Dual effects of disorder on the strongly-coupled system composed of a single quantum dot and a photonic crystal L3 cavity

  • GengYan Chen
  • Jing-Feng Liu
  • Yi-Cong Yu
  • RenMing Liu
  • GuiXin Zhu
  • YongZhu Chen
  • ZhanXu Chen
  • Xue-Hua WangEmail author


Light-matter interaction in the strong coupling regime enables light control at the single-photon level. We develop numerical method and analytical expressions to calculate the decay kinetics of an initially excited two-level quantum emitter in dielectric nanostructure and single-mode cavity, respectively. We use these methods to discover the dual effects of disorder on the stronglycoupled system composed of a single quantum dot and a photonic crystal L3 cavity. The quality factor is sensitive to disorder, while the g factor and vacuum Rabi splitting are robust against disorder. A small amount of disorder may either decrease or increase the light localization and the light-matter interaction. Our methods offer flexible and efficient theoretical tools for the investigation of light-matter interaction, especially cavity quantum electrodynamics. Our findings significantly lower the requirements for optimization effort and fabrication precision and open up many promising practical possibilities.


cavity quantum electrodynamics light-matter interaction photonic crystal 


  1. 1.
    G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, Nat. Phys. 2, 81 (2006).CrossRefGoogle Scholar
  2. 2.
    P. Lodahl, S. Mahmoodian, and S. Stobbe, Rev. Mod. Phys. 87, 347 (2015), arXiv: 1312.1079.ADSCrossRefGoogle Scholar
  3. 3.
    P. Törmä, and W. L. Barnes, Rep. Prog. Phys. 78, 013901 (2015), arXiv: 1405.1661.ADSCrossRefGoogle Scholar
  4. 4.
    D. S. Dovzhenko, S. V. Ryabchuk, Y. P. Rakovich, and I. R. Nabiev, Nanoscale 10, 3589 (2018).CrossRefGoogle Scholar
  5. 5.
    H. Walther, B. T. H. Varcoe, B. G. Englert, and T. Becker, Rep. Prog. Phys. 69, 1325 (2006).ADSCrossRefGoogle Scholar
  6. 6.
    B. Lounis, and M. Orrit, Rep. Prog. Phys. 68, 1129 (2005).ADSCrossRefGoogle Scholar
  7. 7.
    D. E. Chang, V. Vuletic, and M. D. Lukin, Nat. Photon. 8, 685 (2014).ADSCrossRefGoogle Scholar
  8. 8.
    H. J. Kimble, Nature 453, 1023 (2008), arXiv: 0806.4195.ADSCrossRefGoogle Scholar
  9. 9.
    D. Sanvitto, and S. Kéna-Cohen, Nat. Mater. 15, 1061 (2016).ADSCrossRefGoogle Scholar
  10. 10.
    R. Liu, Z. K. Zhou, Y. C. Yu, T. Zhang, H. Wang, G. Liu, Y. Wei, H. Chen, and X. H. Wang, Phys. Rev. Lett. 118, 237401 (2017).ADSCrossRefGoogle Scholar
  11. 11.
    Y. Akahane, T. Asano, B. S. Song, and S. Noda, Nature 425, 944 (2003).ADSCrossRefGoogle Scholar
  12. 12.
    B. S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).ADSCrossRefGoogle Scholar
  13. 13.
    J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 2008).zbMATHGoogle Scholar
  14. 14.
    T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).ADSCrossRefGoogle Scholar
  15. 15.
    K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, Nature 445, 896 (2007).ADSCrossRefGoogle Scholar
  16. 16.
    D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, Nature 450, 857 (2007).ADSCrossRefGoogle Scholar
  17. 17.
    A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, Nat. Phys. 4, 859 (2008), arXiv: 0804.2740.CrossRefGoogle Scholar
  18. 18.
    M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, Nat. Phys. 6, 279 (2010), arXiv: 0905.3063.CrossRefGoogle Scholar
  19. 19.
    Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, Nat. Photon. 6, 56 (2012).ADSCrossRefGoogle Scholar
  20. 20.
    H. Kim, T. C. Shen, K. Roy-Choudhury, G. S. Solomon, and E. Waks, Phys. Rev. Lett. 113, 027403 (2014), arXiv: 1310.3638.ADSCrossRefGoogle Scholar
  21. 21.
    Y. Ota, R. Ohta, N. Kumagai, S. Iwamoto, and Y. Arakawa, Phys. Rev. Lett. 114, 143603 (2015), arXiv: 1503.01855.ADSCrossRefGoogle Scholar
  22. 22.
    T. M. Sweeney, S. G. Carter, A. S. Bracker, M. Kim, C. S. Kim, L. Yang, P. M. Vora, P. G. Brereton, E. R. Cleveland, and D. Gammon, Nat. Photon. 8, 442 (2014), arXiv: 1402.4494.ADSCrossRefGoogle Scholar
  23. 23.
    A. Lyasota, S. Borghardt, C. Jarlov, B. Dwir, P. Gallo, A. Rudra, and E. Kapon, J. Cryst. Growth 414, 192 (2015).ADSCrossRefGoogle Scholar
  24. 24.
    C. Jarlov, É. Wodey, A. Lyasota, M. Calic, P. Gallo, B. Dwir, A. Rudra, and E. Kapon, Phys. Rev. Lett. 117, 076801 (2016).ADSCrossRefGoogle Scholar
  25. 25.
    S. Lichtmannecker, M. Florian, T. Reichert, M. Blauth, M. Bichler, F. Jahnke, J. J. Finley, C. Gies, and M. Kaniber, Sci. Rep. 7, 7420 (2017), arXiv: 1602.03998.ADSCrossRefGoogle Scholar
  26. 26.
    D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. D. Lukin, Nano Lett. 10, 3922 (2010), arXiv: 1005.2204.ADSCrossRefGoogle Scholar
  27. 27.
    A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, Phys. Rev. Lett. 109, 033604 (2012), arXiv: 1202.0806.ADSCrossRefGoogle Scholar
  28. 28.
    B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. de Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lonc R, Nano Lett. 13, 5791 (2013).ADSCrossRefGoogle Scholar
  29. 29.
    S. Wu, S. Buckley, J. R. Schaibley, L. Feng, J. Yan, D. G. Mandrus, F. Hatami, W. Yao, J. Vuckovic, A. Majumdar, and X. Xu, Nature 520, 69 (2015).ADSCrossRefGoogle Scholar
  30. 30.
    A. Gopinath, E. Miyazono, A. Faraon, and P. W. K. Rothemund, Nature 535, 401 (2016).ADSCrossRefGoogle Scholar
  31. 31.
    F. Pyatkov, V. Fütterling, S. Khasminskaya, B. S. Flavel, F. Hennrich, M. M. Kappes, R. Krupke, and W. H. P. Pernice, Nat. Photon. 10, 420 (2016).ADSCrossRefGoogle Scholar
  32. 32.
    M. S. Hwang, H. R. Kim, K. H. Kim, K. Y. Jeong, J. S. Park, J. H. Choi, J. H. Kang, J. M. Lee, W. I. Park, J. H. Song, M. K. Seo, and H. G. Park, Nano Lett. 17, 1892 (2017).ADSCrossRefGoogle Scholar
  33. 33.
    Y. Ota, R. Moriya, N. Yabuki, M. Arai, M. Kakuda, S. Iwamoto, T. Machida, and Y. Arakawa, Appl. Phys. Lett. 110, 223105 (2017).ADSCrossRefGoogle Scholar
  34. 34.
    A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, Nano Lett. 13, 3281 (2013).ADSCrossRefGoogle Scholar
  35. 35.
    G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, Phys. Rev. Lett. 114, 157401 (2015), arXiv: 1501.02123.ADSCrossRefGoogle Scholar
  36. 36.
