International Journal of Theoretical Physics

, Volume 58, Issue 4, pp 1237–1248 | Cite as

Dynamic Manipulation of Single-Photon Transport along a Waveguide by Dipole-Coupled Two-Level Atoms in a Quadratic Optomechanical Cavity

  • Zhonghua Zhu
  • Yuqing ZhangEmail author
  • Ke Zeng
  • Jiawei Zhang
  • Zhaohui Peng
  • Chunlei Jiang
  • Yifeng Chai
  • Lei Tan


Single-photon transport along a one-dimensional waveguide side coupled to a quadratic optomechanical cavity embedded in two two-level atoms with dipole-dipole interaction (DDI) are explored theoretically. The transmission and reflection amplitudes are derived using a real-space approach. The effects of the optomechanical coupling strength, the DDI, atom-cavity detuning, and atomic dissipation on the single-photon transport properties are analyzed. In single-photon strong-coupling regime, vacuum Rabi-splitting and electromagnetically induced transparency (EIT)-like transmission spectra are observed. It is found that the DDI can shift the reflected resonant points, change the distance and the minima of the two vacuum Rabi-splitting dips, and modify the EIT-like spectra. Therefore, single-photon transport can be well controlled by such a hybrid atom-optomechanical system.


Single-photon Optomechanical cavity Dipole-dipole interaction Vacuum Rabi-splitting Electromagnetically induced transparency 



This work was partly supported by the National Natural Science Foundation of China under Grant Nos. 11504104, 11704115, 11405052, 11874190.


