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Photons statistics in a hybrid electro-optomechanical system: effect of optomechanical interaction

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Abstract

In this paper, an electro-optomechanical system in which a microwave cavity and an optical one are simultaneously coupled to a mechanical oscillator, is considered. There are also two applied driving fields to the cavities and finally, dissipation effects are taken into account for this system. Using the Heisenberg–Langevin method, temporal evolution of the second order correlation functions (for optical field, mechanical oscillator and their cross correlations), are evaluated. We show that how the optomechanical coupling can affect on the correlation functions of the system. In this way we will show that the presence of optomechanical interaction in the system can lead to photon blockade effect. Moreover, we show that the presence and increasing of the optomechanical coupling lead to appearing squeezed states in the mean photon number of the optical cavity.

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References

  1. M. Aspelmeyer, T.J. Kippenberg, F. Marquardt, Cavity optomechanics. Rev. Mod. Phys. 86(4), 1391 (2014)

    ADS  Google Scholar 

  2. P. Meystre, A short walk through quantum optomechanics. Ann. Phys. 525(3), 215–233 (2013)

    MATH  Google Scholar 

  3. M. Aspelmeyer, P. Meystre, K. Schwab, Quantum optomechanics. Phys. Today 65(7), 29–35 (2012)

    Google Scholar 

  4. M. Lucamarini, D. Vitali, P. Tombesi, Scheme for a quantum-limited force measurement with an optomechanical device. Phys. Rev. A 74(6), 063816 (2006)

    ADS  Google Scholar 

  5. C. Doolin, P. Kim, B. Hauer, A. MacDonald, J. Davis, Multidimensional optomechanical cantilevers for high-frequency force sensing. New J. Phys. 16(3), 035001 (2014)

    ADS  Google Scholar 

  6. F. Liu, S. Alaie, Z.C. Leseman, M. Hossein-Zadeh, Sub-pg mass sensing and measurement with an optomechanical oscillator. Opt. Express 21(17), 19555–19567 (2013)

    ADS  Google Scholar 

  7. M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, P. Zoller, Hybrid quantum devices and quantum engineering. Phys. Scr. 2009(T137), 014001 (2009)

    Google Scholar 

  8. K. Stannigel, P. Komar, S. Habraken, S. Bennett, M.D. Lukin, P. Zoller, P. Rabl, Optomechanical quantum information processing with photons and phonons. Phys. Rev. Lett. 109(1), 013603 (2012)

    ADS  Google Scholar 

  9. T.P. Purdy, P.-L. Yu, R. Peterson, N. Kampel, C. Regal, Strong optomechanical squeezing of light. Phys. Rev. X 3(3), 031012 (2013)

    Google Scholar 

  10. J. Ali, N. Pornsuwancharoen, P. Youplao, M. Aziz, I. Amiri, K. Chaiwong, S. Chiangga, G. Singh, P. Yupapin, Coherent light squeezing states within a modified microring system. Results Phys. 9, 211–214 (2018)

    ADS  Google Scholar 

  11. R. Schnabel, Squeezed states of light and their applications in laser interferometers. Phys. Rep. 684, 1–51 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  12. A.H. Safavi-Naeini, T.M. 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(7341), 69 (2011)

    ADS  Google Scholar 

  13. G. Agarwal, S. Huang, Electromagnetically induced transparency in mechanical effects of light. Phys. Rev. A 81(4), 041803 (2010)

    ADS  Google Scholar 

  14. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, T.J. Kippenberg, Optomechanically induced transparency. Science 330(6010), 1520–1523 (2010)

    ADS  Google Scholar 

  15. Z.-Q. Yin, W. Yang, L. Sun, L. Duan, Quantum network of superconducting qubits through an optomechanical interface. Phys. Rev. A 91(1), 012333 (2015)

