Skip to main content
SpringerLink
Log in

Generation of two-mode squeezing of mechanical oscillators in the multi-mode optomechanical systems

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We investigate the generation of two-mode mechanical squeezing in the multi-mode optomechanical systems with N mechanical oscillators. The cavity field is driven by an external field with time-varying amplitude. It is shown that the two-mode squeezed states of two arbitrary oscillators can be generated for an appropriate choice of the driving field. Our results show that the stronger squeezing can be achieved by increasing the driving field amplitude and enhancing the coupling between the mechanical oscillators and cavity field. In the addition, we find that the mechanical squeezed states are also affected by the number of mechanical oscillators: the more the mechanical oscillators, the larger the strength of squeezing.

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. Zhu, J.P., Li, G.X.: Ground-state cooling of a nanomechanical resonator with a triple quantum dot via quantum interference. Phys. Rev. A 86(5), 053828 (2012)

    Article  ADS  Google Scholar 

  2. Huang, S.M., Agarwal, G.S.: Enhancement of cavity cooling of a micromechanical mirror using parametric interactions. Phys. Rev. A 79(1), 013821 (2009)

    Article  ADS  Google Scholar 

  3. Gigan, S., Böhm, H.R., Paternostro, M., Blaser, F., Langer, G., Hertzberg, J.B., Schwab, K.C., Bauerle, D., Aspelmeyer, M., Zeilinger, A.: Self-cooling of a micromirror by radiation pressure. Nature 444(7115), 67 (2006)

    Article  ADS  Google Scholar 

  4. Arcizet, O., Cohadon, P.F., Briant, T., Pinard, M., Heidmann, A.: Radiation-pressure cooling and optomechanical instability of a micromirror. Nature 444(7115), 71 (2006)

    Article  ADS  Google Scholar 

  5. Aspelmeyer, M., Meystre, P., Schwab, K.: Quantum optomechanics. Phys. Today 65(7), 29 (2012)

    Article  Google Scholar 

  6. Bose, S., Jacobs, K., Knight, P.L.: Preparation of nonclassical states in cavities with a moving mirror. Phys. Rev. A 56(5), 4175 (1997)

    Article  ADS  Google Scholar 

  7. Kleckner, D., Pikovski, I., Jeffrey, E., Ament, L., Eliel, E., Brink, J.V., Bouwmeester, D.: Creating and verifying a quantum superposition in a micro-optomechanical system. New J. Phys. 10(9), 095020 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Vitali, D., Gigan, S., Ferreira, A., Böhm, H.R., 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)

    Article  ADS  Google Scholar 

  10. Hartmann, M.J., Plenio, M.B.: Steady state entanglement in the mechanical vibrations of two dielectric membranes. Phys. Rev. Lett. 101(20), 200503 (2008)

    Article  ADS  Google Scholar 

  11. Zhang, F.Y., Yan, W.B., Yang, C.P.: Generalized coupling system between a superconducting qubit and two nanomechanical resonators. Phys. Rev. A 98(4), 042331 (2018)

    Article  ADS  Google Scholar 

  12. Nunnenkamp, A., Børkje, K., Harris, J.G.E., Girvin, S.M.: Cooling and squeezing via quadratic optomechanical coupling. Phys. Rev. A 82(2), 021806 (2010)

    Article  ADS  Google Scholar 

  13. Wallquist, M., Hammerer, K., Zoller, P., Genes, C., Ludwig, M., Marquardt, F., Treutlein, P., Ye, J., Kimble, H.J.: Single-atom cavity QED and optomicromechanics. Phys. Rev. A 81(2), 023816 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Gong, Z.R., Ian, H., Liu, Y.X., Sun, C.P., Nori, F.: Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system. Phys. Rev. A 80(6), 065801 (2009)

    Article  ADS  Google Scholar 

  16. Caves, C.M., Thorne, K.S., Drever, R.W.P., Sandberg, V.D., Zimmermann, M.: On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys. 52(2), 341 (1980)

