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Interaction-induced topological transition in spin-orbit coupled ultracold bosons

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Abstract

Recent experiments in ultracold atoms have reported the realization of quantum anomalous Hall phases in spin-orbit coupled systems. Motivated by such advances, we investigate spin-orbit coupled Bose-Bose mixtures in a two-dimensional square optical Raman lattice. Complete phase diagrams are obtained via a nonperturbative real-space bosonic dynamical mean-field theory. Various quantum phases are predicted, including Mott phases with z-ferromagnetic, xy-antiferromagnetic and vortex textures, and superfluid phases with the exotic spin orders, induced by the competition between the lattice hopping and spin-orbit coupling. To explain the underlying physics in the Mott regime, an effective Hamiltonian is derived based on second-order perturbation theory, where pseudospin order stems from the interplay of effective Dzyaloshinskii-Moriya superexchange and Heisenberg interactions. In the presence of the Zeeman field, the competition of strong interaction and Zeeman energy facilitates a topological phase, which is confirmed both by the nontrivial topological Bott index and spectral function with topological edge states. Our work indicates that spin-orbit coupling can induce rich non-Abelian topological physics in strongly correlated ultracold atomic systems.

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References

  1. J. Maciejko, T. L. Hughes, and S. C. Zhang, Annu. Rev. Condens. Matter Phys. 2, 31 (2011).

    Article  ADS  Google Scholar 

  2. X. L. Qi, and S. C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).

    Article  ADS  Google Scholar 

  3. M. Z. Hasan, and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).

    Article  ADS  Google Scholar 

  4. X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. B 83, 205101 (2011).

    Article  ADS  Google Scholar 

  5. J. Maciejko, and R. Nandkishore, Phys. Rev. B 90, 035126 (2014).

    Article  ADS  Google Scholar 

  6. S. Rao, arXiv: 1603.02821.

  7. S. Seki, and M. Mochizuki, Theoretical Model of Magnetic Skyrmions, (Springer International Publishing, Cham, 2016), pp. 1–13.

    Google Scholar 

  8. C. Marrows, Physics 8, 40 (2015).

    Article  Google Scholar 

  9. C. W. J. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013).

    Article  ADS  Google Scholar 

  10. S. R. Elliott, and M. Franz, Rev. Mod. Phys. 87, 137 (2015).

    Article  ADS  Google Scholar 

  11. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008).

    Article  ADS  Google Scholar 

  12. G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).

    Article  ADS  Google Scholar 

  13. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).

    Article  ADS  Google Scholar 

  14. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).

    Article  ADS  Google Scholar 

  15. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).

    Article  ADS  Google Scholar 

  16. H. Zhai, Int. J. Mod. Phys. B 26, 1230001 (2012).

    Article  ADS  Google Scholar 

  17. J. Zhang, H. Hu, X.-J. Liu, and H. Pu, Fermi gases with synthetic spinorbit coupling, in Annual Review of Cold Atoms and Molecules (World Scientific, Singapore, 2014). pp. 81–143.

    Chapter  Google Scholar 

  18. H. Zhai, Rep. Prog. Phys. 78, 026001 (2015).

    Article  ADS  Google Scholar 

  19. E. Howard, Contemp. Phys. 61, 310 (2020).

    Article  ADS  Google Scholar 

  20. D. W. Zhang, Y. Q. Zhu, Y. X. Zhao, H. Yan, and S. L. Zhu, Adv. Phys. 67, 253 (2018).

    Article  ADS  Google Scholar 

  21. N. R. Cooper, J. Dalibard, and I. B. Spielman, Rev. Mod. Phys. 91, 015005 (2019).

    Article  ADS  Google Scholar 

  22. Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Nature 471, 83 (2011).

    Article  ADS  Google Scholar 

  23. Z. Wu, L. Zhang, W. Sun, X. T. Xu, B. Z. Wang, S. C. Ji, Y. Deng, S. Chen, X. J. Liu, and J. W. Pan, Science 354, 83 (2016).

    Article  ADS  Google Scholar 

  24. W. Sun, B. Z. Wang, X. T. Xu, C. R. Yi, L. Zhang, Z. Wu, Y. Deng, X. J. Liu, S. Chen, and J. W. Pan, Phys. Rev. Lett. 121, 150401 (2018).

    Article  ADS  Google Scholar 

  25. C.-R. Yi, J.-L. Yu, W. Sun, X.-T. Xu, S. Chen, and J.-W. Pan, arXiv: 1904.11656.

  26. L. Huang, Z. Meng, P. Wang, P. Peng, S. L. Zhang, L. Chen, D. Li, Q. Zhou, and J. Zhang, Nat. Phys. 12, 540 (2016).

    Article  Google Scholar 

  27. Z. Meng, L. Huang, P. Peng, D. Li, L. Chen, Y. Xu, C. Zhang, P. Wang, and J. Zhang, Phys. Rev. Lett. 117, 235304 (2016).

