Skip to main content
SpringerLink
Log in

Parity-Time-Symmetric Optical Lattices in Atomic Configurations

  • Chapter
  • First Online:
Parity-time Symmetry and Its Applications

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 280))

  • 2690 Accesses

Abstract

In this chapter, we show how to theoretically design and experimentally construct exact parity-time (PT) symmetric optical lattices with gain and loss in atomic configurations. By making use of the advantages of light-induced atomic coherence in multi-level atomic systems, spatially extended gain and loss arrays with real-time reconfigurability and multiple-parameter tunability can be effectively obtained in hot atomic vapors. We have constructed periodically alternative gain-loss structures with two very different schemes based on spatially-arranged optical induction techniques. With the required symmetric/antisymmetric spatial distributions for the real/imaginary parts of the refraction index satisfied, PT-symmetric optical lattices can be achieved with easy controllability. The dynamic behaviors of light propagating inside the induced non-Hermitian optical lattices are investigated by measuring the relative phase difference between two adjacent gain and loss channels.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Garanovich, I.L., Longhi, S., Sukhorukov, A.A., Kivshar, Y.S.: Light propagation and localization in modulated photonic lattices and waveguides. Phys. Rep. 518, 1–79 (2012)

    Article  ADS  Google Scholar 

  2. Christodoulides, D.N., Lederer, F., Silberberg, Y.: Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature. 424, 817–823 (2003)

    Article  ADS  Google Scholar 

  3. Sheng, J., Wang, J., Miri, M.A., Christodoulides, D.N., Xiao, M.: Observation of discrete diffraction patterns in an optically induced lattice. Opt. Express. 23, 19777–19782 (2015)

    Article  ADS  Google Scholar 

  4. Fleischer, J.W., Carmon, T., Segev, M., Efremidis, N.K., Christodoulides, D.N.: Observation of discrete solitons in optically induced real time waveguide arrays. Phys. Rev. Lett. 90, 023902 (2003)

    Article  ADS  Google Scholar 

  5. Zhang, Y., Zhang, D., Zhang, Z., Li, C., Zhang, Y., Li, F., Belić, M.R., Xiao, M.: Optical Bloch oscillation and zener tunneling in an atomic system. Optica. 4, 571–575 (2017)

    Article  Google Scholar 

  6. Schindler, J., Li, A., Zheng, M.C., Ellis, F.M., Kottos, T.: Experimental study of active LRC circuits with PT symmetries. Phys. Rev. A. 84, 040101R (2011)

    Article  ADS  Google Scholar 

  7. Bender, N., Factor, S., Bodyfelt, J.D., Ramezani, H., Christodoulides, D.N., Ellis, F.M., Kottos, T.: Observation of asymmetric transport in structures with active nonlinearities. Phys. Rev. Lett. 110, 234101 (2013)

    Article  ADS  Google Scholar 

  8. Zhu, X., Ramezani, H., Shi, C., Zhu, J., Zhang, X.: PT-Symmetric acoustics. Phys. Rev. X. 4, 031042 (2014)

    Google Scholar 

  9. Fleury, R., Sounas, D., Alù, A.: An invisible acoustic sensor based on parity-time symmetry. Nat. Commun. 6, 5905 (2015)

    Article  ADS  Google Scholar 

  10. Ruter, C.E., Makris, K.G., EI-Ganainy, R., Christodoulides, D.N., Segev, M., Kip, D.: Observation of parity-time symmetry in optics. Nat. Phys. 6, 192–195 (2010)

    Article  Google Scholar 

  11. Christodoulides, D.N., Miri, M.A.: PT symmetry in optics and photonics. Proc. SPIE. 9162, 91621P (2014)

    Article  ADS  Google Scholar 

  12. Guo, A., Salamo, G.J., Duchesne, D., Morandotti, R., Volatier-Ravat, M., Aimez, V., Siviloglou, G.A., Christodoulides, D.N.: Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009)

    Article  ADS  Google Scholar 

  13. Chong, Y.D., Ge, L., Cao, H., Stone, A.D.: Coherent perfect absorbers: time-reversed lasers. Phys. Rev. Lett. 105, 053901 (2010)

    Article  ADS  Google Scholar 

  14. Longhi, S., Feng, L.: PT-symmetric microring laser-absorber. Opt. Lett. 39, 5026–5029 (2014)

    Article  ADS  Google Scholar 

  15. Peng, B., Özdemir, S.K., Lei, F., Monifi, F., Gianfreda, M., Long, G.L., Fan, S., Nori, F., Bender, C.M., Yang, L.: Parity-time-symmetric whispering-gallery microcavities. Nat. Phys. 10, 394–398 (2014)

