Skip to main content
SpringerLink
Log in

Controllable asymmetric diffraction grating with PT symmetry in quantum dot molecules

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

A controllable and high-efficient asymmetric diffraction grating based on PT symmetry is proposed in multi-quantum dot molecular system. The proposed scheme utilizes the particle number modulation besides the modulation of the standing wave driving field. The interaction of the two modulations can change the parity of absorption and exhibits the striking PT symmetry, which is the key to realize the asymmetric diffraction grating. We observe that the positive and negative directions of the diffraction can be adjusted by changing the sign of the modulation amplitude or the sign of the detuning of the probe and driving fields. The increase in the interaction length can transfer the energy of the probe field to the high-order diffraction direction. By adjusting these parameters, high-efficiency diffraction can be achieved in the specified direction. Our scheme provides a feasible scheme for effectively controlling the diffraction direction and greatly improving the diffraction efficiency, which is beneficial to various applications of quantum information processing and large-angle all-optical splitter.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: There is no associated data available.]

References

  1. C.M. Bender, S. Boettcher, Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. C.M. Bender, S. Boettcher, P.N. Meisinger, PT-symmetric quantum mechanics. J. Math. Phys. 40, 2201 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  5. M.G. Silveirinha, Spontaneous parity-time-symmetry breaking in moving media. Phys. Rev. A 90, 013842 (2014)

    Article  ADS  Google Scholar 

  6. J.M. Zeuner, M.C. Rechtsman, Y. Plotnik, Y. Lumer, S. Nolte, M.S. Rudner, M. Segev, A. Szameit, Observation of a topological transition in the bulk of a non-hermitian system. Phys. Rev. Lett. 115, 040402 (2015)

    Article  ADS  Google Scholar 

  7. L. Jin, Z. Song, Bulk-boundary correspondence in a non-hermitian system in one dimension with chiral inversion symmetry. Phys. Rev. B 99, 081103 (2019)

    Article  ADS  Google Scholar 

  8. W. Cao, X. Lu, X. Meng, J. Sun, H. Shen, Y. Xiao, Reservoir-mediated quantum correlations in non-hermitian optical system. Phys. Rev. Lett. 124, 030401 (2020)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. C. Hang, G. Huang, V.V. Konotop, PT symmetry with a system of three-level atoms. Phys. Rev. Lett. 110, 083604 (2013)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. A. Szameit, M.C. Rechtsman, O. Bahat-Treidel, M. Segev, PT-symmetry in honeycomb photonic lattices. Phys. Rev. A 84, 021806 (2011)

    Article  ADS  Google Scholar 

  14. M. Turduev, M. Botey, I. Giden, R. Herrero, H. Kurt, E. Ozbay, K. Staliunas, Two-dimensional complex parity-time-symmetric photonic structures. Phys. Rev. A 91, 023825 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  15. M. Abbas, A. Khurshid, I. Hussain, Ziauddin, Investigation of P T-and P T-antisymmetry in two dimensional (2D) optical lattices. Opt. Exp. 28, 8003 (2020)

    Article  Google Scholar 

  16. Y.L. Chaung, A. Shamsi, M. Abbas, Ziauddin, Coherent control of nonreciprocal reflections with spatial modulation coupling in parity-time symmetric atomic lattice. Opt. Exp. 28, 1701 (2020)

    Article  Google Scholar 

  17. B. He, S.B. Yan, J. Wang, M. Xiao, Quantum noise effects with kerr-nonlinearity enhancement in coupled gain-loss waveguides. Phys. Rev. A 91, 053832 (2015)

    Article  ADS  Google Scholar 

  18. H. Benisty, A. Lupu, A. Degiron, Transverse periodic PT symmetry for modal demultiplexing in optical waveguides. Phys. Rev. A 91, 053825 (2015)

    Article  ADS  Google Scholar 

  19. X.Y. Lü, H. Jing, J.Y. Ma, Y. Wu, PT-symmetry-breaking chaos in optomechanics. Phys. Rev. Lett. 114, 253601 (2015)

    Article  ADS  Google Scholar 

  20. X.W. Xu, Y.X. Liu, C.P. Sun, Y. Li, Mechanical PT symmetry in coupled optomechanical systems. Phys. Rev. A 92, 013852 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. L. Feng, M. Ayache, J.Q. Huang, Y.L. Xu, M.H. Lu, Y.F. Chen, Y. Fainman, A. Scherer, Nonreciprocal light propagation in a silicon photonic circuit. Science 333, 729–733 (2011)

    Article  ADS  Google Scholar 

  25. S. Longhi, Bloch oscillations in complex crystals with pt symmetry. Phys. Rev. Lett. 103, 123601 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  27. T. Shui, W.-X. Yang, S. Liu, L. Li, Z. Zhu, Asymmetric diffraction by atomic gratings with optical PT symmetry in the Raman-Nath regime. Phys. Rev. A 97, 033819 (2018)