    ADS  Google Scholar 

  16. M.A. Sillanpää, P.J. Hakonen, Optomechanics: Hardware for a quantum network. Nature 507(7490), 45 (2014)

    ADS  Google Scholar 

  17. Z.-L. Xiang, S. Ashhab, J. You, F. Nori, Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems. Rev. Mod. Phys. 85(2), 623 (2013)

    ADS  Google Scholar 

  18. M. Winger, T. Blasius, T.M. Alegre, A.H. Safavi-Naeini, S. Meenehan, J. Cohen, S. Stobbe, O. Painter, A chip-scale integrated cavity-electro-optomechanics platform. Opt. Express 19(25), 24905–24921 (2011)

    ADS  Google Scholar 

  19. M. Tsang, Cavity quantum electro-optics. ii. input-output relations between traveling optical and microwave fields, Phys. Rev. A 84 (4), 043845 (2011)

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

    ADS  Google Scholar 

  21. S. Barzanjeh, S. Guha, C. Weedbrook, D. Vitali, J.H. Shapiro, S. Pirandola, Microwave quantum illumination. Phys. Rev. Lett. 114(8), 080503 (2015)

    ADS  Google Scholar 

  22. J. Bochmann, A. Vainsencher, D.D. Awschalom, A.N. Cleland, Nanomechanical coupling between microwave and optical photons. Nat. Phys. 9(11), 712 (2013)

    Google Scholar 

  23. R.W. Andrews, R.W. Peterson, T.P. Purdy, K. Cicak, R.W. Simmonds, C.A. Regal, K.W. Lehnert, Bidirectional and efficient conversion between microwave and optical light. Nat. Phys. 10(4), 321 (2014)

    Google Scholar 

  24. T. Palomaki, J. Teufel, R. Simmonds, K. Lehnert, Entangling mechanical motion with microwave fields. Science 342(6159), 710–713 (2013)

    ADS  Google Scholar 

  25. Y.-D. Wang, A.A. Clerk, Reservoir-engineered entanglement in optomechanical systems. Phys. Rev. Lett. 110(25), 253601 (2013)

    ADS  Google Scholar 

  26. K. Qu, G. Agarwal, Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems. Phys. Rev. A 87(3), 031802 (2013)

    ADS  Google Scholar 

  27. M.J. Salehi, H.R. Baghshahi, S.Y. Mirafzali, Quantum correlation and squeezing dynamics of a dissipative nonlinear optomechanical oscillator: Heisenberg-langevin approach. Eur. Phys. J. Plus 133(11), 471 (2018)

    Google Scholar 

  28. S.K. Singh, S. Muniandy, Temporal dynamics and nonclassical photon statistics of quadratically coupled optomechanical systems. Int. J. Theor. Phys. 55(1), 287–301 (2016)

    MATH  Google Scholar 

  29. S. Singh, C.R. Ooi, Quantum correlations of quadratic optomechanical oscillator. J. Opt. Soc. Am. B 31(10), 2390–2398 (2014)

    ADS  Google Scholar 

  30. M.O. Scully, M.S. Zubairy, Quantum Optics (Cambridge University Press, 1997)

  31. M. Fox, Quantum optics: an introduction, Vol. 15, OUP Oxford (2006)

  32. A. Imamolu, H. Schmidt, G. Woods, M. Deutsch, Strongly interacting photons in a nonlinear cavity. Phys. Rev. Lett. 79(8), 1467 (1997)

    ADS  Google Scholar 

  33. A.J. Hoffman, S.J. Srinivasan, S. Schmidt, L. Spietz, J. Aumentado, H.E. Türeci, A.A. Houck, Dispersive photon blockade in a superconducting circuit. Phys. Rev. Lett. 107(5), 053602 (2011)

    ADS  Google Scholar 

  34. 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(7047), 87 (2005)

    ADS  Google Scholar 

  35. M.A. Nielsen, I.L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2000)

    MATH  Google Scholar 

  36. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Quantum cryptography. Rev. Mod. Phys. 74(1), 145 (2002)

