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Nonreciprocal generation of Schrödinger cat state induced by topology

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Abstract

The Schrödinger cat state produced differently in two directions is anticipated to be a critical quantum resource in quantum information technologies. By exploring the interplay between quantum nonreciprocity and topology in a one-dimensional microcavity array, we obtain the Schrödinger cat state (a pure quantum state) in a chosen direction at the edge cavity, whereas a classical state in the other direction. This nonreciprocal generation of the cat state originates from the topologically protected chirality-mode excitation in the nontrivial phase, but in the trivial phase, the nonreciprocal generation of cat state vanishes. Thus, our proposal is switchable by tuning the parameters so that a topological phase transition occurs. Moreover, the obtained cat state has nonreciprocal high fidelity, nonclassicality, and quantum coherence, which are sufficient to be used in various one-way quantum technologies, e.g., invisible quantum sensing, noise-tolerant quantum computing, and chiral quantum networks. Our work provides a general approach to control quantum nonreciprocities with the topological effect, which substantially broadens the fields of nonreciprocal photonics and topological physics.

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References

  1. M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, Nat. Phys. 7, 799 (2011).

    Article  Google Scholar 

  2. J. Joo, W. J. Munro, and T. P. Spiller, Phys. Rev. Lett. 107, 083601 (2011).

    Article  ADS  PubMed  Google Scholar 

  3. T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, Phys. Rev. A 68, 042319 (2003), arXiv: 1101.5044.

    Article  ADS  Google Scholar 

  4. M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, New J. Phys. 16, 045014 (2014), arXiv: 1312.2017.

    Article  ADS  Google Scholar 

  5. J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, Phys. Rev. Lett. 97, 083604 (2006), arXiv: quantph/0602198.

    Article  ADS  PubMed  CAS  Google Scholar 

  6. F. X. Sun, S. S. Zheng, Y. Xiao, Q. Gong, Q. He, and K. Xia, Phys. Rev. Lett. 127, 087203 (2021), arXiv: 2108.05095.

    Article  ADS  PubMed  CAS  Google Scholar 

  7. G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Nature 495, 205 (2013), arXiv: 1211.2228.

    Article  ADS  PubMed  CAS  Google Scholar 

  8. S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A 56, 4175 (1997), arXiv: quant-ph/9708002.

    Article  ADS  CAS  Google Scholar 

  9. G. S. Agarwal, R. R. Puri, and R. P. Singh, Phys. Rev. A 56, 2249 (1997).

    Article  ADS  CAS  Google Scholar 

  10. C. S. Muñoz, A. Lara, J. Puebla, and F. Nori, Phys. Rev. Lett. 121, 123604 (2018), arXiv: 1802.01306.

    Article  ADS  Google Scholar 

  11. W. Qin, A. Miranowicz, H. Jing, and F. Nori, Phys. Rev. Lett. 127, 093602 (2021), arXiv: 2101.03662.

    Article  ADS  PubMed  CAS  Google Scholar 

  12. P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, Nature 541, 473 (2017), arXiv: 1608.00446.

    Article  ADS  PubMed  CAS  Google Scholar 

  13. Z. Yu, and S. Fan, Nat. Photon. 3, 91 (2009).

    Article  ADS  CAS  Google Scholar 

  14. D. L. Sounas, and A. Alú, Nat. Photon. 11, 774 (2017).

    Article  ADS  CAS  Google Scholar 

  15. B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014).

    Article  CAS  Google Scholar 

  16. L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, Nat. Photon. 8, 524 (2014).

    Article  ADS  CAS  Google Scholar 

  17. M. Hafezi, and P. Rabl, Opt. Express 20, 7672 (2012), arXiv: 1110.3538.

    Article  ADS  PubMed  Google Scholar 

  18. Z. Shen, Y. L. Zhang, Y. Chen, C. L. Zou, Y. F. Xiao, X. B. Zou, F. W. Sun, G. C. Guo, and C. H. Dong, Nat. Photon. 10, 657 (2016), arXiv: 1604.02297.

    Article  ADS  CAS  Google Scholar 

  19. S. Maayani, R. Dahan, Y. Kligerman, E. Moses, A. U. Hassan, H. Jing, F. Nori, D. N. Christodoulides, and T. Carmon, Nature 558, 569 (2018).

    Article  ADS  PubMed  CAS  Google Scholar 

  20. Y. P. Wang, J. W. Rao, Y. Yang, P. C. Xu, Y. S. Gui, B. M. Yao, J. Q. You, and C. M. Hu, Phys. Rev. Lett. 123, 127202 (2019).

    Article  ADS  PubMed  CAS  Google Scholar 

  21. C. Liang, B. Liu, A. N. Xu, X. Wen, C. Lu, K. Xia, M. K. Tey, Y. C. Liu, and L. You, Phys. Rev. Lett. 125, 123901 (2020).

