Skip to main content
SpringerLink
Log in

Enhancement of tripartite entanglement via periodically modulated fields with an atom-assisted optomechanical system

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We propose a model for controlling and enhancing the entanglement between the two cavity fields and mirror with a hybrid optomechanical system consisting of \(\Lambda \)-type three-level \({ }^{85} \textrm{Rb}\) atomic ensembles driven by two externally modulated laser fields. When one (another) cavity mode is driven at the red (blue) mechanical sideband and both cavity modes are blue-detuned by the mechanical frequency to the respective atomic resonant transitions, the dynamic coupling control of the cavity field and mirror can be realized by periodically modulating the amplitudes of the two incident laser fields. Compared to the unmodulated case, the periodic modulation of the laser fields in a cavity optomechanical system embedded with a small number of atoms has the capability to enhance the entanglement between the two cavity fields and mirror. This scheme provides a new approach to the generation and control of entanglement in cavity optomechanical systems.

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

References

  1. Schrödinger, E.: Discussion of probability relations between separated systems. In: Mathematical Proceedings of the Cambridge Philosophical Society, vol. 31, pp. 555–563 (1935). Cambridge University Press

  2. Jones, J.A., Jaksch, D.: Quantum information, computation and communication. Quantum Information (2012)

  3. Solki, H., Motazedifard, A., Naderi, M.H.: Improving photon blockade, entanglement, and mechanical-cat-state generation in a generalized cross-Kerr optomechanical circuit. Phys. Rev. A 108(6), 063505 (2023)

    ADS  MathSciNet  Google Scholar 

  4. Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photonics 5(4), 222–229 (2011)

    ADS  Google Scholar 

  5. Motazedifard, A., Bemani, F., Naderi, M.H., Roknizadeh, R., Vitali, D.: force sensing based on coherent quantum noise cancellation in a hybrid optomechanical cavity with squeezed-vacuum injection. New J. Phys. 18(7), 073040 (2016)

    ADS  Google Scholar 

  6. Kronwald, A., Marquardt, F., Clerk, A.A.: Dissipative optomechanical squeezing of light. New J. Phys. 16(6), 063058 (2014)

    ADS  Google Scholar 

  7. Motazedifard, A., Dalafi, A., Bemani, F., Naderi, M.H.: Force sensing in hybrid Bose–Einstein-condensate optomechanics based on parametric amplification. Phys. Rev. A 100, 023815 (2019)

    ADS  Google Scholar 

  8. Liao, J.-Q., Wu, Q.-Q., Nori, F., et al.: Entangling two macroscopic mechanical mirrors in a two-cavity optomechanical system. Phys. Rev. A 89(1), 014302 (2014)

    ADS  Google Scholar 

  9. Schwab, K.C., Roukes, M.L.: Putting mechanics into quantum mechanics. Phys. Today 58(7), 36–42 (2005)

    Google Scholar 

  10. Pontin, A., Bonaldi, M., Borrielli, A., Marconi, L., Marino, F., Pandraud, G., Prodi, G.A., Sarro, P.M., Serra, E., Marin, F.: Dynamical two-mode squeezing of thermal fluctuations in a cavity optomechanical system. Phys. Rev. Lett. 116, 103601 (2016)

    ADS  Google Scholar 

  11. Liu, Y.-C., Hu, Y.-W., Wong, C.W., Xiao, Y.-F.: Review of cavity optomechanical cooling. Chin. Phys. B 22(11), 114213 (2013)

    ADS  Google Scholar 

  12. Paternostro, M., Vitali, D., Gigan, S., Kim, M., Brukner, C., Eisert, J., Aspelmeyer, M.: Creating and probing multipartite macroscopic entanglement with light. Phys. Rev. Lett. 99(25), 250401 (2007)

    ADS  Google Scholar 

  13. Akram, U., Munro, W., Nemoto, K., Milburn, G.: Photon-phonon entanglement in coupled optomechanical arrays. Phys. Rev. A 86(4), 042306 (2012)

    ADS  Google Scholar 

  14. Yang, X., Wang, P., Cheng, M., Yin, Z.: Generation of quintupartite entanglement with an atom-assisted dual-cavity optomechanical system. J. Mod. Opt. 68(8), 450–456 (2021)

    ADS  MathSciNet  Google Scholar 

  15. Genes, C., Mari, A., Tombesi, P., Vitali, D.: Robust entanglement of a micromechanical resonator with output optical fields. Phys. Rev. A 78(3), 032316 (2008)