    X. Chen, Y. H. Chen, J. Qin, D. Zhao, B. Ding, R. J. Blaikie, and M. Qiu, Nano Lett. 17, 3246 (2017), arXiv: 1607.07620.ADSCrossRefGoogle Scholar
  37. 37.
    B. M. Garraway, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci. 369, 1137 (2011).ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    W. J. Fan, Z. B. Hao, Z. Li, Y. S. Zhao, and Y. Luo, J. Lightw. Technol. 28, 1455 (2010).ADSCrossRefGoogle Scholar
  39. 39.
    S. L. Portalupi, M. Galli, M. Belotti, L. C. Andreani, T. F. Krauss, and L. O’Faolain, Phys. Rev. B 84, 045423 (2011).ADSCrossRefGoogle Scholar
  40. 40.
    M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, Opt. Express 21, 28233 (2013).ADSCrossRefGoogle Scholar
  41. 41.
    H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, Phys. Rev. B 79, 085112 (2009).ADSCrossRefGoogle Scholar
  42. 42.
    T. Asano, B. S. Song, and S. Noda, Opt. Express 14, 1996 (2006).ADSCrossRefGoogle Scholar
  43. 43.
    Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, Opt. Express 19, 11916 (2011).ADSCrossRefGoogle Scholar
  44. 44.
    R. Benevides, F. G. S. Santos, G. O. Luiz, G. S. Wiederhecker, and T. P. M. Alegre, Sci. Rep. 7, 2491 (2017), arXiv: 1701.03410.ADSCrossRefGoogle Scholar
  45. 45.
    Y. Akahane, T. Asano, B. S. Song, and S. Noda, Opt. Express 13, 1202 (2005).ADSCrossRefGoogle Scholar
  46. 46.
    Y. Takahashi, H. Hagino, Y. Tanaka, B. S. Song, T. Asano, and S. Noda, Opt. Express 15, 17206 (2007).ADSCrossRefGoogle Scholar
  47. 47.
    Y. Tanaka, T. Asano, and S. Noda, J. Lightwave Technol. 26, 1532 (2008).ADSCrossRefGoogle Scholar
  48. 48.
    Y. Takahashi, Y. Tanaka, H. Hagino, T. Sugiya, Y. Sato, T. Asano, and S. Noda, Opt. Express 17, 18093 (2009).ADSCrossRefGoogle Scholar
  49. 49.
    Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, Appl. Phys. Lett. 104, 241101 (2014).ADSCrossRefGoogle Scholar
  50. 50.
    D. Wang, Z. Yu, Y. Liu, X. Guo, C. Shu, S. Zhou, and J. Zhang, J. Opt. 15, 125102 (2013).ADSCrossRefGoogle Scholar
  51. 51.
    M. Minkov, and V. Savona, Sci. Rep. 4, 5124 (2014).ADSCrossRefGoogle Scholar
  52. 52.
    P. W. Anderson, Phys. Rev. 109, 1492 (1958).ADSCrossRefGoogle Scholar
  53. 53.
    J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).ADSCrossRefGoogle Scholar
  54. 54.
    A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, Phys. Today 62, 24 (2009).CrossRefGoogle Scholar
  55. 55.
    D. S. Wiersma, Nat. Photon. 7, 188 (2013).ADSCrossRefGoogle Scholar
  56. 56.
    P. D. García, G. Kiršanske, A. Javadi, S. Stobbe, and P. Lodahl, Phys. Rev. B 96, 144201 (2017), arXiv: 1709.10310.ADSCrossRefGoogle Scholar
  57. 57.
    T. Crane, O. J. Trojak, J. P. Vasco, S. Hughes, and L. Sapienza, ACS Photon. 4, 2274 (2017).CrossRefGoogle Scholar
  58. 58.
    L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010), arXiv: 1003.2525.ADSCrossRefGoogle Scholar
  59. 59.
