Entanglement of a Jaynes-Cummings atom and two Tavis-Cummings atoms
Bagrov A. R. 1, Bashkirov E. K.1
1 Samara National Research University named after Academician S.P. Korolev, Samara, Russia
Email: bashkirov.ek@ssau.ru

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We demonstrated an exact solution of the quantum Liouville equation for a model consisting of three identical two-level atoms (qubits) A, B and C, and two independent resonators. Qubit A is assumed to be trapped in the first ideal resonator, and the two remaining qubits B and C are trapped in the second high-Q resonator. All qubits resonantly interact with the corresponding mode of the quantized thermal electromagnetic field of the resonator. Entanglement is assumed between the qubits at the initial time. We focus our attention on biseparable and genuine entangled W- and GHZ-type qubit states. Based on the exact solution, the Peres-Horodecki criterion (negativity) and the fidelity are calculated. Using the specified entanglement criteria, the dynamics of two- and three-qubit entanglement are analyzed for various resonator thermal field intensities, and a comparative analysis of the qubit entanglement dynamics in the model under consideration is conducted with previously studied three-qubit models. It is shown that qubits never transit to initial states during their evolution, which fundamentally distinguishes their behavior from that of qubits in previously studied three-qubit models. Keywords: qubits, genuine entangled W-type states and GHZ-states, biseparable states, thermal fields, entanglement, independent resonators, negativity, fidelity, quantum Liouville equation, sudden death of entanglement.
  1. M.A. Nielsen, I.L. Chuang. Quantum Computation and Quantum Information. 10th Anniversary Edition (Cambridge University Press: NY., USA, 2010), 702 p. DOI: 10.1017/CBO9780511976667
  2. A. Barenco et al. Phys. Rev. A, 52, 3457 (1995). DOI: 10.1103/PhysRevA.52.3457
  3. Y. Shi. Quantum Information and Computation, 3, 84 (2003)
  4. E. Barnes, C. Arenz, A.J.G. Pitchford, S.E. Economou. Phys. Rev. B, 96 (2), 024504 (2017). DOI: 10.1103/PhysRevB.96.024504
  5. M. Li, L. Jia, J. Wang, S. Shen, S.M. Fei. Phys. Rev. A, 96, 052314 (2017). DOI: 10.1103/PhysRevA.96.052314
  6. M.D. Reed, L. DiCarlo, S.E. Nigg, L. Sun, L. Frunzio, S.M. Girvin, R.J. Schoelkopf. Nature, 482, 382 (2012). DOI: 10.1038/nature10786
  7. A. Isar. Open Systems Information Dynamics, 16 (2), 205 (2009). DOI: 10.1142/S1230161209000153
  8. L. Aolita, R. Chaves, D. Cavalcanti, A. Acin, L. Davidovich. Phys. Rev. Lett., 100 (8), 080501 (2008). DOI: 10.1103/PhysRevLett.100.080501
  9. Z.-L. Xiang, S. Ashhab, J.Q. You, F. Nori. Rev. Mod. Phys., 85, 623 (2013). DOI: 10.1103/revmodphys.85.623
  10. I.M. Georgescu, S. Ashhab, F. Nori. Rev. Mod. Phys., 86, 153 (2014). DOI: 10.1103/RevModPhys.86.153
  11. G. Wendin. Rep. Prog. Phys., 80 (10), 106001 (2017). DOI: 10.1088/1361-6633/aa7e1a
  12. G.-Q. Li, X.-Y. Pan. Chin. Phys. B, 27 (2), 020304 (2018). DOI: 10.1088/1674-1056/27/2/020304
  13. D.J. van Woerkom, P. Scarlino, J.H. Ungerer, C. Muller, J.V. Koski, A.J. Landig, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, A. Wallraff. Phys. Rev. X, 8, 041018 (2018). DOI: 10.1103/PhysRevX.8.041018
  14. B.W. Shore, P.L. Knight. J. Mod. Opt., 40 (7), 1195 (1993). DOI: 10.1080/09500349314551321
  15. J. Larson, T. Mavrogordatos. The Jaynes-Cummings Model and Its Descendants: Modern research directions. (IoP Publishing, Bristol 2021), 426 p. DOI: 10.1088/978-0-7503-3447-1
  16. M. Neeley, R.C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A.D. O'Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A.N. Cleland, J.M. Martinis. Nature, 467, 570 (2010). DOI: 10.1038/nature09418
  17. L. DiCarlo, M.D. Reed, L. Sun, B.R. Johnson, J.M. Chow, J.M. Gambetta, L. Frunzio, S.M. Girvin, M.H. Devoret, R.J. Schoelkopf. Nature, 467, 574 (2010). DOI: 10.1038/nature09416
  18. Ch.F. Roos, M. Riebe, H. Hoffner, W. Honsel, J. Benhelm, G.P.T. Lancaster, Ch. Becher, F. Schmidt-Kaler, R. Blatt. Nature, 429, 734 (2004). DOI: 10.1038/nature02570
  19. D.C. Cole, J.J. Wu, S.D. Erickson, P.-Y. Hou, A.C. Wilson, D. Leibfried, F. Reiter. New J. Phys., 23, 073001 (2021). DOI: 10.1088/1367-2630/ac09c8
  20. P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup. Science, 320, 1326 (2008). DOI: 10.1126/science.1157233
  21. K. Takeda, A. Noiri, T. Nakajima, J. Yoneda, T. Kobayashi, S. Tarucha. Nature Nanotechnol., 16, 965 (2021). DOI: 10.1038/s41565-021-00925-0
  22. A.R. Bagrov, E.K. Bashkirov. ZhTF, 94 (3), 341 (2024) (in Russian). DOI: 10.61011/JTF.2024.03.57370.301-23
  23. A.R. Bagrov, E.K. Bashkirov. ZhTF, 95 (5), 853 (2025) (in Russian). DOI: 10.61011/JTF.2025.05.60275.433-24
  24. E.K. Bashkirov, A.R. Bagrov. Quantum Inf. Process., 24 (5), 154 (2025). DOI: 10.1007/s11128-025-04772-z
  25. E.K. Bashkirov, A.R. Bagrov. Laser Phys., 35 (6), 065203 (2025). DOI: 10.1088/1555-6611/addd90
  26. R. Jozsa. J. Mod. Opt., 41, 2315 (1994). DOI: 10.1080/09500349414552171
  27. A. Peres. Phys. Rev. Lett., 77 (8), 1413 (1996). DOI: 10.1103/PhysRevLett.77.1413

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