Quantum simulation of the Weyl equation with a trapped ion

  • De-Sheng LiEmail author
  • Chun-Wang Wu
  • Lin-Ze He
  • Wei Wu
  • Ping-Xing Chen


The Weyl equation describes chiral massless relativistic particles, called Weyl fermions, which have important relations to neutrinos. A direct observation of the dynamics of Weyl fermions in an experiment is difficult to achieve. This study investigates a method of simulating the Weyl equation in \(1+2\) dimension by a single trapped ion. The predictions about a two-dimensional Zitterbewegung and an especially interesting phenomenon of Weyl fermions can be tested by the future trapped ion experiment, which might enhance our understanding of neutrinos.


Quantum simulation Weyl equation Trapped ion 



This work was supported by the National Basic Research Program of China under Grant No. 2016YFA0301903 and the National Natural Science Foundation of China under Grant Nos. 11174370, 11304387, 61632021, 11305262, 61205108, and 11574398.


  1. 1.
    Patrignani, C., Richardson, P., Zenin, O., Zhu, R.Y., Vogt, A., Pagan Griso, S., Garren, L., Groom, D., Karliner, M., Asner, D., et al., Review of particle physics, 2016–2017, Chin. Phys. C 40, 100001 (2016)Google Scholar
  2. 2.
    Cirac, J.I., Zoller, P.: Goals and opportunities in quantum simulation. Nat. Phys. 8(4), 264 (2012)CrossRefGoogle Scholar
  3. 3.
    Blatt, R., Roos, C.F.: Quantum simulations with trapped ions. Nat. Phys. 8(4), 277 (2012)CrossRefGoogle Scholar
  4. 4.
    Georgescu, I.M., Ashhab, S., Nori, F.: Quantum simulation. Physics 86(1), 153 (2013)Google Scholar
  5. 5.
    Georgescu, I., Ashhab, S., Nori, F.: Quantum simulation. Rev. Mod. Phys. 86(1), 153 (2014)ADSCrossRefGoogle Scholar
  6. 6.
    Arrazola, I., Pedernales, J.S., Lamata, L., Solano, E.: Digital-Analog quantum simulation of spin models in trapped ions. Sci. Rep. 6(1), 30534 (2016)ADSCrossRefGoogle Scholar
  7. 7.
    Garay, L.J., Anglin, J.R., Cirac, J.I., Zoller, P.: Sonic analog of gravitational black holes in Bose–Einstein condensates. Phys. Rev. Lett. 85(22), 4643 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    Gerritsma, R., Lanyon, B.P., Kirchmair, G., Zhringer, F., Hempel, C., Casanova, J., Garcaripoll, J.J., Solano, E., Blatt, R., Roos, C.F.: Quantum simulation of the Klein paradox with trapped ions. Phys. Rev. Lett. 106(6), 060503 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    Casanova, J., Sabin, C., Leon, J., Egusquiza, I.L., Gerritsma, R., Roos, C.F., Garciaripoll, J.J., Solano, E.: Quantum simulation of the Majorana equation and unphysical operations. Phys. Rev. X 1(2), 1 (2012)Google Scholar
  10. 10.
    Casanova, J., Lamata, L., Egusquiza, I., Gerritsma, R., Roos, C., García-Ripoll, J., Solano, E.: Quantum simulation of quantum field theories in trapped ions. Phys. Rev. Lett. 107(26), 260501 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    Zhang, X., Zhang, K., Shen, Y., Zhang, S., Zhang, J., Yung, M., Casanova, J., Pedernales, J.S., Lamata, L., Solano, E., Kim, K.: Experimental quantum simulation of fermion-antifermion scattering via Boson exchange in a trapped ion. Nat. Commun. 9(1), 195 (2018)ADSCrossRefGoogle Scholar
  12. 12.
    Lamata, L., Leon, J., Schatz, T., Solano, E.: Dirac equation and quantum relativistic effects in a single trapped ion. Phys. Rev. Lett. 98(25), 253005 (2007)ADSCrossRefGoogle Scholar
  13. 13.
    Gerritsma, R., Kirchmair, G., Zhringer, F., Solano, E., Blatt, R., Roos, C.F.: Quantum simulation of the Dirac equation. Nature 463(7277), 68 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    Barut, A.O., Bracken, A.J., Thacker, W.D.: The Zitterbewegung of the neutrino. Lett. Math. Phys. 8(6), 477 (1984)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Guertin, R.F., Guth, E.: Zitterbewegung in relativistic spin-0 and -1/2 Hamiltonian theories. Phys. Rev. D 7(4), 1057 (1973)ADSCrossRefGoogle Scholar
  16. 16.
    Rusin, T.M., Zawadzki, W.: Zitterbewegung of relativistic electrons in a magnetic field and its simulation by trapped ions. Phys. Rev. D 82(12), 463 (2010)CrossRefGoogle Scholar
  17. 17.
    Qu, C., Hamner, C., Gong, M., Zhang, C., Engels, P.: Observation of Zitterbewegung in a spin-orbit-coupled Bose–Einstein condensate. Phys. Rev. A 88(2), 2859 (2013)CrossRefGoogle Scholar
  18. 18.
    Leibfried, D., Blatt, R., Monroe, C., Wineland, D.J.: Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75(1), 281 (2003)ADSCrossRefGoogle Scholar
  19. 19.
    Haffner, H., Roos, C.F., Blatt, R.: Quantum computing with trapped ions. Phys. Rep. 469(4), 155 (2008)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Wallentowitz, S., Vogel, W.: Reconstruction of the quantum mechanical state of a trapped ion. Phys. Rev. Lett. 75(16), 2932 (1995)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Interdisciplinary Center for Quantum InformationNational University of Defense TechnologyChangshaPeople’s Republic of China

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