    Article  ADS  Google Scholar 

  28. X.Y. Zhu, Y.L. Xu, Y. Zou, X.C. Sun, C. He, M.H. Lu, X.P. Liu, Y.F. Chen, Asymmetric diffraction based on a passive parity-time grating. Appl. Phys. Lett. 109, 111101 (2016)

    Article  ADS  Google Scholar 

  29. A.A. Naeimi, E. Darabi, A. Mortezapour, G. Naeimi, Phase-controlled Optical PT symmetry and asymmetric light diffraction in one-and two-dimensional optical lattices. Eur. Phys. J. Plus 135, 791 (2020)

    Article  Google Scholar 

  30. Y.M. Liu, F. Gao, C.H. Fan, J.H. Wu, Asymmetric light diffraction of an atomic grating with PT symmetry. Opt. Lett. 42, 4283–4286 (2017)

    Article  ADS  Google Scholar 

  31. S.C. Tian, R.G. Wan, L.J. Wang, S.L. Shu, H.Y. Lu, X. Zhang, C.Z. Tong, J.L. Feng, M. Xiao, L.J. Wang, Asymmetric light diffraction of two-dimensional electromagnetically induced grating with PT symmetry in asymmetric double quantum wells. Opt. Exp. 26, 32918–32930 (2018)

    Article  Google Scholar 

  32. T. Shui, W.X. Yang, L. Li, X. Wang, Lop-sided raman–nath diffraction in PT-antisymmetric atomic lattices. Opt. Lett. 44, 2089–2092 (2019)

    Article  ADS  Google Scholar 

  33. D. Ma, D. Yu, X. Zhao, J. Qian, Unidirectional and controllable higher-order diffraction by a Rydberg electromagnetically induced grating. Phys. Rev. A 99, 033826 (2019)

    Article  ADS  Google Scholar 

  34. S. Ziauddin, I. Asghar, R.U. Hussain, M. Abbas, Coherent control of symmetric and asymmetric diffraction grating via relative phase. J. Mod. Optic 67, 737 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  35. P. Michler, Single semiconductor quantum dots, vol. 231 (Springer, 2009)

  36. P. Lodahl, S. Mahmoodian, S. Stobbe, Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87, 347 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  37. X. Li, Y. Wu, D. Steel, D. Gammon, T. Stievater, D. Katzer, D. Park, C. Piermarocchi, L. Sham, An all-optical quantum gate in a semiconductor quantum dot. Science 301, 809–811 (2003)

    Article  ADS  Google Scholar 

  38. M.C. Phillips, H. Wang, I. Rumyantsev, N.H. Kwong, R. Takayama, R. Binder, Electromagnetically induced transparency in semiconductors via biexciton coherence. Phys. Rev. Lett. 91, 183602 (2003)

    Article  ADS  Google Scholar 

  39. T. Kim, K.H. Kim, S. Kim, S.M. Choi, H. Jang, H.K. Seo, H. Lee, D.Y. Chung, E. Jang, Efficient and Stable Blue Quantum Dot Light-Emitting Diode. Nature 586, 385–389 (2020)

    Article  ADS  Google Scholar 

  40. L. Xu, J. Li, B. Cai, J. Song, F. Zhang, T. Fang, H. Zeng, A bilateral interfacial passivation strategy promoting efficiency and stability of perovskite quantum dot light-emitting diodes. Nat. Commun. 11, 1–12 (2020)

    ADS  Google Scholar 

  41. E.A. Chekhovich, S.F.C. da Silva, A. Rastelli, Nuclear spin quantum register in an optically active semiconductor quantum dot. Nat. Nanotechnol. 15, 999–1004 (2020)

    Article  ADS  Google Scholar 

  42. L. Hu, Q. Zhao, S. Huang, J. Zheng, X. Guan, R. Patterson, J. Kim, L. Shi, C.H. Lin, Q. Lei et al., Flexible and efficient perovskite quantum dot solar cells via hybrid interfacial architecture. Nat. Commun. 12, 1–9 (2021)

    ADS  Google Scholar 

  43. P.A. Mortemousque, E. Chanrion, B. Jadot, H. Flentje, A. Ludwig, A.D. Wieck, M. Urdampilleta, C. Bäuerle, T. Meunier, Coherent control of individual electron spins in a two-dimensional quantum dot array. Nat. Nanotechnol. 16, 296–301 (2021)

    Article  ADS  Google Scholar 

  44. M. Abbas, S. Qamar et al., Spatially structured transparency and transfer of optical vortices via four-wave mixing in a quantum-dot nanostructure. Phys. Rev. A 101, 023821 (2020)