    ADS  MATH  Google Scholar 

  37. X.-B. Wang, T. Hiroshima, A. Tomita, M. Hayashi, Quantum information with gaussian states. Phys. Rep. 448(1–4), 1–111 (2007)

    ADS  MathSciNet  Google Scholar 

  38. X.-W. Xu, Y.-J. Li, Y.-X. Liu, Photon-induced tunneling in optomechanical systems. Phys. Rev. A 87(2), 025803 (2013)

    ADS  Google Scholar 

  39. P. Komar, S. Bennett, K. Stannigel, S. Habraken, P. Rabl, P. Zoller, M.D. Lukin, Single-photon nonlinearities in two-mode optomechanics. Phys. Rev. A 87(1), 013839 (2013)

    ADS  Google Scholar 

  40. A. Miranowicz, J. Bajer, N. Lambert, Y.-X. Liu, F. Nori, Tunable multiphonon blockade in coupled nanomechanical resonators. Phys. Rev. A 93(1), 013808 (2016)

    ADS  Google Scholar 

  41. Ö. Soykal, C. Tahan, Toward engineered quantum many-body phonon systems. Phys. Rev. B 88(13), 134511 (2013)

    ADS  Google Scholar 

  42. A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P.W. Pinkse, K. Murr, G. Rempe, Two-photon gateway in one-atom cavity quantum electrodynamics. Phys. Rev. Lett. 101(20), 203602 (2008)

    ADS  Google Scholar 

  43. A. Reinhard, T. Volz, M. Winger, A. Badolato, K.J. Hennessy, E.L. Hu, A. Imamoğlu, Strongly correlated photons on a chip. Nat. Photonics 6(2), 93 (2012)

    ADS  Google Scholar 

  44. A. Rundquist, M. Bajcsy, A. Majumdar, T. Sarmiento, K. Fischer, K.G. Lagoudakis, S. Buckley, A.Y. Piggott, J. Vučković, Nonclassical higher-order photon correlations with a quantum dot strongly coupled to a photonic-crystal nanocavity. Phys. Rev. A 90(2), 023846 (2014)

    ADS  Google Scholar 

  45. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, J. Vučković, Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade. Nat. Phys. 4(11), 859 (2008)

    Google Scholar 

  46. X.-W. Xu, H.-Q. Shi, A.-X. Chen, Y.-X. Liu, Cross-correlation between photons and phonons in quadratically coupled optomechanical systems. Phys. Rev. A 98(1), 013821 (2018)

    ADS  Google Scholar 

  47. M. Abdi, P. Tombesi, D. Vitali, Entangling two distant non-interacting microwave modes. Ann. Phys. 527(1–2), 139–146 (2015)

    MathSciNet  MATH  Google Scholar 

  48. D. Vitali, P. Tombesi, M. Woolley, A. Doherty, G. Milburn, Entangling a nanomechanical resonator and a superconducting microwave cavity. Phys. Rev. A 76(4), 042336 (2007)

    ADS  Google Scholar 

  49. R.H. Brown, R.Q. Twiss et al., Correlation between photons in two coherent beams of light. Nature 177(4497), 27–29 (1956)

    ADS  Google Scholar 

  50. D.F. Walls, Squeezed states of light, nature 306 (5939), 141 (1983)

    ADS  Google Scholar 

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Authors and Affiliations

  1. Malek Ashtar University of Technology, Tehran, Iran

    A. Asrar

  2. Department of Physics, Faculty of Science, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

    M. J. Salehi & A. Asghari Nejad

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  1. A. Asrar
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  3. A. Asghari Nejad
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Correspondence to A. Asrar.

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Asrar, A., Salehi, M.J. & Nejad, A.A. Photons statistics in a hybrid electro-optomechanical system: effect of optomechanical interaction. Eur. Phys. J. Plus 135, 278 (2020). https://doi.org/10.1140/epjp/s13360-019-00001-6

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