    Article  ADS  Google Scholar 

  28. X. J. Liu, K. T. Law, and T. K. Ng, Phys. Rev. Lett. 112, 086401 (2014).

    Article  ADS  Google Scholar 

  29. J. S. Pan, W. Zhang, W. Yi, and G. C. Guo, Phys. Rev. A 94, 043619 (2016).

    Article  ADS  Google Scholar 

  30. C. Wang, C. Gao, C. M. Jian, and H. Zhai, Phys. Rev. Lett. 105, 160403 (2010).

    Article  ADS  Google Scholar 

  31. G. H. Huang, G. Q. Luo, Z. Wu, and Z. F. Xu, Phys. Rev. A 103, 043328 (2021).

    Article  ADS  Google Scholar 

  32. S. A. Parameswaran, R. Roy, and S. L. Sondhi, Compt. Rend. Phys. 14, 816 (2013).

    Article  ADS  Google Scholar 

  33. A. Elben, J. Yu, G. Zhu, M. Hafezi, F. Pollmann, P. Zoller, and B. Vermersch, Sci. Adv. 6, (2020).

  34. D. Cocks, P. P. Orth, S. Rachel, M. Buchhold, K. Le Hur, and W. Hofstetter, Phys. Rev. Lett. 109, 205303 (2012).

    Article  ADS  Google Scholar 

  35. J. C. Budich, B. Trauzettel, and G. Sangiovanni, Phys. Rev. B 87, 235104 (2013).

    Article  ADS  Google Scholar 

  36. T. I. Vanhala, T. Siro, L. Liang, M. Troyer, A. Harju, and P. Törmä, Phys. Rev. Lett. 116, 225305 (2016).

    Article  ADS  Google Scholar 

  37. K. Jiang, S. Zhou, X. Dai, and Z. Wang, Phys. Rev. Lett. 120, 157205 (2018).

    Article  ADS  Google Scholar 

  38. M. Hafez-Torbati, J. H. Zheng, B. Irsigler, and W. Hofstetter, Phys. Rev. B 101, 245159 (2020).

    Article  ADS  Google Scholar 

  39. B. Irsigler, T. Grass, J. H. Zheng, M. Barbier, and W. Hofstetter, Phys. Rev. B 103, 125132 (2021).

    Article  ADS  Google Scholar 

  40. M. Ebrahimkhas, G. S. Uhrig, W. Hofstetter, and M. Hafez-Torbati, Phys. Rev. B 106, 205107 (2022).

    Article  ADS  Google Scholar 

  41. W. S. Cole, S. Zhang, A. Paramekanti, and N. Trivedi, Phys. Rev. Lett. 109, 085302 (2012).

    Article  ADS  Google Scholar 

  42. J. Radić, A. Di Ciolo, K. Sun, and V. Galitski, Phys. Rev. Lett. 109, 085303 (2012).

    Article  ADS  Google Scholar 

  43. L. He, A. Ji, and W. Hofstetter, Phys. Rev. A 92, 023630 (2015).

    Article  ADS  Google Scholar 

  44. S. Zhang, W. S. Cole, A. Paramekanti, and N. Trivedi, Spin-Orbit Coupling in Optical Lattices (World Scientific, Singapore, 2014). pp. 135–179.

    Google Scholar 

  45. S. Kolkowitz, S. L. Bromley, T. Bothwell, M. L. Wall, G. E. Marti, A. P. Koller, X. Zhang, A. M. Rey, and J. Ye, Nature 542, 66 (2017).

    Article  ADS  Google Scholar 

  46. S. L. Bromley, S. Kolkowitz, T. Bothwell, D. Kedar, A. Safavi-Naini, M. L. Wall, C. Salomon, A. M. Rey, and J. Ye, Nat. Phys. 14, 399 (2018).

    Article  Google Scholar 

  47. S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A. M. Rey, A. Polkovnikov, E. A. Demler, M. D. Lukin, and I. Bloch, Science 319, 295 (2008).

    Article  ADS  Google Scholar 

  48. G. Thalhammer, G. Barontini, L. De Sarlo, J. Catani, F. Minardi, and M. Inguscio, Phys. Rev. Lett. 100, 210402 (2008).

