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Quantum statistics and blockade of phonon and photon in a dissipative quadratically coupled optomechanical system

  • Regular Article – Quantum Optics
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Abstract

There exists a tight relation between single-phonon and -photon source devices with the phonon and photon blockade implementations. These sources possess significant practical applications in quantum information processing and engineering. In this paper, we present a scheme to investigate the quantum statistics, as well as the phonon and photon blockade phenomena in an optomechanical system with quadratic coupling whose cavity has a moving membrane that is placed in the node (or antinode) of the optomechanical cavity. Strong nonlinear interaction between the optical and mechanical modes is induced by a driving field through radiation pressure. Also, the effective coupling strength can be adjusted by controlling the amplitude of an external pump field. Using the obtained effective Hamiltonian, we examine the steady state equal-time second-order correlation function via solving the Lindblad master equation which includes optical and mechanical dissipation sources. Our numerical results show that, with suitable adjustment of the system feasible parameters, we can achieve sub-Poissonian behavior, and as a result, an acceptable degree of phonon blockade. While using the same parameters, for the photon blockade, we arrive at a moderate or even weakly degree of the blockade. It should be emphasized that, as is shown, it is possible to make the scenario vice versa. By this, we mean that one can use a set of parameters by which a high (low) degree of photon (phonon) blockade is occurred. Moreover, we present a set of parameters for an optimal simultaneous occurrence of moderate phonon and photon blockade.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’s comment: The data is displayed in Table 1].

References

  1. C.J. Zhu, Y.P. Yang, G.S. Agarwal, Collective multiphoton blockade in cavity quantum electrodynamics. Phys. Rev. A 95, 063842 (2017)

    ADS  Google Scholar 

  2. M.J. Faghihi, M.K. Tavassoly, Dynamics of entropy and nonclassical properties of the state of a \(\lambda \)-type three-level atom interacting with a single-mode cavity field with intensity-dependent coupling in a Kerr medium. J. Phys. B: At. Mol. Opt. Phys. 45, 035502 (2012)

    ADS  Google Scholar 

  3. W. Lin, C.G. Liao, Enhancement of asymmetric steering via interference effects induced by twofold modulations in a cavity optomechanical system. Eur. Phys. J. Plus 136, 324 (2021)

    Google Scholar 

  4. X.Y. Lü, Y. Wu, J.R. Johansson, H. Jing, J. Zhang, F. Nori, Squeezed optomechanics with phase-matched amplification and dissipation. Phys. Rev. Lett. 114, 093602 (2015)

    ADS  Google Scholar 

  5. T.S. Yin, X.Y. Lü, L.L. Zheng, M. Wang, S. Li, Y. Wu, Nonlinear effects in modulated quantum optomechanics. Phys. Rev. A 95, 053861 (2017)

    ADS  Google Scholar 

  6. C. Weedbrook, S. Pirandola, R.G. Patrón, N.J. Cerf, T.C. Ralph, J.H. Shapiro, S. Lloyd, Gaussian quantum information. Rev. Mod. Phys. 84, 621 (2012)

    ADS  Google Scholar 

  7. M. Rafeie, M.K. Tavassoly, M. SetodehKheirabady, Macroscopic mechanical entanglement stability in two distant dissipative optomechanical systems. Ann. Phys. 534, 2100455 (2022)

    MathSciNet  Google Scholar 

  8. N. Liu, J. Li, J.Q. Liang, Entanglement in a tripartite cavity-optomechanical system. Int. J. Theor. Phys. 52, 706 (2013)

    MATH  Google Scholar 

  9. T.J. Kippenberg, K.J. Vahala, Cavity optomechanics: back-action at the mesoscale. Science 321, 1172 (2008)

    ADS  Google Scholar 

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

    Google Scholar 

  11. M. Aspelmeyer, T.J. Kippenberg, F. Marquardt, Cavity Optomechanics: Nano-and Micromechanical Resonators Interacting with Light, vol. 86 (Springer, Berlin, 2014)

    Google Scholar 

  12. Y. Yu, H.Y. Liu, Photon antibunching in unconventional photon blockade with Kerr nonlinearities. J. Mod. Opt. 64, 1342 (2017)

    ADS  Google Scholar 

  13. C. Zhai, R. Huang, H. Jing, L.M. Kuang, Mechanical switch of photon blockade and photon-induced tunneling. Opt. Express 27, 27649 (2019)

