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

- 166 Downloads

## Abstract

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.

## Keywords

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

### Acknowledgements

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.

## References

- 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). https://doi.org/10.1103/PhysRevA.74.043818 ADSCrossRefGoogle Scholar - 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). https://doi.org/10.1038/nature03804 ADSCrossRefGoogle Scholar - 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). https://doi.org/10.1364/OE.24.019988 ADSCrossRefGoogle Scholar - 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). https://doi.org/10.1103/PhysRevA.52.1394 ADSCrossRefGoogle Scholar - Dicke, R.H.: Coherence in spontaneous radiation processes. Phys. Rev.
**93**, 99–110 (1954). https://doi.org/10.1103/PhysRev.93.99 ADSCrossRefzbMATHGoogle Scholar - 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). https://doi.org/10.1088/1751-8121/aad165 - Dutra, S.M.: Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box. Wiley, New York (2005)Google Scholar
- 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). https://doi.org/10.1103/PhysRevA.82.063821 ADSCrossRefGoogle Scholar - Glauber, R.J., Lewenstein, M.: Quantum optics of dielectric media. Phys. Rev. A
**43**, 467–491 (1991). https://doi.org/10.1103/PhysRevA.43.467 ADSCrossRefGoogle Scholar - Griffiths, D.J.: Introduction to Electrodynamics. Prentice Hall, Upper Saddle River (1962)Google Scholar
- 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). https://doi.org/10.1038/nature18592 ADSCrossRefGoogle Scholar - Kittel, C., McEuen, P.: Introduction to Solid State Physics. Wiley, New York (2015)Google Scholar
- Loudon, R.: The Quantum Theory of Light. Oxford University Press, Oxford (2010)zbMATHGoogle Scholar
- 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). http://stacks.iop.org/0256-307X/30/i=5/a=054202 - Rephaeli, E., Fan, S.: Dissipation in few-photon waveguide transport. Photon. Res.
**1**(3), 110–114 (2013). https://doi.org/10.1364/PRJ.1.000110. http://www.osapublishing.org/prj/abstract.cfm?URI=prj-1-3-110 - 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). https://doi.org/10.1103/PhysRevA.82.033804 ADSCrossRefGoogle Scholar - 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). https://doi.org/10.1103/PhysRevA.84.063832 ADSCrossRefGoogle Scholar - Schwartz, M.D.: Quantum field Theory and the Standard Model. Cambridge University Press, Cambridge (2014)Google Scholar
- Shapiro, J.H.: Single-photon Kerr nonlinearities do not help quantum computation. Phys. Rev. A
**73**, 062305 (2006). https://doi.org/10.1103/PhysRevA.73.062305 ADSCrossRefGoogle Scholar - Shen, J.T., Fan, S.: Coherent photon transport from spontaneous emission in one-dimensional waveguides. Opt. Lett.
**30**(15), 2001–2003 (2005). https://doi.org/10.1364/OL.30.002001. http://ol.osa.org/abstract.cfm?URI=ol-30-15-2001 - Shen, J.-T., Fan, S.: Strongly correlated multiparticle transport in one dimension through a quantum impurity. Phys. Rev. A
**76**, 062709 (2007a). https://doi.org/10.1103/PhysRevA.76.062709 ADSCrossRefGoogle Scholar - 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). https://doi.org/10.1103/PhysRevLett.98.153003 ADSCrossRefGoogle Scholar - 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). https://doi.org/10.1103/PhysRevA.79.023837 ADSCrossRefGoogle Scholar - 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). https://doi.org/10.1103/PhysRevA.84.063803 ADSCrossRefGoogle Scholar - 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). https://doi.org/10.1038/nature13188 CrossRefGoogle Scholar - 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). https://doi.org/10.1103/PhysRevA.78.063832 ADSCrossRefGoogle Scholar - 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). https://doi.org/10.1364/OE.23.010374 ADSCrossRefGoogle Scholar - Zang, X., Jiang, C.: Single-photon transport properties in a waveguidecavity system. J. Phys. B At. Mol. Opt. Phys.
**43**(6), 065505 (2010). http://stacks.iop.org/0953-4075/43/i=6/a=065505