Influence of detuning and Kerr nonlinearity on atom-atom entanglement in the double two-photon Jaynes–Cummings model

Cite item


In this work, the authors investigated the dynamics of entanglement of two identical two-level atoms (qubits) in the framework of the two-photon double Jaynes–Cummings model, taking into account the detuning between atoms and the double frequency of the field modes of the resonators, as well as the Kerr medium in both resonators. The authors derived the time dependence of the negativity parameter for the Bell initial states of the atoms and the vacuum states of the resonator fields. The results showed that detuning and Kerr nonlinearity leads to stabilization of the entanglement for all initial Bell-type atomic states. For some initial atomic entanglement states, the detuning and Kerr environment in the resonators can prevent the effect of sudden death of the atom-atom entanglement.

About the authors

Rodion K. Zakharov

Samara National Research University


Evgeny K. Bashkirov

Samara National Research University

Author for correspondence.


  1. Georgescu I.M., Ashhab S., Nori F. Quantum simulation. Rev. Mod. Phys, 2014, vol. 88, pp. 153–186. DOI:
  2. Buluta I., Ashab S., Nori F. Neutral and artificial atoms for quantum computation. Rep. Prog. Phys, 2011, vol. 74, p. 104401. DOI:
  3. Scully M.O., Zubairy M.S. Quantum Optics. Cambridge: Cambridge University Press, 1997, 630 p.
  4. Bashkirov E.K. Thermal entanglement between a Jaynes–Cummings atom and an isolated atom. Intern. J. Theor. Phys, 2018, vol. 57, no. 12, pp. 3761–3771. DOI:
  5. Yönac M.Y., Yu T., Eberly J.H. Sudden death of entanglement of two Jaynes–Cummings atoms. J. Phys. B: At. Mol. Opt. Phys, 2006, vol. 39, pp. 621–625. DOI:
  6. Yönac M.Y., Yu T., Eberly J.H. Pairwise concurrence dynamics: a four-qubit model. J. Phys. B: At. Mol. Opt. Phys, 2007, vol. 40, pp. 45–59. DOI:
  7. Xie Q., Fang M.-F. Entanglement dynamics of atoms in double Jaynes–Cummings models with Kerr medium. Commun. Theor. Phys, 2010, vol. 54, no. 5, pp. 840–844. DOI:
  8. Zhu W.-T. et al. Dynamics of two qubits coupled independently to cavities in the ultrastrong coupling regime: analytical results. Chin. Phys. Lett, 2016, vol. 33, no. 5, p. 050302. DOI:
  9. Liao Q. et al. The entanglement dynamics of two atoms in a double two-photon Jaynes–Cummings model. Chinese Journal of Physics, 2010, vol. 51, no. 2, pp. 404–411. DOI:
  10. Bashkirov E.K., Evseev M.M. The influence of dipole-dipole interaction on entanglement of two superconducting qubits in the framework of double Jaynes–Cummins model. J. Phys.: Conference Ser, 2017, vol. 917, no. 6, p. 062011. DOI:
  11. Bashkirov E.K. Entanglement between two dipole-coupled qubits interacting with two independent slightly detuned cavity modes. Intern. J. Theor. Phys, 2019, vol. 58, no. 7, pp. 2346–2356. DOI:

Copyright (c) 2021 Zakharov R., Bashkirov E.

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