    ADS  Google Scholar 

  14. J.Y. Yang, Z. Jin, J.S. Liu, H.F. Wang, A.D. Zhu, Unconventional phonon blockade in a Tavis-cummings coupled optomechanical system. Ann. Phys. 532, 2000299 (2020)

    MathSciNet  Google Scholar 

  15. M. Wang, T.S. Yin, Z.Y. Sun, H.G. Cheng, B.F. Zhan, L.L. Zheng, Unconventional phonon blockade via atom–photon–phonon interaction in hybrid optomechanical systems. Opt. Express 30, 10251 (2022)

    ADS  Google Scholar 

  16. H. Tan, G. Li, P. Meystre, Dissipation-driven two-mode mechanical squeezed states in optomechanical systems. Phys. Rev. A 87, 033829 (2013)

    ADS  Google Scholar 

  17. U. SatyaSainadh, M. AnilKumar, Squeezing of the mechanical motion and beating 3 db limit using dispersive optomechanical interactions. J. Mod. Opt. 64, 1121 (2017)

    ADS  Google Scholar 

  18. S. Huang, A. Chen, Mechanical squeezing in a dissipative optomechanical system with two driving tones. Phys. Rev. A 103, 023501 (2021)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  20. T.A. Palomaki, J.D. Teufel, R.W. Simmonds, K.W. Lehnert, Entangling mechanical motion with microwave fields. Science 342, 710 (2013)

    ADS  Google Scholar 

  21. C.G. Liao, X. Shang, H. Xie, X.M. Lin, Dissipation-driven entanglement between two microwave fields in a four-mode hybrid cavity optomechanical system. Opt. Express 30, 10306 (2022)

    ADS  Google Scholar 

  22. J. Chan, T.P. Alegre, A.H. SafaviNaeini, J.T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, O. Painter, Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89 (2011)

    ADS  Google Scholar 

  23. F. Marquardt, J.P. Chen, A.A. Clerk, S.M. Girvin, Quantum theory of cavity-assisted sideband cooling of mechanical motion. Phys. Rev. Lett. 99, 093902 (2007)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  25. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, T.J. Kippenberg, Optomechanically induced transparency. Science 330, 1520 (2010)

    ADS  Google Scholar 

  26. A.H. SafaviNaeini, T.P. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J.T. Hill, D.E. Chang, O. Painter, Electromagnetically induced transparency and slow light with optomechanics. Nature 472, 69 (2011)

    ADS  Google Scholar 

  27. G.S. Agarwal, S. Huang, Electromagnetically induced transparency in mechanical effects of light. Phys. Rev. A 81, 041803 (2010)

    ADS  Google Scholar 

  28. T.P. Purdy, D.W.C. Brooks, T. Botter, N. Brahms, Z.Y. Ma, D.M. Stamper Kurn, Tunable cavity optomechanics with ultracold atoms. Phys. Rev. Lett. 105, 133602 (2010)

    ADS  Google Scholar 

  29. J.D. Thompson, B.M. Zwickl, A.M. Jayich, F. Marquardt, S.M. Girvin, J.G.E. Harris, Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 72 (2008)

    ADS  Google Scholar 

  30. T.S. Yin, Q. Bin, G.L. Zhu, G.R. Jin, A. Chen, Phonon blockade in a hybrid system via the second-order magnetic gradient. Phys. Rev. A 100, 063840 (2019)

    ADS  Google Scholar 

  31. L.L. Zheng, T.S. Yin, Q. Bin, X.Y. Lü, Y. Wu, Single-photon-induced phonon blockade in a hybrid spin-optomechanical system. Phys. Rev. A 99, 013804 (2019)

    ADS  Google Scholar 

  32. H. Xie, C.G. Liao, X. Shang, M.Y. Ye, X.M. Lin, Phonon blockade in a quadratically coupled optomechanical system. Phys. Rev. A 96, 013861 (2017)

    ADS  Google Scholar 

  33. M. HassaniNadiki, M.K. Tavassoly, Phonon blockade in a system consisting of two optomechanical cavities with quadratic cavity-membrane coupling and phonon hopping. Eur. Phys. J. D 76, 1 (2022)

    Google Scholar 

  34. Z.Y. Li, G.R. Jin, T.S. Yin, A. Chen, Two-phonon blockade in quadratically coupled optomechanical systems. Photonics 9, 70 (2022)

