes-Cummings interactions