    ADS  Google Scholar 

  16. Barzanjeh, S., Vitali, D., Tombesi, P., Milburn, G.: Entangling optical and microwave cavity modes by means of a nanomechanical resonator. Phys. Rev. A 84(4), 042342 (2011)

    ADS  Google Scholar 

  17. Vitali, D., Gigan, S., Ferreira, A., Böhm, H., Tombesi, P., Guerreiro, A., Vedral, V., Zeilinger, A., Aspelmeyer, M.: Optomechanical entanglement between a movable mirror and a cavity field. Phys. Rev. Lett. 98(3), 030405 (2007)

    ADS  Google Scholar 

  18. Børkje, K., Nunnenkamp, A., Girvin, S.: Proposal for entangling remote micromechanical oscillators via optical measurements. Phys. Rev. Lett. 107(12), 123601 (2011)

    ADS  Google Scholar 

  19. Motazedifard, A., Dalafi, A., Naderi, M.H.: Negative cavity photon spectral function in an optomechanical system with two parametrically-driven mechanical modes. Opt. Express 31(22), 36615–36637 (2023)

    ADS  Google Scholar 

  20. Motazedifard, A., Dalafi, A., Naderi, M.H., Roknizadeh, R.: Strong quadrature squeezing and quantum amplification in a coupled Bose–Einstein condensate-optomechanical cavity based on parametric modulation. Ann. Phys. 405, 202–219 (2019)

    ADS  MathSciNet  Google Scholar 

  21. Motazedifard, A., Dalafi, A., Naderi, M.H., Roknizadeh, R.: Controllable generation of photons and phonons in a coupled Bose–Einstein condensate-optomechanical cavity via the parametric dynamical casimir effect. Ann. Phys. 396, 202–219 (2018)

    ADS  Google Scholar 

  22. Mari, A., Eisert, J.: Gently modulating optomechanical systems. Phys. Rev. Lett. 103(21), 213603 (2009)

    ADS  Google Scholar 

  23. Chen, R.-X., Shen, L.-T., Yang, Z.-B., Wu, H.-Z., Zheng, S.-B.: Enhancement of entanglement in distant mechanical vibrations via modulation in a coupled optomechanical system. Phys. Rev. A 89(2), 023843 (2014)

    ADS  Google Scholar 

  24. Mari, A., Eisert, J.: Opto-and electro-mechanical entanglement improved by modulation. New J. Phys. 14(7), 075014 (2012)

    ADS  Google Scholar 

  25. Gu, W.-J., Li, G.-X.: Squeezing of the mirror motion via periodic modulations in a dissipative optomechanical system. Opt. Express 21(17), 20423–20440 (2013)

    ADS  Google Scholar 

  26. Liao, C.-G., Xie, H., Shang, X., Chen, Z.-H., Lin, X.-M.: Enhancement of steady-state bosonic squeezing and entanglement in a dissipative optomechanical system. Opt. Express 26(11), 13783–13799 (2018)

    ADS  Google Scholar 

  27. Hu, C.-S., Yang, Z.-B., Wu, H., Li, Y., Zheng, S.-B.: Twofold mechanical squeezing in a cavity optomechanical system. Phys. Rev. A 98(2), 023807 (2018)

    ADS  Google Scholar 

  28. Zhang, Z.-C., Wang, Y.-P., Yu, Y.-F., Zhang, Z.-M.: Quantum squeezing in a modulated optomechanical system. Opt. Express 26(9), 11915–11927 (2018)

    ADS  Google Scholar 

  29. Farace, A., Giovannetti, V.: Enhancing quantum effects via periodic modulations in optomechanical systems. Phys. Rev. A 86(1), 013820 (2012)

    ADS  Google Scholar 

  30. Chakraborty, S., Sarma, A.K.: Entanglement dynamics of two coupled mechanical oscillators in modulated optomechanics. Phys. Rev. A 97(2), 022336 (2018)

    ADS  Google Scholar 

  31. Bai, C.-H., Wang, D.-Y., Zhang, S., Liu, S., Wang, H.-F.: Modulation-based atom-mirror entanglement and mechanical squeezing in an unresolved-sideband optomechanical system. Ann. Phys. 531(7), 1800271 (2019)

    MathSciNet  Google Scholar 

  32. Sangouard, N., Simon, C., De Riedmatten, H., Gisin, N.: Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83(1), 33 (2011)

    ADS  Google Scholar 

  33. El Bir, O., El Baz, M.: Mirrors-light-atoms entanglement in ring optomechanical cavity. Quantum Inf. Process. 22(9), 338 (2023)