    Google Scholar 

  35. X.W. Xu, Y.J. Zhao, H. Wang, H. Jing, A. X. Chen. Nonreciprocal photon blockade via quadratic optomechanical coupling. arXiv preprint arXiv:1809.07596, 2018

  36. K. Wang, Y.P. Gao, T.T. Pang, T.J. Wang, C. Wang, Enhanced photon blockade in quadratically coupled optomechanical system. Europhys. Lett. 131, 24003 (2020)

    ADS  Google Scholar 

  37. J.Q. Liao, F. Nori, Photon blockade in quadratically coupled optomechanical systems. Phys. Rev. A 88, 023853 (2013)

    ADS  Google Scholar 

  38. P. Rabl, Photon blockade effect in optomechanical systems. Phys. Rev. Lett. 107, 063601 (2011)

    ADS  Google Scholar 

  39. A. Nunnenkamp, K. Børkje, S.M. Girvin, Single-photon optomechanics. Phys. Rev. Lett. 107, 063602 (2011)

    ADS  Google Scholar 

  40. T.S. Yin, X.Y. Lü, L.L. Wan, S.W. Bin, Y. Wu, Enhanced photon–phonon cross-Kerr nonlinearity with two-photon driving. Opt. Lett. 43, 2050 (2018)

    ADS  Google Scholar 

  41. X.W. Xu, H.Q. Shi, A.X. Chen, Yx. Liu, Cross-correlation between photons and phonons in quadratically coupled optomechanical systems. Phys. Rev. A 98, 013821 (2018)

    ADS  Google Scholar 

  42. W.J. Gu, Z. Yi, Y. Yan, L.H. Sun, Generation of optical and mechanical squeezing in the linear-and-quadratic optomechanics. Ann. Phys. 531, 1800399 (2019)

    Google Scholar 

  43. S. Sainadh, M.A. Kumar, Effects of linear and quadratic dispersive couplings on optical squeezing in an optomechanical system. Phys. Rev. A 92, 033824 (2015)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  45. L.F. Buchmann, L. Zhang, A. Chiruvelli, P. Meystre, Macroscopic tunneling of a membrane in an optomechanical double-well potential. Phys. Rev. Lett. 108, 210403 (2012)

    ADS  Google Scholar 

  46. H. Flayac, V. Savona, Unconventional photon blockade. Phys. Rev. A 96, 053810 (2017)

    ADS  Google Scholar 

  47. C. Zhao, X. Li, S. Chao, R. Peng, C. Li, L. Zhou, Simultaneous blockade of a photon, phonon, and magnon induced by a two-level atom. Phys. Rev. A 101, 063838 (2020)

    ADS  Google Scholar 

  48. A. Imamoḡlu, H. Schmidt, G. Woods, M. Deutsch, Strongly interacting photons in a nonlinear cavity. Phys. Rev. Lett. 79, 1467 (1997)

    ADS  Google Scholar 

  49. S. Hong, R. Riedinger, I. Marinković, A. Wallucks, S.G. Hofer, R.A. Norte, M. Aspelmeyer, S. Gröblacher, Hanbury brown and Twiss interferometry of single phonons from an optomechanical resonator. Science 358, 203 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  50. N. Lörch, K. Hammerer, Sub-poissonian phonon lasing in three-mode optomechanics. Phys. Rev. A 91, 061803 (2015)

    ADS  Google Scholar 

  51. K.M. Birnbaum, A. Boca, R. Miller, A.D. Boozer, T.E. Northup, H.J. Kimble, Photon blockade in an optical cavity with one trapped atom. Nature 436, 87 (2005)

    ADS  Google Scholar 

  52. C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J.M. Fink, A.A. Abdumalikov Jr., M. Baur, S. Filipp, M.P. Da Silva, A. Blais et al., Observation of resonant photon blockade at microwave frequencies using correlation function measurements. Phys. Rev. Lett. 106, 243601 (2011)

    ADS  Google Scholar 

  53. S. Buckley, K. Rivoire, J. Vučković, Engineered quantum dot single-photon sources. Rep. Prog. Phys. 75(12), 126503 (2012)

    ADS  Google Scholar 

  54. I. Söllner, L. Midolo, P. Lodahl, Deterministic single-phonon source triggered by a single photon. Phys. Rev. Lett. 116, 234301 (2016)