    Article  ADS  Google Scholar 

  17. Barish, B.C., Weiss, R.: LIGO and the detection of gravitational waves. Phys. Today 52(10), 44 (1999)

    Article  Google Scholar 

  18. Lloyd, S., Braunstein, S.L.: Quantum computation over continuous variables. Phys. Rev. Lett. 82(8), 1784 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  19. Braunstein, S.L., Loock, P.V.: Quantum information with continuous variables. Rev. Mod. Phys. 77(2), 513 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  20. Furusawa, A., Serensen, J.L., Braunstein, S.L., Fuchs, C.A., Kimble, H.J., Polzik, E.S.: Unconditional quantum teleportation. Science 282(5389), 706 (1998)

    Article  ADS  Google Scholar 

  21. Li, Z., Ma, S.L., Li, F.L.: Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems. Phys. Rev. A 92(2), 023856 (2015)

    Article  ADS  Google Scholar 

  22. Mann, N., Thorwart, M.: Enhancing nanomechanical squeezing by atomic interactions in a hybrid atom-optomechanical system. Phys. Rev. A 98(6), 063804 (2018)

    Article  ADS  Google Scholar 

  23. Qu, K.N., Agarwal, G.S.: Strong squeezing via phonon mediated spontaneous generation of photon pairs. New J. Phys. 16(11), 113004 (2014)

    Article  ADS  Google Scholar 

  24. Purdy, T.P., Yu, P.L., Peterson, R.W., Kampel, N.S., Regal, C.A.: Strong optomechanical squeezing of light. Phys. Rev. X 3(3), 031012 (2013)

    Google Scholar 

  25. Han, X., Wang, D.Y., Bai, C.H., Cui, W.X., Zhang, S., Wang, H.F.: Mechanical squeezing beyond resolved sideband and weak-coupling limits with frequency modulation. Phys. Rev. A 100(3), 033812 (2019)

    Article  ADS  Google Scholar 

  26. Bai, C.H., Wang, D.Y., Zhang, S., Liu, S.T., Wang, H.F.: Engineering of strong mechanical squeezing via the joint effect between duffing nonlinearity and parametric pump driving. Photon. Res. 7(11), 1229 (2019)

    Article  Google Scholar 

  27. Rojas-Rojas, S., Barriga, E., Muñoz, C., Solano, P., Hermann-Avigliano, C.: Manipulation of multimode squeezing in a coupled waveguide array. Phys. Rev. A 100(2), 023841 (2019)

    Article  ADS  Google Scholar 

  28. Zhang, R., Fang, Y.N., Wang, Y.Y., Chesi, S., Wang, Y.D.: Strong mechanical squeezing in an unresolved-sideband optomechanical system. Phys. Rev. A 99(4), 043805 (2019)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  30. Agarwal, G.: Quantum Optics. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  31. Caves, C.M., Schumaker, B.L.: New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states. Phys. Rev. A 31(5), 3068 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  32. Groblacher, S., Hammerer, K., Vanner, M.R., Aspelmeyer, M.: Observation of strong coupling between a micromechanical resonator and an optical cavity field. Nature 460(7256), 724 (2009)

    Article  ADS  Google Scholar 

  33. Gorodetsky, M.L., Schliesser, A., Anetsberger, G., Deleglise, S., Kippenberg, T.J.: Determination of the vacuum optomechanical coupling rate using frequency noise calibration. Opt. Express 18(22), 23236 (2010)

    Article  ADS  Google Scholar 

  34. Kipf, T., Agarwal, G.S.: Superradiance and collective gain in multimode optomechanics. Phys. Rev. A 90(5), 053808 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Y. Han is supported by special fund of theoretical physics under Grant Number 11547134. L. Xue is supported by special fund of theoretical physics under Grant Number 11547213. B. Chen is supported by special fund of theoretical physics under Grant Number 11847065.

Author information

Authors and Affiliations

  1. College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan, 030024, People’s Republic of China

    Yan Han, Lin Xue & Bo Chen

Authors
  1. Yan Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lin Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bo Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Han.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Han, Y., Xue, L. & Chen, B. Generation of two-mode squeezing of mechanical oscillators in the multi-mode optomechanical systems. Quantum Inf Process 19, 135 (2020). https://doi.org/10.1007/s11128-020-02631-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02631-7

Keywords

Search

Navigation