    Article  Google Scholar 

  45. D. Nielsen, S.L. Chuang, Four-wave mixing and wavelength conversion in quantum dots. Phys. Rev. B 81, 035305 (2010)

    Article  ADS  Google Scholar 

  46. A. Muller, E.B. Flagg, P. Bianucci, X. Wang, D.G. Deppe, W. Ma, J. Zhang, G. Salamo, M. Xiao, C.-K. Shih, Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity. Phys. Rev. Lett. 99, 187402 (2007)

    Article  ADS  Google Scholar 

  47. F. Aydin, H. Sari, E. Kasapoglu, S. Sakiroglu, I. Sokmen, The anisotropy effects on the shallow-donor impurity states and optical transitions in quantum dots. Eur. Phys. J. Plus 136, 832 (2021)

    Article  Google Scholar 

  48. H. Borges, A. Alcalde, S.E. Ulloa, Exchange interaction and tunneling-induced transparency in coupled quantum dots. Phys. Rev. B 90, 205311 (2014)

    Article  ADS  Google Scholar 

  49. H.Y. Ramírez, S.-J. Cheng, Tunneling effects on fine-structure splitting in quantum-dot molecules. Phys. Rev. Lett. 104, 206402 (2010)

    Article  ADS  Google Scholar 

  50. H.J. Krenner, M. Sabathil, E.C. Clark, A. Kress, D. Schuh, M. Bichler, G. Abstreiter, J.J. Finley, Direct observation of controlled coupling in an individual quantum dot molecule. Phys. Rev. Lett. 94, 057402 (2005)

    Article  ADS  Google Scholar 

  51. K. Müller, A. Bechtold, C. Ruppert, M. Zecherle, G. Reithmaier, M. Bichler, H.J. Krenner, G. Abstreiter, A. Holleitner, J.M. Villas-Bôas et al., Electrical control of interdot electron tunneling in a double ingaas quantum-dot nanostructure. Phys. Rev. Lett. 108, 197402 (2012)

    Article  ADS  Google Scholar 

  52. H. Borges, L. Sanz, J. Villas-Bôas, O.D. Neto, A. Alcalde, Tunneling induced transparency and slow light in quantum dot molecules. Phys. Rev. B 85, 115425 (2012)

    Article  ADS  Google Scholar 

  53. Y. Peng, A. Yang, B. Chen, L. Li, S. Liu, H. Guo, Tunable, high sensitive measurement of inter-dot transition via tunneling induced absorption Appl. Phys. Lett. 109, 141101 (2016)

    Google Scholar 

  54. M. Mahdavi, Z.A. Sabegh, M. Mohammadi, M. Mahmoudi, H.R. Hamedi, Manipulation and exchange of light with orbital angular momentum in quantum-dot molecules. Phys. Rev. A 101, 063811 (2020)

    Article  ADS  Google Scholar 

  55. Z. Li, Y. Cheng, J. Wei, X. Zheng, Y. Yan, Kondo-peak splitting and resonance enhancement caused by interdot tunneling in coupled double quantum dots. Phys. Rev. B 98, 115133 (2018)

    Article  ADS  Google Scholar 

  56. Y.S. Hu, G.L. Cheng, A.X. Chen, Tunneling-induced phase grating in quantum dot molecules. Opt. Express 28, 29805–29814 (2020)

    Article  ADS  Google Scholar 

  57. J. Kim, S.L. Chuang, P.C. Ku, C.J. Chang-Hasnain, Slow light using semiconductor quantum dots. J. Physics: Condens. Matter 16, S3727 (2004)

    ADS  Google Scholar 

  58. G. Ortner, M. Schwab, P. Borri, W. Langbein, U. Woggon, M. Bayer, S. Fafard, Z. Wasilewski, P. Hawrylak, Y. Lyanda-Geller et al., Exciton states in self-assembled inas/gaas quantum dot molecules. Phys. E: Low-dimensional Syst. 25, 249–260 (2004)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This study was acknowledged by National Natural Science Foundation of China (Grants Nos. 11905064, 11775190, and 11565013) and the Scientific Research Foundation of Jiangxi Provincial Education Department (Grant No. GJJ200624).

Author information

Authors and Affiliations

  1. Department of Applied Physics, East China Jiaotong University, Nanchang, 330013, China

    Yongsheng Hu, Ruijin Sun & Guangling Cheng

  2. Department of Physics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Aixi Chen

Authors
  1. Yongsheng Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ruijin Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guangling Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aixi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guangling Cheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, Y., Sun, R., Cheng, G. et al. Controllable asymmetric diffraction grating with PT symmetry in quantum dot molecules. Eur. Phys. J. Plus 137, 690 (2022). https://doi.org/10.1140/epjp/s13360-022-02877-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-02877-3

Search

Navigation