    ADS  Google Scholar 

  55. M. A. Nielsen, I. Chuang, Quantum computation and quantum information (In the United States of America by Cambridge University Press, New York, 2002)

  56. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    ADS  MATH  Google Scholar 

  57. M. HassaniNadiki, M.K. Tavassoly, The influence of thermal photons on the dynamics of a quantum optomechanics system with quadratic cavity-membrane couplings. Ann. Phys. 386, 275 (2017)

    ADS  Google Scholar 

  58. H. Xie, G.W. Lin, X. Chen, Z.H. Chen, X.M. Lin, Single-photon nonlinearities in a strongly driven optomechanical system with quadratic coupling. Phys. Rev. A 93, 063860 (2016)

  59. H. Xie, C.G. Liao, X. Shang, Z.H. Chen, X.M. Lin, Optically induced phonon blockade in an optomechanical system with second-order nonlinearity. Phys. Rev. A 98(2), 023819 (2018)

    ADS  Google Scholar 

  60. H. Carmichael, Statistical Methods in Quantum Optics 1 (Springer, Berlin, 1999)

    MATH  Google Scholar 

  61. D. Manzano, A short introduction to the Lindblad master equation. AIP Adv. 10, 025106 (2020)

    ADS  Google Scholar 

  62. J.R. Johansson, P.D. Nation, F. Nori, Qutip 2: a python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 184, 1234 (2013)

    ADS  Google Scholar 

  63. H. Flayac, D. Gerace, V. Savona, An all-silicon single-photon source by unconventional photon blockade. Sci. Rep. 5, 1 (2015)

    Google Scholar 

  64. D.M. Jackson, D.A. Gangloff, J.H. Bodey, L. Zaporski, C. Bachorz, E. Clarke, M. Hugues, C. Le Gall, M. Atatüre, Quantum sensing of a coherent single spin excitation in a nuclear ensemble. Nat. Phys. 17, 585 (2021)

    Google Scholar 

  65. C.J. Hood, M.S. Chapman, T.W. Lynn, H.J. Kimble, Real-time cavity qed with single atoms. Phys. Rev. Lett. 80, 4157 (1998)

    ADS  Google Scholar 

  66. S. Bose, K. Jacobs, P.L. Knight, Scheme to probe the decoherence of a macroscopic object. Phys. Rev. A 59, 3204 (1999)

    ADS  Google Scholar 

  67. S.M. Spillane, T.J. Kippenberg, K.J. Vahala, K.W. Goh, E. Wilcut, H.J. Kimble, Ultrahigh-q toroidal microresonators for cavity quantum electrodynamics. Phys. Rev. A 71, 013817 (2005)

    ADS  Google Scholar 

  68. Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, S. Noda, Strong coupling between distant photonic nanocavities and its dynamic control. Nat. Photon. 6, 56 (2012)

    ADS  Google Scholar 

  69. J. Volz, R. Gehr, G. Dubois, J. Esteve, J. Reichel, Measurement of the internal state of a single atom without energy exchange. Nature 475, 210 (2011)

    Google Scholar 

  70. J.C. Sankey, C. Yang, B.M. Zwickl, A.M. Jayich, J.G.E. Harris, Strong and tunable nonlinear optomechanical coupling in a low-loss system. Nat. Phys. 6, 707 (2010)

    Google Scholar 

  71. N.E. FlowersJacobs, S.W. Hoch, J.C. Sankey, A. Kashkanova, A.M. Jayich, C. Deutsch, J. Reichel, J.G.E. Harris, Fiber-cavity-based optomechanical device. Appl. Phys. Lett. 101, 221109 (2012)

    ADS  Google Scholar 

  72. H.K. Li, Y.C. Liu, X. Yi, C.L. Zou, X.X. Ren, Y.F. Xiao, Proposal for a near-field optomechanical system with enhanced linear and quadratic coupling. Phys. Rev. A 85, 053832 (2012)

    ADS  Google Scholar 

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  1. Laser and Optics Group, Faculty of Physics, Yazd University, Yazd, 89195-741, Iran

    M. Rafeie & M. K. Tavassoly

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Rafeie, M., Tavassoly, M.K. Quantum statistics and blockade of phonon and photon in a dissipative quadratically coupled optomechanical system. Eur. Phys. J. D 77, 63 (2023). https://doi.org/10.1140/epjd/s10053-023-00644-2

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