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

Victor A. S. V. Bittencourt, Alex E. Bernardini, and Massimo Blasone
Phys. Rev. A 93, 053823 – Published 17 May 2016

Abstract

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 SU(2)SU(2) group structure. Using the correspondence of the method of simulating a 3+1 dimensional Dirac-like Hamiltonian for bispinor 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 Poincaré classes of coupling potentials, one also identifies the SU(2)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.

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  • Received 24 January 2016

DOI:https://doi.org/10.1103/PhysRevA.93.053823

©2016 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalQuantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Victor A. S. V. Bittencourt* and Alex E. Bernardini

  • Departamento de Física, Universidade Federal de São Carlos, P. O. Box 676, 13565-905, São Carlos, SP, Brasil

Massimo Blasone

  • Dipartimento di Fisica, Università Di Salerno, Via Giovanni Paolo II, 132 84084 Fisciano, Italy

  • *vbittencourt@df.ufscar.br
  • alexeb@ufscar.br
  • blasone@sa.infn.it; also at: INFN Sezione di Napoli, Gruppo collegato di Salerno, Italy.

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Issue

Vol. 93, Iss. 5 — May 2016

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