    ADS  MathSciNet  Google Scholar 

  34. Yang, X., Zhou, Y., Xiao, M.: Generation of multipartite continuous-variable entanglement via atomic spin wave. Phys. Rev. A 85(5), 052307 (2012)

    ADS  MathSciNet  Google Scholar 

  35. Yang, X., Xiao, M.: Electromagnetically induced entanglement. Sci. Rep. 5(1), 13609 (2015)

    ADS  Google Scholar 

  36. Ma, Y.-H., Zhou, L.: Enhanced entanglement between a movable mirror and a cavity field assisted by two-level atoms. J. Appl. Phys. 111(10) (2012)

  37. Chen, Y., Chen, A.-X.: Robust mechanical entanglement in an atom-assisted hybrid optomechanical system. Quantum Inf. Process. 21(11), 370 (2022)

    ADS  MathSciNet  Google Scholar 

  38. Zhou, L., Han, Y., Jing, J., Zhang, W.: Entanglement of nanomechanical oscillators and two-mode fields induced by atomic coherence. Phys. Rev. A 83(5), 052117 (2011)

    ADS  Google Scholar 

  39. Genes, C., Vitali, D., Tombesi, P.: Emergence of atom-light-mirror entanglement inside an optical cavity. Phys. Rev. A 77(5), 050307 (2008)

    ADS  Google Scholar 

  40. Ian, H., Gong, Z., Liu, Y.-X., Sun, C., Nori, F.: Cavity optomechanical coupling assisted by an atomic gas. Phys. Rev. A 78(1), 013824 (2008)

    ADS  Google Scholar 

  41. Yang, X., Liu, J., Yan, X., Xiao, M.: Enhanced multipartite entanglement via quantum coherence with an atom-assisted optomechanical system. J. Phys. B: At. Mol. Opt. Phys. 51(20), 205501 (2018)

    ADS  Google Scholar 

  42. Genes, C., Mari, A., Vitali, D., Tombesi, P.: Quantum effects in optomechanical systems. Adv. At. Mol. Opt. Phy. 57, 33–86 (2009)

    ADS  Google Scholar 

  43. Gardiner, C., Zoller, P.: Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics. Springer

  44. Yang, X., Xiao, M.: Electromagnetically induced entanglement. Sci. Rep. 5, 13609 (2015)

    ADS  Google Scholar 

  45. Fleischhauer, M.: Correlation of high-frequency phase fluctuations in electromagnetically induced transparency. Phys. Rev. Lett. 72, 989–992 (1994)

    ADS  Google Scholar 

  46. Benguria, R., Kac, M.: Quantum Langevin equation. Phys. Rev. Lett. 46(1), 1 (1981)

    ADS  MathSciNet  Google Scholar 

  47. Yang, X., Xue, B., Zhang, J., Zhu, S.: A universal quantum information processor for scalable quantum communication and networks. Sci. Rep. 4(1), 6629 (2014)

    Google Scholar 

  48. Ludwig, M., Kubala, B., Marquardt, F.: The optomechanical instability in the quantum regime. New J. Phys. 10(9), 095013 (2008)

    ADS  Google Scholar 

  49. DeJesus, E.X., Kaufman, C.: Routh–Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations. Phys. Rev. A 35(12), 5288 (1987)

    ADS  MathSciNet  Google Scholar 

  50. Adesso, G., Serafini, A., Illuminati, F.: Extremal entanglement and mixedness in continuous variable systems. Phys. Rev. A 70(2), 022318 (2004)

    ADS  Google Scholar 

  51. Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65(3), 032314 (2002)

    ADS  Google Scholar 

  52. Ma, J., You, C., Si, L.-G., Xiong, H., Li, J., Yang, X., Wu, Y.: Formation and manipulation of optomechanical chaos via a bichromatic driving. Phys. Rev. A 90(4), 043839 (2014)

    ADS  Google Scholar 

  53. Feigenbaum, M.J.: The universal metric properties of nonlinear transformations. J. Stat. Phys. 21, 669–706 (1979)

    ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 12174243)

Author information

Authors and Affiliations

  1. Department of Physics, Shanghai University, Shanghai, 200444, China

    Jiaxin Wen, Yi Lu, Zhenghong Li & Xihua Yang

Authors
  1. Jiaxin Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhenghong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xihua Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xihua Yang.

Ethics declarations

Conflict of interest

We declared that we have no conflict of interest to this work.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wen, J., Lu, Y., Li, Z. et al. Enhancement of tripartite entanglement via periodically modulated fields with an atom-assisted optomechanical system. Quantum Inf Process 23, 107 (2024). https://doi.org/10.1007/s11128-024-04326-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-024-04326-9

Keywords

Search

Navigation