  1. 1.
    Englund, D., Faraon, A., Fushman, L., Stoltz, N., Petroff, P., Vuckovic, J.: Controlling cavity reflectivity with a single quantum dot. Nature 450, 857 (2007)ADSCrossRefGoogle Scholar
  2. 2.
    Shen, J.T., Fan, S.H.: Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system. Phys. Rev. Lett. 98, 153003 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    Ji, A.C., Sun, Q., Xie, X.C., Liu, W.M.: Josephson effect for photons in two weakly linked microcavities. Phys. Rev. Lett. 102, 023602 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    Qi, R., Yu, X.L., Li, Z.B., Liu, W.M.: Non-Abelian Josephson effect between two F = 2 spinor bose-Einstein condensates in double optical traps. Phys. Rev. Lett. 102, 185301 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    Ji, A.C., Liu, W.M., Song, J.L., Zhou, F.: Dynamical creation of fractionalized vortices and vortex lattices. Phys. Rev. Lett. 101, 010402 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    Shen, J.T., Fan, S.H.: Theory of single-photon transport in a single-mode waveguide.I. Coupling to a cavity containing a two-level atom. Phys. Rev. A 79, 023837 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    Yan, C.H., Wei, L.F., Jia, W.Z., Shen, J.T.: Controlling resonant photonic transport along optical waveguides by two-level atoms. Phys. Rev. A 84, 045801 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    Zang, X.F., Zhou, T., Cai, B., Zhu, Y.M.: Controlling single-photon transport properties in a waveguide coupled with two separated atoms. J. Phys. B 46, 145504 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    Liao, Z.Y., Zeng, X.D., Zhu, S.Y., Suhail Zubairy, M.: Single-photon transport through an atomic chain coupled to a one-dimensional nanophotonic waveguide. Phys. Rev. A 92, 023806 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    Chen, G.Y., Lambert, N., Chou, C.H., Chen, Y.N., Nori, F.: Surface plasmons in a metal nanowire coupled to colloidal quantum dots: Scattering properties and quantum entanglement. Phys. Rev. B 84, 045310 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    Milde, F., Knorr, A., Hughes, S.: Role of electron-phonon scattering on the vacuum Rabi splitting of a single-quantum dot and a photonic crystal nanocavity. Phys. Rev. B 78, 035330 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Shen, J.T., Fan, S.H.: Theory of single-photon transport in a single-mode waveguide. II. Coupling to a whisperinggallery resonator containing a two-level atom. Phys. Rev. A 79, 023838 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    Astafiev, O., Zagoskin, A.M., Abdumalikov, A.A. Jr., Pashkin, Y.A., Yamamoto, T., Inomata, K., Nakamura, Y., Tsai, J.S.: Resonance fluorescence of a single artificial atom. Science 327, 840 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    Roy, D.: Two-photon scattering by a driven three-level emitter in a one-dimensional waveguide and electromagnetically induced transparency. Phys. Rev. Lett. 106, 053601 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    Chen, Y.L., Xiao, Y.F., Zhou, X.X., Zou, X.B., Zhou, Z.W., Guo, G.C.: Single-photon transport in a transmission line resonator interacting with two capacitively coupled Cooper-pair boxes. J. Phys. B 41, 175503 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    Aspelmeyer, M., Kippenberg, T.J., Marquardt, F.: Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    Xue, Z.Y., Yang, L.N., Zhou, J.: Circuit electromechanics with single photon strong coupling. Appl. Phys. Lett. 107, 023102 (2015)ADSCrossRefGoogle Scholar
  18. 18.
    Jia, W.Z., Wang, Z.D.: Single-photon transport in a one-dimensional waveguide coupling to a hybrid atom-optomechanical system. Phys. Rev. A 88, 063821 (2013)ADSCrossRefGoogle Scholar
  19. 19.
    Ren, X.X., Li, H.K., Yan, M.Y., Liu, Y.C., Xiao, Y.F., Gong, Q.H.: Single-photon transport and mechanical NOON-state generation in microcavity optomechanics. Phys. Rev. A 87, 033807 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    Chen, W., Clerk, A.A.: Photon propagation in a one-dimensional optomechanical lattice. Phys. Rev. A 89, 033854 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    Liu, J.Y., Zhang, W.Z., Li, X., Yan, W.B., Zhou, L.: The correlated two-photon transport in a one-dimensional waveguide coupling to a hybrid atom-optomechanical system. Int. J. Theor. Phys. 55, 4620 (2016)CrossRefzbMATHGoogle Scholar
  22. 22.
    Liao, J.Q., Nori, F.: Single-photon quadratic optomechanics. Sci. Rep. 4, 6302 (2014)CrossRefGoogle Scholar
  23. 23.
    Xie, H., Liao, C.G., Shang, X., Ye, M.Y., Lin, X.M.: Phonon blockade in a quadratically coupled optomechanical system. Phys. Rev. A 96, 013861 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    Liao, J.Q., Nori, F.: Photon blockade in quadratically coupled optomechanical systems. Phys. Rev. A 88, 023853 (2013)ADSCrossRefGoogle Scholar
  25. 25.
    Si, L.G., Xiong, H., Suhail Zubairy, M., Wu, Y.: Optomechanically induced opacity and amplification in a quadratically coupled optomechanical system. Phys. Rev. A 95, 033803 (2017)ADSCrossRefGoogle Scholar
  26. 26.
    Gu, W.J., Yi, Z., Sun, L.H., Xu, D.H.: Mechanical cooling in single-photon optomechanics with quadratic nonlinearity. Phys. Rev. A 92, 023811 (2015)ADSCrossRefGoogle Scholar
  27. 27.
    Qiao, L.: Single-photon transport through a waveguide coupling to a quadratic optomechanical system. Phys. Rev. A 96, 013860 (2017)ADSCrossRefGoogle Scholar
  28. 28.
    Peng, J.S., Li, G.X.: Effects of the dipole-dipole interaction on dynamic properties and atomic coherent trapping of a two-atom system. Phys. Rev. A 47, 4212 (1993)ADSCrossRefGoogle Scholar
  29. 29.
    Zheng, H., Gauthier, D.J., Baranger, H.U.: Cavity-Free photon blockade induced by many-body bound states. Phys. Rev. Lett. 107, 223601 (2011)ADSCrossRefGoogle Scholar
  30. 30.
    Schoelkopf, R.J., Girvin, S.M.: Wiring up quantum systems. Nature (London) 451, 664 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    Zhang, Y.Q., Tan, L., Barker, P.: Effects of dipole-dipole interaction on the transmitted spectrum of two-level atoms trapped in an optical cavity. Phys. Rev. A 89, 043838 (2014)ADSCrossRefGoogle Scholar
  32. 32.
    Houck, A.A., Schreier, J.A., Johnson, B.R., Chow, J.M., Koch, J., Gambetta, J.M., Schuster, D.I., Frunzio, L., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Controlling the spontaneous emission of a superconducting transmon qubit. Phys. Rev. Lett. 101, 080502 (2008)ADSCrossRefGoogle Scholar
  33. 33.
    Lodahl, P., Van Driel, A.F., Nikolaev, I.S., Irman, A., Overgaag, K., Vanmaekelbergh, D., Vos, W.L.: Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals. Nature 430, 654 (2004)ADSCrossRefGoogle Scholar
  34. 34.
    Lund-Hansen, T., Stobbe, S., Julsgaard, B., Thyrrestrup, H., Sunner, T., Kamp, M., Lodahl, P.: Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide. Phys. Rev. Lett. 101, 113903 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Physics and Electronics ScienceHunan University of Science and TechnologyXiangtanPeople’s Republic of China
  2. 2.Institute of Theoretical PhysicsLanzhou UniversityLanzhouPeople’s Republic of China

Personalised recommendations