Single photon two-level atom interactions in 1-D dielectric waveguide: quantum mechanical formalism and applications

  • Fatih DinçEmail author
  • İlke Ercan


In this paper, we propose an effective model to describe the interactions between a two-level atom and scattered light in a 1-D dielectric waveguide. The proposed formalism allows us to incorporate the effect of changing optical media inside the continuum while demonstrating a non-classical derivation of Fresnel Law. We obtain the transport characteristics of the two-level system, explore its high-Q bandreject filter property and discuss the implications of radiative and non-radiative dissipation. In addition, we apply our formalism to a modified Fabry–Pérot interferometer and show the variation in its spontaneous emission characteristics with changing interferometer length. Finally, we conclude with further remarks on the link between the waveguide and cavity quantum electrodynamics.


Single photon scattering 1D dielectric waveguide Fabry–Perot interferometer Atom–light interactions 



The authors would like thank Professor Ataç İmamoğlu for intellectually stimulating discussions, Professor Teoman Turgut for insightful comments on the manuscript and Professor Şükrü Ekin Kocabaş for inspiration and guidance on the modified Fabry–Pérot interferometer study.


  1. Bermel, P., Rodriguez, A., Johnson, S.G., Joannopoulos, J.D., Soljacic, M.: Single-photon all-optical switching using waveguide-cavity quantum electrodynamics. Phys. Rev. A 74, 043818 (2006). ADSCrossRefGoogle Scholar
  2. Birnbaum, K.M., Boca, A., Miller, R., Boozer, A.D., Northup, T.E., Kimble, H.J.: Photon blockade in an optical cavity with one trapped atom. Nature 436(7047), 87–90 (2005). ADSCrossRefGoogle Scholar
  3. Cheng, M.-T., Ma, X.-S., Zhang, J.-Y., Wang, B.: Single photon transport in two waveguides chirally coupled by a quantum emitter. Opt. Express 24(17), 19988–19993 (2016). ADSCrossRefGoogle Scholar
  4. Deutsch, I.H., Spreeuw, R.J.C., Rolston, S.L., Phillips, W.D.: Photonic band gaps in optical lattices. Phys. Rev. A 52, 1394–1410 (1995). ADSCrossRefGoogle Scholar
  5. Dicke, R.H.: Coherence in spontaneous radiation processes. Phys. Rev. 93, 99–110 (1954). ADSCrossRefzbMATHGoogle Scholar
  6. Dinç, F., Ercan, I.: Quantum mechanical treatment of two-level atoms coupled to continuum with an ultraviolet cutoff. J. Phys. A: Math. Theor. 51(35), 355301 (2018).
  7. Dutra, S.M.: Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box. Wiley, New York (2005)Google Scholar
  8. Fan, S., Kocabas, S.E., Shen, J.-T.: Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit. Phys. Rev. A 82, 063821 (2010). ADSCrossRefGoogle Scholar
  9. Glauber, R.J., Lewenstein, M.: Quantum optics of dielectric media. Phys. Rev. A 43, 467–491 (1991). ADSCrossRefGoogle Scholar
  10. Griffiths, D.J.: Introduction to Electrodynamics. Prentice Hall, Upper Saddle River (1962)Google Scholar
  11. Hacker, B., Welte, S., Rempe, G., Ritter, S.: A photonphoton quantum gate based on a single atom in an optical resonator. Nature 536(7615), 193–196 (2016). ADSCrossRefGoogle Scholar
  12. Kittel, C., McEuen, P.: Introduction to Solid State Physics. Wiley, New York (2015)Google Scholar
  13. Loudon, R.: The Quantum Theory of Light. Oxford University Press, Oxford (2010)zbMATHGoogle Scholar
  14. Mu-Tian, C., Meng-Ting, D., Yan-Yan, S., Ya-Qin, L.: Single-photon transmission characteristics in a pair of coupled-resonator waveguides linked by a nanocavity containing a quantum emitter. Chin. Phys. Lett. 30(5), 054202 (2013).
  15. Rephaeli, E., Fan, S.: Dissipation in few-photon waveguide transport. Photon. Res. 1(3), 110–114 (2013).
  16. Rephaeli, E., Shen, J.-T., Fan, S.: Full inversion of a two-level atom with a single-photon pulse in one-dimensional geometries. Phys. Rev. A 82, 033804 (2010). ADSCrossRefGoogle Scholar
  17. Rephaeli, E., Kocabas, S.E., Fan, S.: Few-photon transport in a waveguide coupled to a pair of colocated two-level atoms. Phys. Rev. A 84, 063832 (2011). ADSCrossRefGoogle Scholar
  18. Schwartz, M.D.: Quantum field Theory and the Standard Model. Cambridge University Press, Cambridge (2014)Google Scholar
  19. Shapiro, J.H.: Single-photon Kerr nonlinearities do not help quantum computation. Phys. Rev. A 73, 062305 (2006). ADSCrossRefGoogle Scholar
  20. Shen, J.T., Fan, S.: Coherent photon transport from spontaneous emission in one-dimensional waveguides. Opt. Lett. 30(15), 2001–2003 (2005).
  21. Shen, J.-T., Fan, S.: Strongly correlated multiparticle transport in one dimension through a quantum impurity. Phys. Rev. A 76, 062709 (2007a). ADSCrossRefGoogle Scholar
  22. Shen, J.-T., Fan, S.: Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system. Phys. Rev. Lett. 98, 153003 (2007b). ADSCrossRefGoogle Scholar
  23. Shen, J.-T., Fan, S.: 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
  24. Shi, T., Fan, S., Sun, C.P.: Two-photon transport in a waveguide coupled to a cavity in a two-level system. Phys. Rev. A 84, 063803 (2011). ADSCrossRefGoogle Scholar
  25. Tiecke, T.G., Thompson, J.D., de Leon, N.P., Liu, L.R., Vuletic, V., Lukin, M.D.: Nanophotonic quantum phase switch with a single atom. Nat. Res. Lett. 508, 241–244 (2014). CrossRefGoogle Scholar
  26. Tsoi, T.S., Law, C.K.: Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide. Phys. Rev. A 78, 063832 (2008). ADSCrossRefGoogle Scholar
  27. Yan, C., Wei, L.: Single photon transport along a one-dimensional waveguide with a side manipulated cavity QED system. Opt. Express 23(8), 10374–10384 (2015). ADSCrossRefGoogle Scholar
  28. Zang, X., Jiang, C.: Single-photon transport properties in a waveguidecavity system. J. Phys. B At. Mol. Opt. Phys. 43(6), 065505 (2010).

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Electrical and Electronics Engineering DepartmentBoğaziçi UniversityIstanbulTurkey

Personalised recommendations