    Article  ADS  Google Scholar 

  49. Y. Li, L. He, and W. Hofstetter, Phys. Rev. A 93, 033622 (2016).

    Article  ADS  Google Scholar 

  50. L. He, Y. Li, E. Altman, and W. Hofstetter, Phys. Rev. A 86, 043620 (2012).

    Article  ADS  Google Scholar 

  51. X. Zan, J. Liu, J. Han, J. Wu, and Y. Li, Sci. Rep. 8, 9143 (2018).

    Article  ADS  Google Scholar 

  52. Y. Li, M. R. Bakhtiari, L. He, and W. Hofstetter, Phys. Rev. B 84, 144411 (2011).

    Article  ADS  Google Scholar 

  53. R. Cao, J. Han, J. Wu, J. Yuan, L. He, and Y. Li, Phys. Rev. A 105, 063308 (2022).

    Article  ADS  Google Scholar 

  54. Z. Wang, and S. C. Zhang, Phys. Rev. X 2, 031008 (2012).

    Google Scholar 

  55. Z. Wang, and S. C. Zhang, Phys. Rev. B 86, 165116 (2012).

    Article  ADS  Google Scholar 

  56. Z. Wang, and B. Yan, J. Phys.-Condens. Matter 25, 155601 (2013).

    Article  ADS  Google Scholar 

  57. R. M. White, M. Sparks, and I. Ortenburger, Phys. Rev. 139, A450 (1965).

    Article  ADS  Google Scholar 

  58. J. Bellissard, A. van Elst, and H. Schulz-Baldes, J. Math. Phys. 35, 5373 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  59. T. A. Loring, and M. B. Hastings, Europhys. Lett. 92, 67004 (2010).

    Article  ADS  Google Scholar 

  60. M. B. Hastings, and T. A. Loring, J. Math. Phys. 51, (2010).

  61. H. Huang, and F. Liu, Phys. Rev. Lett. 121, 126401 (2018).

    Article  ADS  Google Scholar 

  62. H. Huang, and F. Liu, Phys. Rev. B 98, 125130 (2018).

    Article  ADS  Google Scholar 

  63. X. S. Wang, A. Brataas, and R. E. Troncoso, Phys. Rev. Lett. 125, 217202 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  64. D. Sénéchal, D. Perez, and M. Pioro-Ladriére, Phys. Rev. Lett. 84, 522 (2000).

    Article  ADS  Google Scholar 

  65. D. Sénéchal, D. Perez, and D. Plouffe, Phys. Rev. B 66, 075129 (2002).

    Article  ADS  Google Scholar 

  66. I. Vasić, A. Petrescu, K. Le Hur, and W. Hofstetter, Phys. Rev. B 91, 094502 (2015).

    Article  ADS  Google Scholar 

  67. I. Ozfidan, J. Han, and J. Maciejko, Phys. Rev. B 94, 214510 (2016).

    Article  ADS  Google Scholar 

  68. L. M. Duan, E. Demler, and M. D. Lukin, Phys. Rev. Lett. 91, 090402 (2003).

    Article  ADS  Google Scholar 

  69. Z. Cai, X. Zhou, and C. Wu, Phys. Rev. A 85, 061605 (2012).

    Article  ADS  Google Scholar 

  70. M. Gong, Y. Qian, M. Yan, V. W. Scarola, and C. Zhang, Sci. Rep. 5, 10050 (2015).

    Article  ADS  Google Scholar 

  71. F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  72. C. K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Rev. Mod. Phys. 88, 035005 (2016).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, National University of Defense Technology, Changsha, 410073, China

    Jinsen Han, Hui Tan, Rui Cao, Jiayu Dai, Yongqiang Li & Jianmin Yuan

  2. Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha, 410073, China

    Jinsen Han, Jiayu Dai & Yongqiang Li

  3. School of Physics and Electronics, Hunan University, Changsha, 410082, China

    Xiansi Wang

  4. Department of Physics, Graduate School of China Academy of Engineering Physics, Beijing, 100193, China

    Jianmin Yuan

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  1. Jinsen Han
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Correspondence to Xiansi Wang or Yongqiang Li.

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Conflict of interest The authors declare that they have no conflict of interest.

Additional information

This work was supported by the National Key Research and Development Program of China (Grant No. 2017YFA0403200), the NSAF (Grant Nos. U1830206, and U1930403), the National Natural Science Foundation of China (Grant Nos. 11774429, 12174093, and 12074431), the Science and Technology Innovation Program of Hunan Province (Grant No. 2021RC4026), and the Excellent Youth Foundation of Hunan Scientific Committee (Grant No. 2021JJ10044). The authors thank Xiong-Jun Liu, Liang He and Tao Qin for the helpful discussion.

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Han, J., Wang, X., Tan, H. et al. Interaction-induced topological transition in spin-orbit coupled ultracold bosons. Sci. China Phys. Mech. Astron. 66, 293012 (2023). https://doi.org/10.1007/s11433-023-2166-y

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