    Article  ADS  PubMed  CAS  Google Scholar 

  22. J. Tang, W. Nie, L. Tang, M. Chen, X. Su, Y. Lu, F. Nori, and K. Xia, Phys. Rev. Lett. 128, 203602 (2022), arXiv: 2111.06104.

    Article  ADS  PubMed  CAS  Google Scholar 

  23. L. Tang, J. Tang, M. Chen, F. Nori, M. Xiao, and K. Xia, Phys. Rev. Lett. 128, 083604 (2022), arXiv: 2110.05016.

    Article  ADS  PubMed  CAS  Google Scholar 

  24. M. X. Dong, K. Y. Xia, W. H. Zhang, Y. C. Yu, Y. H. Ye, E. Z. Li, L. Zeng, D. S. Ding, B. S. Shi, G. C. Guo, and F. Nori, Sci. Adv. 7, eabe8924 (2021).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  25. R. Huang, A. Miranowicz, J. Q. Liao, F. Nori, and H. Jing, Phys. Rev. Lett. 121, 153601 (2018), arXiv: 1807.10084.

    Article  ADS  PubMed  CAS  Google Scholar 

  26. B. Li, R. Huang, X. Xu, A. Miranowicz, and H. Jing, Photon. Res. 7, 630 (2019), arXiv: 1901.10784.

    Article  CAS  Google Scholar 

  27. X. Y. Yao, H. Ali, F. L. Li, and P. B. Li, Phys. Rev. Appl. 17, 054004 (2022), arXiv: 2110.11016.

    Article  ADS  Google Scholar 

  28. Y. Wang, W. Xiong, Z. Xu, G. Q. Zhang, and J. Q. You, Sci. China-Phys. Mech. Astron. 65, 260314 (2022), arXiv: 2112.02351.

    Article  ADS  Google Scholar 

  29. Y. F. Jiao, S. D. Zhang, Y. L. Zhang, A. Miranowicz, L. M. Kuang, and H. Jing, Phys. Rev. Lett. 125, 143605 (2020), arXiv: 2002.11148.

    Article  ADS  PubMed  CAS  Google Scholar 

  30. Z. B. Yang, J. X. Liu, A. D. Zhu, H. Y. Liu, and R. C. Yang, Annalen der Physik 532, 2000196 (2020).

    Article  ADS  CAS  Google Scholar 

  31. Y. F. Jiao, J. X. Liu, Y. Li, R. Yang, L. M. Kuang, and H. Jing, Phys. Rev. Appl. 18, 064008 (2022), arXiv: 2208.10001.

    Article  ADS  CAS  Google Scholar 

  32. J. X. Liu, Y. F. Jiao, Y. Li, X. W. Xu, Q. Y. He, and H. Jing, Sci. China-Phys. Mech. Astron. 66, 230312 (2023), arXiv: 2209.12508.

    Article  ADS  Google Scholar 

  33. A. Graf, S. D. Rogers, J. Staffa, U. A. Javid, D. H. Griffith, and Q. Lin, Phys. Rev. Lett. 128, 213605 (2022).

    Article  ADS  PubMed  CAS  Google Scholar 

  34. Y. Xiang, Y. Zuo, X. W. Xu, R. Huang, and H. Jing, Phys. Rev. A 108, 043702 (2023) arXiv: 2303.17997.

    Article  ADS  CAS  Google Scholar 

  35. F. D. M. Haldane, and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008), arXiv: cond-mat/0503588.

    Article  ADS  PubMed  CAS  Google Scholar 

  36. L. Lu, J. D. Joannopoulos, and M. Soljačcić Nat. Photon. 8, 821 (2014), arXiv: 1408.6730.

    Article  CAS  Google Scholar 

  37. V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, Phys. Rev. X 5, 031011 (2015), arXiv: 1409.5375.

    Google Scholar 

  38. S. D. Huber, Nat. Phys. 12, 621 (2016).

    Article  CAS  Google Scholar 

  39. M. J. Tuo, L. H. Zhang, D. Liu, R. W. Peng, R. H. Fan, Z. G. Chen, Y. Wu, D. X. Qi, and M. Wang, Phys. Rev. B 99, 205432 (2019).

    Article  ADS  CAS  Google Scholar 

  40. T. Özawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, Ö. Zilberberg, and I. Carusotto, Rev. Mod. Phys. 91, 015006 (2019), arXiv: 1802.04173.

    Article  ADS  Google Scholar 

  41. X. D. Chen, W. M. Deng, F. L. Shi, F. L. Zhao, M. Chen, and J. W. Dong, Phys. Rev. Lett. 122, 233902 (2019), arXiv: 1812.08326.