    Article  Google Scholar 

  16. Chang, L., Jiang, X., Hua, S., Yang, C., Wen, J., Jiang, L., Li, G., Wang, G., Xiao, M.: Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators. Nat. Photon. 8, 524–529 (2014)

    Article  ADS  Google Scholar 

  17. Makris, K.G., El-Ganainy, R., Christodoulides, D.N., Musslimani, Z.H.: PT-symmetric optical lattices. Phys. Rev. A. 81, 063807 (2010)

    Article  ADS  Google Scholar 

  18. Dmitriev, S.V., Sukhorukov, A.A., Kivshar, Y.S.: Binary parity-time-symmetric nonlinear lattices with balanced gain and loss. Opt. Lett. 35, 2976–2978 (2010)

    Article  ADS  Google Scholar 

  19. Musslimani, Z.H., Makris, K.G., El-Ganainy, R., Christodoulides, D.N.: Optical solitons in PT periodic potentials. Phys. Rev. Lett. 100, 030402 (2008)

    Article  ADS  Google Scholar 

  20. He, Y., Zhu, X., Mihalache, D., Liu, J., Chen, Z.: Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices. Phys. Rev. A. 85, 013831 (2012)

    Article  ADS  Google Scholar 

  21. Wimmer, M., Regensburger, A., Miri, M.A., Bersch, C., Christodoulides, D.N., Peschel, U.: Observation of optical solitons in PT-symmetric lattices. Nat. Commun. 6, 7782 (2015)

    Article  Google Scholar 

  22. Abdullaev, F.K., Kartashov, Y.V., Konotop, V.V., Zezyulinm, D.A.: Solitons in PT-symmetric nonlinear lattices. Phys. Rev. A. 83, 041805R (2011)

    Article  ADS  Google Scholar 

  23. Longhi, S.: Bloch oscillations in complex crystals with PT symmetry. Phys. Rev. Lett. 103, 123601 (2009)

    Article  ADS  Google Scholar 

  24. Wimmer, M., Miri, M.A., Christodoulides, D.N., Peschel, U.: Observation of Bloch oscillations in complex PT-symmetric photonic lattices. Sci. Rep. 5, 17760 (2015)

    Article  ADS  Google Scholar 

  25. Yin, X.B., Zhang, X.: Unidirectional light propagation at exceptional points. Nat. Mater. 12, 175–177 (2013)

    Article  ADS  Google Scholar 

  26. Lin, Z., Ramezani, H., Eichelkraut, T., Kottos, T., Cao, H., Christodoulides, D.N.: Unidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett. 106, 213901 (2011)

    Article  ADS  Google Scholar 

  27. Feng, L., Xu, Y.L., Fegadolli, W.S., Lu, M.H., Oliveira, J.E.B., Almeida, V.R., Chen, Y.F., Scherer, A.: Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. Nat. Mater. 12, 108–113 (2013)

    Article  ADS  Google Scholar 

  28. Regensburger, A., Bersch, C., Miri, M.A., Onishchukov, G., Christodoulides, D.N., Peschel, U.: Parity-time synthetic photonic lattices. Nature. 488, 167–171 (2012)

    Article  ADS  Google Scholar 

  29. Eichelkraut, T., Heilmann, R., Weimann, S., Stützer, S., Dreisow, F., Christodoulides, D.N., Nolte, S., Szameit, A.: Mobility transition from ballistic to diffusive transport in non-Hermitian lattices. Nat. Commun. 4, 2533 (2013)

    Article  ADS  Google Scholar 

  30. Wu, J.H., Artoni, M., La Rocca, G.C.: Parity-time-antisymmetric atomic lattices without gain. Phys. Rev. A. 91, 033811 (2015)

    Article  ADS  Google Scholar 

  31. Miri, M.A., Regensburger, A., Peschel, U., Christodoulides, D.N.: Optical mesh lattices with PT symmetry. Phys. Rev. A. 86, 023807 (2012)

    Article  ADS  Google Scholar 

  32. Ramezani, H., Christodoulides, D.N., Kovanis, V., Vitebskiy, I., Kottos, T.: PT-symmetric Talbot effects. Phys. Rev. Lett. 109, 033902 (2012)

