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Dicke Quantum Phase Transition for a Bose-Einstein Condensate in a Two-Mode Optical Cavity

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Abstract

In this paper we mainly discuss the ground state properties of the two-mode Dicke model, which is realized in an ensemble of two-level atoms interacting simultaneously with two quantized cavity fields. We reveal rich phase diagrams and discover the second-order quantum phase transition from the normal phase to the superradiant phase by means of the spin-coherent-state variational method. While the critical phase transition point can be shifted by the detuning of the cavity mode or the atom-field coupling imbalance parameter. The collective atom-field coupling imbalance parameter can make the phase transition point symmetrically shift left or right in the resonance or non-resonance. If the two collective atom-photon coupling strengths are not equal in the resonance, the system may be in different phases, while the phases occupied are completely symmetrical. When one of the coupling constants vanishes or two couplings are equal, the ground-states’s properties and related QPT reduce to that of a standard or an ordinary Dicke model.

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References

  1. Dicke, R.H.: Phys. Rev. 93, 99 (1954)

    Article  ADS  Google Scholar 

  2. Wang, Y.K., Hioe, F.T.: Phys. Rev. A 7, 831 (1973)

    Article  ADS  Google Scholar 

  3. Hioe, F.T.: Rev, Phys. A 8, 1440 (1973)

    Article  Google Scholar 

  4. Baumann, K., Guerlin, C., Brennecke, F., Esslinger, T.: Nature (London) 464, 1301 (2010)

    Article  ADS  Google Scholar 

  5. Baumann, K., Mottl, R., Brennecke, F., Esslinger, T.: Phys. Rev. Lett. 107, 140402 (2011)

    Article  ADS  Google Scholar 

  6. Brennecke, F., Donner, T., Ritter, S., Bourdel, T., Köhl, M., Esslinger, T.: Nature (London) 450, 268 (2007)

    Article  ADS  Google Scholar 

  7. Colombe, Y., Steinmetz, T., Dubois, G., Linke, F., Hunger, D., Reichel, J.: Nature (London) 450, 272 (2007)

    Article  ADS  Google Scholar 

  8. Zhang, G.F., Ji, A.L., Fan, H., Liu, W.M.: Ann. Phys. 327, 2074 (2012)

    Article  ADS  Google Scholar 

  9. Jiang, L., Zhang, G.F.: Int. J. Theor. Phys. 56, 906 (2017)

    Article  Google Scholar 

  10. Cai, J.T., Abliz, A., Zhang, G.F., Bai, Y.K.: Opt. Commun. 283, 4415 (2010)

    Article  ADS  Google Scholar 

  11. Thompson, B.V.: J. Phys. A Math. Gen. 10, 89 (1977). 10, L179 (1977)

    Article  ADS  Google Scholar 

  12. Tolkunov, D., Solenov, D.: Phys. Rev. B 75, 024402 (2007)

    Article  ADS  Google Scholar 

  13. Mariantoni, M., Deppe, F., Marx, A., Gross, R., Wilhelm, F.K., Solano, E.: Phys. Rev. B 78, 104508 (2008)

    Article  ADS  Google Scholar 

  14. Norris, D.G., Cahoon, E.J., Orozco, L.A.: Phys. Rev. A 80, 043830 (2009)

    Article  ADS  Google Scholar 

  15. Yang, C.-P., Su, Q.-P., Zheng, S.-B., Han, S.: Phys. Rev. A 87, 022320 (2013)

    Article  ADS  Google Scholar 

  16. Ji, A.-C., Xie, X.C., Liu, W.M.: Phys. Rev. Lett. 99, 183602 (2007)

    Article  ADS  Google Scholar 

  17. Ji, A.-C., Liu, W.M., Song, J.L., Zhou, F.: Phys. Rev. Lett. 101, 010402 (2008)

    Article  ADS  Google Scholar 

  18. Larson, J., Levin, S.: Phys. Rev. Lett. 103, 013602 (2009)

    Article  ADS  Google Scholar 

  19. Larson, J.: Rev, Phys. A 81, 051803 (2010)

    Article  Google Scholar 

  20. Qi, R., Yu, X.-L., Li, Z.B., Liu, W.M.: Phys. Rev. Lett. 102, 185301 (2009)

    Article  ADS  Google Scholar 

  21. Ji, A.-C., Sun, Q., Xie, X.C., Liu, W.M.: Phys. Rev. Lett. 102, 023602 (2009)

    Article  ADS  Google Scholar 

  22. Gopalakrishnan, S., Lev, B.L., Goldbart, P.M.: Nat. Phys. 5, 845 (2009). Phys. Rev. A, 82, 043612 (2010)

    Article  Google Scholar 

  23. Gopalakrishnan, S., Lev, B.L., Goldbart, P.M.: Phys. Rev. Lett. 107, 277201 (2011)

    Article  ADS  Google Scholar 

  24. Strack, P., Sachdev, S.: Phys. Rev. Lett. 107, 277202 (2011)

    Article  Google Scholar 

  25. Buchhold, M., Strack, P., Sachdev, S., Diehl, S.: Phys. Rev. A 87, 063622 (2013)

    Article  ADS  Google Scholar 

  26. Andreanov, A., Müller, M.: Phys. Rev. Lett. 109, 177201 (2012)

    Article  ADS  Google Scholar 

  27. Krimer, D.O., Liertzer, M., Rotter, S., Tureci, H.E.: arXiv:1306.4787

  28. Wickenbrock, A., Hemmerling, M., Robb, G.R.M., Emary, C., Renzoni, F.: Phys. Rev. A 87, 043817 (2013)

    Article  ADS  Google Scholar 

  29. Zhu, H.J., Zhang, G.F., Fan, H.: Sci. Rep. 6, 19751 (2016)

    Article  ADS  Google Scholar 

  30. Quezada, L.F., Nahmad-Achar, E.: Phys. Rev. A 95, 013849 (2017)

    Article  ADS  Google Scholar 

  31. Fan, J.T., Yang, Z.W., Zhang, Y.W., Ma, J., Chen, G., Jia, S.T.: Phys. Rev. A 89, 023812 (2014)

    Article  ADS  Google Scholar 

  32. Zhao, X.Q., Liu, N., Liang, J.-Q.: Phys. Rev. A 90, 023622 (2014)

    Article  ADS  Google Scholar 

  33. Wang, Z., Lian, J.L., Liang, J.-Q., Yu, Y.M., Liu, W.-M.: Phys. Rev. A 93, 033630 (2016)

    Article  ADS  Google Scholar 

  34. Lai, Y.-Z., Liang, J.-Q., MüLler-Kirsten, H.J.W., Zhou, J.-G.: Phys. Rev. A 53, 3691 (1996)

    Article  ADS  Google Scholar 

  35. Chen, Z.-D., Liang, J.-Q., Shen, S.-Q., Xie, W.-F.: Phys. Rev. A 69, 023611 (2004)

    Article  ADS  Google Scholar 

  36. Bhattacherjee, A.B.: Phys. Lett. A 378, 3244 (2014)

    Article  ADS  Google Scholar 

  37. Liu, N., Li, J.D., Liang, J.-Q.: vol. 87 (2013)

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11772177, 61505100, 51502189, 61575112), and the natural science foundation of Shanxi Province (Grant No. 201701D221001).

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Authors and Affiliations

  1. Institute of Theoretical Physics, Shanxi University, Taiyuan, Shanxi, 030006, China

    Ni Liu, Xiuqin Zhao & J.-Q. Liang

  2. Department of Physics, Taiyuan Normal University, Taiyuan, Shanxi, 030001, China

    Xiuqin Zhao

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  1. Ni Liu
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  2. Xiuqin Zhao
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  3. J.-Q. Liang
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Correspondence to Ni Liu.

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Liu, N., Zhao, X. & Liang, JQ. Dicke Quantum Phase Transition for a Bose-Einstein Condensate in a Two-Mode Optical Cavity. Int J Theor Phys 58, 558–574 (2019). https://doi.org/10.1007/s10773-018-3954-5

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