    Article  ADS  PubMed  CAS  Google Scholar 

  42. Y. J. Gao, X. Xiong, Z. Wang, F. Chen, R. W. Peng, and M. Wang, Phys. Rev. X 10, 031035 (2020), arXiv: 1905.07537.

    CAS  Google Scholar 

  43. Y. Wang, X. L. Pang, Y. H. Lu, J. Gao, Y. J. Chang, L. F. Qiao, Z. Q. Jiao, H. Tang, and X. M. Jin, Optica 6, 955 (2019), arXiv: 1810.01435.

    Article  ADS  CAS  Google Scholar 

  44. W. Nie, Z. H. Peng, F. Nori, and Y. X. Liu, Phys. Rev. Lett. 124, 023603 (2020), arXiv: 1902.10883.

    Article  ADS  PubMed  CAS  Google Scholar 

  45. G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, Science 359, eaar4003 (2018).

    Article  PubMed  Google Scholar 

  46. M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Science 359, eaar4005 (2018).

    Article  PubMed  Google Scholar 

  47. S. Malzard, C. Poli, and H. Schomerus, Phys. Rev. Lett. 115, 200402 (2015), arXiv: 1508.03985.

    Article  ADS  PubMed  Google Scholar 

  48. D. De Bernardis, Z. P. Cian, I. Carusotto, M. Hafezi, and P. Rabl, Phys. Rev. Lett. 126, 103603 (2021), arXiv: 2009.05952.

    Article  ADS  PubMed  CAS  Google Scholar 

  49. Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačcić, Phys. Rev. Lett. 100, 013905 (2008), arXiv: 0712.1776.

    Article  ADS  PubMed  Google Scholar 

  50. N. Goldman, J. Beugnon, and F. Gerbier, Phys. Rev. Lett. 108, 255303 (2012).

    Article  ADS  PubMed  Google Scholar 

  51. M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, Nat. Phys. 7, 907 (2011), arXiv: 1102.3256.

    Article  CAS  Google Scholar 

  52. C. Dlaska, B. Vermersch, and P. Zoller, Quantum Sci. Technol. 2, 015001 (2017), arXiv: 1607.01154.

    Article  ADS  Google Scholar 

  53. S. Mittal, J. Fan, S. Faez, A. Migdall, J. M. Taylor, and M. Hafezi, Phys. Rev. Lett. 113, 087403 (2014), arXiv: 1404.0090.

    Article  ADS  PubMed  CAS  Google Scholar 

  54. B. Bahari, A. Ndao, F. Vallini, A. E. Amili, Y. Fainman, and B. Kanté, Science 358, 636 (2017).

    Article  ADS  PubMed  CAS  Google Scholar 

  55. D. D. Solnyshkov, O. Bleu, and G. Malpuech, Appl. Phys. Lett. 112, 031106 (2018).

    Article  ADS  Google Scholar 

  56. J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010), arXiv: 0912.0078.

    Article  ADS  CAS  Google Scholar 

  57. B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Yang, Proc. Natl. Acad. Sci. U.S.A. 113, 6845 (2016).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  58. H. Schmidt, and A. Imamoglu, Opt. Lett. 21, 1936 (1996).

    Article  ADS  PubMed  CAS  Google Scholar 

  59. V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016), arXiv: 1410.8598.

    Article  ADS  MathSciNet  PubMed  CAS  Google Scholar 

  60. J. K. Asbóth, L. Oroszlány, and A. Pályi, A Short Course on Topological Insulators (Springer, New York, 2016), arXiv: 1509.02295.

    Book  Google Scholar 

  61. Z. L. Xiang, M. Zhang, L. Jiang, and P. Rabl, Phys. Rev. X 7, 011035 (2017), arXiv: 1611.10241.

    Google Scholar 

  62. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).

    Article  ADS  PubMed  CAS  Google Scholar 

  63. E. P. Ostby, Photonic Whispering-Gallery Resonators in New Environments (California Institute of Technology, Pasadena, 2009).

    Google Scholar 

  64. P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Nature 546, 274 (2017), arXiv: 1610.01484.

    Article  ADS  PubMed  CAS  Google Scholar 

  65. J. A. Zielińska, and M. W. Mitchell, Opt. Lett. 42, 5298 (2017), arXiv: 1707.09085.

    Article  ADS  PubMed  Google Scholar 

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Authors and Affiliations

  1. School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, and Wuhan Institute of Quantum Technology, Wuhan, 430074, China

    Zi-Hao Li, Ying Wu & Xin-You Lü

  2. Key Laboratory of Optoelectronic Chemical Materials and Devices of Ministry of Education, Jianghan University, Wuhan, 430074, China

    Li-Li Zheng

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This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFA1400700), and the National Natural Science Foundation of China (Grant Nos. 11974125, and 12147143).

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Li, ZH., Zheng, LL., Wu, Y. et al. Nonreciprocal generation of Schrödinger cat state induced by topology. Sci. China Phys. Mech. Astron. 67, 240313 (2023). https://doi.org/10.1007/s11433-023-2301-2

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