    Article  ADS  Google Scholar 

  33. Bendix, O., Fleischmann, R., Kottos, T., Shapiro, B.: Exponentially fragile PT symmetry in lattices with localized eigenmodes. Phys. Rev. Lett. 103, 30402 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  34. Regensburger, A., Miri, M.A., Bersch, C., Näger, J., Onishchukov, G., Christodoulides, D.N., Peschel, U.: Observation of defect states in PT-symmetric optical lattices. Phys. Rev. Lett. 110, 223902 (2013)

    Article  ADS  Google Scholar 

  35. Makris, K.G., El-Ganainy, R., Christodoulides, D.N., Musslimani, Z.H.: Beam dynamics in PT-symmetric optical lattices. Phys. Rev. Lett. 100, 103904 (2008)

    Article  ADS  Google Scholar 

  36. Zheng, M.C., Christodoulides, D.N., Fleischmann, R., Kottos, T.P.T.: Optical lattices and universality in beam dynamics. Phys . Rev. A. 82, 010103R (2010)

    Article  ADS  Google Scholar 

  37. Wu, J.H., Artoni, M., La Rocca, G.C.: Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices. Phys. Rev. Lett. 113, 123004 (2014)

    Article  ADS  Google Scholar 

  38. Sheng, J.T., Miri, M.A., Christodoulides, D.N., Xiao, M.: PT-symmetric optical potentials in a coherent atomic medium. Phys. Rev. A. 88, 041803R (2013)

    Article  ADS  Google Scholar 

  39. Hang, C., Kartashov, Y.V., Huang, G., Konotop, V.V.: Localization of light in a parity-time-symmetric quasi-periodic lattice. Opt. Lett. 40, 2758–2761 (2015)

    Article  ADS  Google Scholar 

  40. Horsley, S.A.R., Artoni, M., La Rocca, G.C.: Spatial Kramers–Kronig relations and the reflection of waves. Nat. Photon. 9, 436–439 (2015)

    Article  ADS  Google Scholar 

  41. Scully, M.O.: Enhancement of the index of refraction via quantum coherence. Phys. Rev. Lett. 67, 1855–1858 (1991)

    Article  ADS  Google Scholar 

  42. Li, H.J., Dou, J.P., Huang, G.: PT symmetry via electromagnetically induced transparency. Opt. Express. 21, 32053–32062 (2013)

    Article  ADS  Google Scholar 

  43. Harris, S.E.: Electromagnetically induced transparency. Phys. Today. 50, 36–42 (1997)

    Article  Google Scholar 

  44. Gea-Banacloche, J., Li, Y.Q., Jin, S.Z., Xiao, M.: Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment. Phys. Rev. A. 51, 576–584 (1995)

    Article  ADS  Google Scholar 

  45. Xiao, M., Li, Y., Jin, S., Gea-Banacloche, J.: Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms. Phys. Rev. Lett. 74, 666–669 (1995)

    Article  ADS  Google Scholar 

  46. Wu, J., Artoni, M., La Rocca, G.C.: Parity-time-antisymmetric atomic lattices without gain. Phys. Rev. A. 91, 033811 (2015)

    Article  ADS  Google Scholar 

  47. Hang, C., Zezyulin, D.A., Konotop, V.V., Huang, G.: Tunable nonlinear parity–time-symmetric defect modes with an atomic cell. Opt. Lett. 38, 4033–4036 (2013)

    Article  ADS  Google Scholar 

  48. Ramezani, H., Kottos, T., El-Ganainy, R., Christodoulides, D.N.: Unidirectional nonlinear PT-symmetric optical structures. Phys. Rev. A. 82, 043803 (2010)

    Article  ADS  Google Scholar 

  49. Childress, L., Walsworth, R., Lukin, M.: Atom-like crystal defects: from quantum computers to biological sensors. Phys. Today. 67, 38–43 (2014)

    Article  Google Scholar 

  50. Pei, L., Lu, X., Bai, J., Miao, X., Wang, R., Wu, L., Ren, S., Jiao, Z., Zhu, H., Fu, P., andZuo, Z.: Resonant stimulated Raman gain and loss spectroscopy in Rb atomic vapor. Phys. Rev. A. 87, 063822 (2013)

    Article  ADS  Google Scholar 

  51. Kang, H.S., Wen, L.L., Zhu, Y.F.: Normal or anomalous dispersion and gain in a resonant coherent medium. Phys. Rev. A. 68, 063806 (2003)

