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Bittencourt, Victor A. S. V.; Mizrahi, S. S.; Bernardini, Alex E.

doi:10.1016/j.aop.2015.02.001

Cited by 12 publications

(10 citation statements)

References 34 publications

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“…[9]. Those outstanding results suggest that the entanglement structure of Dirac bi-spinors [14,21] can be probed via trapped ions even if experimental techniques are still underestimated. In that case, for the trapped ion platforms, the only observable that can straightforwardly be measured by fluorescence techniques isσ z (c. f. Eqs (4)- (7)).…”

Section: Discussionmentioning

confidence: 91%

“…The averaged chirality can also be identified as a measurement of the maximal superposition between two of the four internal ionic levels. To summarize, a complete prospect of quantum transitions and quantum entanglement, via quantum concurrence, for trapped ion systems driven by Jaynes-Cummings interactions can be mapped and computed in terms of the SU(2) ⊗ SU(2) Dirac-like structure, similar as it has been performed in [15,21]. By construction, the SU(2) ⊗ SU(2) spin-parity quantum correlational content can be interpreted in terms of the quantum entanglement of two-qubit ionic states for which the quantum numbers are related to the total angular momentum and to its projection onto the direction of the trapping magnetic field.…”

Section: Introductionmentioning

confidence: 99%

“…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…”

Section: Introductionmentioning

confidence: 99%

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

2016

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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 JaynesCummings 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 bi-spinor 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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Section: Discussionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2016

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“…In a previous issue, one has investigated how a barrier scattering, implemented by a static electric potential via minimal coupling in the Dirac equation, can either create or destroy (spin-parity) entanglement for free particle states [22]. This has inaugurated a new context in which the entanglement content of bi-spinors can be mapped into Dirac-like systems, providing a framework to compute, for example, spin-spin entanglement of nonrelativistic systems, namely, for electron-hole pairs in graphene, and low-energy excitations of trapped ions.…”

Section: Introductionmentioning

confidence: 99%

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

Bittencourt

Bernardini

2016

Annals of Physics

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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.

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“…Under suitable conditions, the ionic (anti)Jaynes-Cummings ((A)JC) Hamiltonian dynamics can be mapped onto the structure of the Dirac equation, reproducing a series of relativistic-like quantum effects [17,18,19]. On the other hand, the two-qubit intrinsic entanglement present on the SU (2)⊗SU (2) bi-spinor structure of Dirac equation solutions is also encoded in the ionic system simulating the Dirac dynamics by quantum numbers related to the total angular momentum and to its projection onto the direction of the external magnetic field (which is applied for lift the degeneracy of the ions internal levels) [13,20,21]. A quantum system not isolated has its correlational properties affected by the coupling with its environment.…”

Section: Introductionmentioning

confidence: 99%

Dirac bi-spinor entanglement under local noise and its simulation by Jaynes-Cummings interactions

Bittencourt

Bernardini

2017

J. Phys.: Conf. Ser.

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Abstract. A description of the effects of the local noise on the quantum entanglement constraining the internal degrees of freedom of Dirac bi-spinor structures driven by arbitrary Poincaré invariant potentials is proposed. Given that the Dirac equation dynamics including external potentials can be simulated by a suitable four level trapped ion setup, 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 external magnetic field (used for lift the ions degeneracy), are recovered by means of a suitable ansatz. This formalism allows the inclusion of noise effects, which leads to disentanglement in the four level trapped ion quantum system. Our results indicate the role of interactions in bi-spinor entanglement, as well as the description of disentanglement in ionic states under local noises. For a state prepared initially in one of the ionic levels, local noise induces entanglement sudden death followed by sudden revivals driven by the noiseless dynamics of the state. Residual quantum correlations are observed in the intervals where such state is separable. Schrödinger cat and Werner states partially loose their initial entanglement content due to the interaction with the noisy environment but presenting entanglement oscillations without sudden death. Because Dirac equation describes low energy excitations of mono layer and bi-layer graphene, the formalism can also be applied to compute, for instance, electron-hole or electron/electron entanglement in various circumstances. IntroductionQuantum correlations has been in the core of recent developments exploring the interface between quantum and classical physics [1,2,3,4]. Quantum entanglement and other quantum correlations are widely considered for the engineering of quantum information protocols, in particular for quantum cryptography [5,6] and quantum computing processes [7]. The nonlocal coherence generated by entanglement is essential to various applications of such quantum information/computing tasks in physical systems [7].One platform suitable for implementing and characterizing quantum correlations is the iontrap technology [8,9], which has provided a phenomenological access to generate and manipulate quantum correlational properties of the trapped ions [10,11,12,13]. Moreover, the trapped ion setup has also been engendered for simulation protocols, such as for simulating open quantum systems and quantum phase transitions [14,15,16]. Simulating Dirac equation structures is another example of a quantum system engendered by trapped ion dynamics. Under suitable conditions, the ionic (anti)Jaynes-Cummings ((A)JC) Hamiltonian dynamics can be mapped onto the structure of the Dirac equation, reproducing a series of relativistic-like quantum effects [17,18,19]. On the other hand, the two-qubit intrinsic entanglement present on the

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

Cited by 12 publications

References 34 publications

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

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

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

Dirac bi-spinor entanglement under local noise and its simulation by Jaynes-Cummings interactions

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