    J. Liu, P. D. Garcia, S. Ek, N. Gregersen, T. Suhr, M. Schubert, J. Mørk, S. Stobbe, and P. Lodahl, Nat. Nanotech. 9, 285 (2014).ADSCrossRefGoogle Scholar
  60. 60.
    P. D. García, and P. Lodahl, Annal. Phys. 529, 1600351 (2017), arXiv: 1611.02038.ADSCrossRefGoogle Scholar
  61. 61.
    H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, Phys. Rev. Lett. 108, 113901 (2012), arXiv: 1112.5674.ADSCrossRefGoogle Scholar
  62. 62.
    J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. A. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, Sci. Rep. 3, 1994 (2013), arXiv: 1306.2042.ADSCrossRefGoogle Scholar
  63. 63.
    J. P. Vasco, and S. Hughes, Phys. Rev. B 95, 224202 (2017), arXiv: 1701.09139.ADSCrossRefGoogle Scholar
  64. 64.
    J. P. Vasco, and S. Hughes, ACS Photon. 5, 1262 (2018).CrossRefGoogle Scholar
  65. 65.
    X. H. Wang, R. Wang, B. Y. Gu, and G. Z. Yang, Phys. Rev. Lett. 88, 093902 (2002).ADSCrossRefGoogle Scholar
  66. 66.
    X. H. Wang, B. Y. Gu, R. Wang, and H. Q. Xu, Phys. Rev. Lett. 91, 113904 (2003).ADSCrossRefGoogle Scholar
  67. 67.
    G. Chen, Y. C. Yu, X. L. Zhuo, Y. G. Huang, H. Jiang, J. F. Liu, C. J. Jin, and X. H. Wang, Phys. Rev. B 87, 195138 (2013).ADSCrossRefGoogle Scholar
  68. 68.
    E. M. Purcell, Phys. Rev. 69, 681 (1946).CrossRefGoogle Scholar
  69. 69.
    A. R. A. Chalcraft, S. Lam, D. O’Brien, T. F. Krauss, M. Sahin, D. Szymanski, D. Sanvitto, R. Oulton, M. S. Skolnick, A. M. Fox, D. M. Whittaker, H. Y. Liu, and M. Hopkinson, Appl. Phys. Lett. 90, 241117 (2007).ADSCrossRefGoogle Scholar
  70. 70.
    A. Taflove, and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (third edition) (Artech House, London, 2005).zbMATHGoogle Scholar
  71. 71.
    G. Chen, J. F. Liu, H. Jiang, X. L. Zhuo, Y. C. Yu, C. Jin, and X. H. Wang, Nanoscale Res. Lett. 8, 187 (2013).ADSCrossRefGoogle Scholar
  72. 72.
    S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).ADSMathSciNetCrossRefGoogle Scholar
  73. 73.
    L. Ramunno, and S. Hughes, Phys. Rev. B 79, 161303 (2009).ADSCrossRefGoogle Scholar
  74. 74.
    A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, Science 308, 1158 (2005).ADSCrossRefGoogle Scholar
  75. 75.
    N. Mann, A. Javadi, P. D. García, P. Lodahl, and S. Hughes, Phys. Rev. A 92, 023849 (2015), arXiv: 1505.02836.ADSCrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • GengYan Chen
    • 1
  • Jing-Feng Liu
    • 2
  • Yi-Cong Yu
    • 3
  • RenMing Liu
    • 4
  • GuiXin Zhu
    • 4
  • YongZhu Chen
    • 1
  • ZhanXu Chen
    • 1
  • Xue-Hua Wang
    • 4
    Email author
  1. 1.School of Optoelectronic EngineeringGuangdong Polytechnic Normal UniversityGuangzhouChina
  2. 2.College of Electronic EngineeringSouth China Agricultural UniversityGuangzhouChina
  3. 3.School of Physics and Optoelectronic EngineeringFoshan UniversityFoshanChina
  4. 4.State Key Laboratory of Optoelectronic Materials and Technologies, School of PhysicsSun Yat-sen UniversityGuangzhouChina

Personalised recommendations