    Article  ADS  Google Scholar 

  52. Zhang, Z., Zhang, Y., Sheng, J., Yang, L., Miri, M.-A., Christodoulides, D.N., He, B., Zhang, Y., Xiao, M.: Observation of parity-time symmetry in optically induced atomic lattices. Phys. Rev. Lett. 117, 123601 (2016)

    Article  ADS  Google Scholar 

  53. Zhang, Z., Feng, J., Liu, X., Sheng, J., Zhang, Y., Zhang, Y., Xiao, M.: Controllable photonic crystal with periodic Raman gain in a coherent atomic medium. Opt. Lett. 4, 919–922 (2018)

    Article  ADS  Google Scholar 

  54. El-Ganainy, R., Makris, K.G., Christodoulides, D.N., Musslimani, Z.H.: Theory of coupled optical PT-symmetric structures. Opt. Lett. 32, 2632–2634 (2007)

    Article  ADS  Google Scholar 

  55. Sheng, J.T., Miri, M.A., Christodoulides, D.N., Xiao, M.: PT symmetry in coherent atomic media. CLEO: 2013 Technical Digest. QTu1E. 5,

    Google Scholar 

  56. Ling, H.Y., Li, Y.Q., Xiao, M.: Electromagnetically induced grating: homogeneously broadened medium. Phys. Rev. A. 57, 1338–1344 (1998)

    Article  ADS  Google Scholar 

  57. Sheng, J., Wang, J., Miri, M.A., Christodoulides, D.N., Xiao, M.: Observation of discrete diffraction patterns in an optically induced lattice. Opt. Express. 23, 19777–19782 (2015)

    Article  ADS  Google Scholar 

  58. Zhang, Z.Y., Liu, X., Zhang, D., Sheng, J.T., Zhang, Y.Q., Zhang, Y.P., Xiao, M.: Observation of electromagnetically induced Talbot effect in an atomic system. Phys. Rev. A. 97, 013603 (2018)

    Article  ADS  Google Scholar 

  59. Marco, O., Alexander, S.: Quasi PT-symmetry in passive photonic lattices. J. Opt. 16, 065501 (2014)

    Article  Google Scholar 

  60. Lupu, A., Benisty, H., Degiron, A.: Switching using PT symmetry in plasmonic systems: positive role of the losses. Opt. Express. 21, 21651–21668 (2013)

    Article  ADS  Google Scholar 

  61. Zhang, Z., Yang, L., Feng, J., Sheng, J., Zhang, Y., Zhang, Y., Xiao, M.: Parity-Time-Symmetric Optical Lattice with Alternating Gain and Loss Atomic Configurations. Laser Photon. Rev. 12, 1800155 (2018)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported in part by National Key R&D Program of China (2017YFA0303703), National Natural Science Foundation of China (61605154, 11474228), Natural Science Foundation of Shaanxi Province (2017JQ6039, 2017JZ019), China Postdoctoral Science Foundation (2016M600776, 2016M600777, and 2017T100734) and Postdoctoral Science Foundation of Shaanxi Province (2017BSHYDZZ54, 2017BSHTDZZ18).

Author information

Authors and Affiliations

  1. Department of Physics, University of Arkansas, Fayetteville, AR, USA

    Zhaoyang Zhang, Jingliang Feng & Min Xiao

  2. Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an, China

    Zhaoyang Zhang, Yiqi Zhang & Yanpeng Zhang

  3. State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China

    Jiteng Sheng

  4. National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing, China

    Min Xiao

Authors
  1. Zhaoyang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yiqi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingliang Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiteng Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yanpeng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Min Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yanpeng Zhang or Min Xiao .

Editor information

Editors and Affiliations

  1. College of Optics and Photonics, University of Central Florida, Orlando, FL, USA

    Demetrios Christodoulides

  2. Department of Mathematics and Statistics, University of Vermont, Burlington, VT, USA

    Jianke Yang

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zhang, Z., Zhang, Y., Feng, J., Sheng, J., Zhang, Y., Xiao, M. (2018). Parity-Time-Symmetric Optical Lattices in Atomic Configurations. In: Christodoulides, D., Yang, J. (eds) Parity-time Symmetry and Its Applications. Springer Tracts in Modern Physics, vol 280. Springer, Singapore. https://doi.org/10.1007/978-981-13-1247-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-1247-2_8

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-1246-5

  • Online ISBN: 978-981-13-1247-2

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation