Nonclassical Properties in Optomechanical System Controlled by Single-photon Catalysis

  • Ji-Zhu Peng
  • Meng-Ran Chen
  • Bing Liu
  • Ye-Jun XuEmail author


A scheme is proposed to investigate the influence of single-photon catalysis operation on the dynamics of optomechanical system. The nonclassicalities of the catalyzed states are studied by analyzing mean photon(phonon) number, photon(phonon) number distribution, Mandel Q parameter, second-order correlation functions and Wigner function. According to the fidelity between the states before and after operation, it is found that the quantum properties of optomechanical states are significantly affected via the optimum catalysis. The optomechanical entanglement can be enhanced in the large catalysis parameter region with the small-amplitude coherent state. In particular, the Wigner function of the mechanical state can be represented by superposition of Wigner function of displaced number-like states in which the weights depend on the value of catalysis parameter. The interesting results show that tuning the catalysis parameter can manipulate efficiently the nonclassical properties of cavity mode and mechanical mode. This work might provide a new pathway to control the nonclassicalities of the optomechanical states, especially the nonclassical mechanical states.


Optomechanical system Quantum catalysis Nonclassical properties Mechanical state 



This work was supported by the National Nature Science Foundation of China (Grants No.11704051) and the Natural Science Foundation of Anhui Province of China (Grants No.1808085MA21).


  1. 1.
    Aspelmeyer, M., Kippenberg, T.J., Marquardt, F.: Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    Xiong, H., Si, L.G., Lü, X.Y., Yang, X.X., Wu, Y.: Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions. Sci. China-Phys. Mech. Astron. 58, 050302 (2015)CrossRefGoogle Scholar
  3. 3.
    Weis, S., Rivière, R., Delèglise, S., Gavartin, E., Arcizet, O., Schliesser, A., Kippenberg, T.J.: Optomechanically induced transparency. Science 330, 1520 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    Xiong, H., Wu, Y.: Fundamentals and applications of optomechanically induced transparency. Appl. Phys. Rev. 5, 031305 (2018)ADSCrossRefGoogle Scholar
  5. 5.
    Dobrindt, J.M., Wilson-Rae, I., Kippenberg, T.J.: Parametric normal-mode splitting in cavity optomechanics. Phys. Rev. Lett. 107, 063601 (2011)CrossRefGoogle Scholar
  6. 6.
    Rabl, P.: Photon blockade effect in optomechanical systems. Phys. Rev. Lett. 101, 263602 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    Zheng, L.L., Yin, T.S., Bin, Q., Lü, X.Y., Wu, Y.: Single-photon-induced phonon blockade in a hybrid spin-optomechanical system. Phys. Rev. A 99, 013804 (2019)ADSCrossRefGoogle Scholar
  8. 8.
    Bin, Q., Lü, X.Y., Bin, S.W., Wu, Y.: Two-photon blockade in a cascaded cavity-quantum-electrodynamics system. Phys. Rev. A 99, 013804 (2019)ADSCrossRefGoogle Scholar
  9. 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, 030405 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    Li, G.L., Xiao, X., Li, Y., Wang, X.G.: Tunable optical nonreciprocity and a phonon-photon router in an optomechanical system with coupled mechanical and optical modes. Phys. Rev. A 97, 023801 (2018)ADSCrossRefGoogle Scholar
  11. 11.
    Lai, D.G., Zou, F., Hou, B.P., Xiao, Y.F., Liao, J.Q.: Simultaneous cooling of coupled mechanical resonators in cavity optomechanics. Phys. Rev. A 98, 023860 (2018)ADSCrossRefGoogle Scholar
  12. 12.
    Bose, S., Jacobs, K., Knight, P.L.: Preparation of nonclassical states in cavities with a moving mirror. Phys. Rev. A 56, 4175 (1997)ADSCrossRefGoogle Scholar
  13. 13.
    Shi, H., Bhattacharya, M.: Quantum mechanical study of a generic quadratically coupled optomechanical system. Phys. Rev. A 87, 043829 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    Liao, J.Q., Tian, L.: Macroscopic quantum superposition in cavity optomechanics. Phys. Rev. Lett. 116, 163602 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    Özdemir, S.K., Miranowicz, A., Koashi, M., Imoto, N.: Quantum-scissors device for optical state truncation: a proposal for practical realization. Phys. Rev. A 64, 063818 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    Escher, B.M., Avelar, A.T., Baseia, A.B.: Synthesis of arbitrary Fock states via conditional measurement on beam splitters. Phys. Rev. A 72, 045803 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    Sanaka, K., Resch, K.J., Zeilinger, A.: Filtering out photonic Fock states. Phys. Rev. Lett. 96, 083601 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    Dakna, M., Knöll, L., Welsch, D.G.: Photon-added state preparation via conditional measurement on a beam splitter. Opt. Commun. 145, 309 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    Dakna, M., Anhut, T., Opatrný, T., Knöll, L., Welsch, D.G.: Generating schrödinger-cat-like states by means of conditional measurements on a beam splitter. Phys. Rev. A 55, 3184 (1997)ADSCrossRefGoogle Scholar
  20. 20.
    Brawley, G.A., Vanner, M.R., Larsen, P.E., Schmid, S., Boisen, A., Bowen, W.P.: Nonlinear optomechanical measurement of mechanical motion. Nat. Commun. 7, 10988 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    Akram, U., Bowen, W.P., Milburn, G.J.: Entangled mechanical cat states via conditional single photon optomechanics. New J. Phys. 15, 093007 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    Latmiral, L., Mintert, F.: Deterministic preparation of highly non-classical macroscopic quantum states. njp Quant. Info. 4, 44 (2018)ADSCrossRefGoogle Scholar
  23. 23.
    Rashid, M., Toros, M., Ulbricht, H.: Wigner function reconstruction in levitated optomechanics. Quantum Meas. Quantum Metrolog. 4, 17 (2017)Google Scholar
  24. 24.
    Huang, G.F., Deng, W.W., Tan, H.T., Cheng, G.L.: Generation of squeezed states and single-phonon states via homodyne detection and photon subtraction on the filtered output of an optomechanical cavity. Phys. Rev. A 99, 043819 (2019)ADSCrossRefGoogle Scholar
  25. 25.
    Xu, X.X., Yuan, H.C.: Generating single-photon catalyzed coherent states with quantum-optical catalysis. Phys. Lett. A 380, 2342 (2016)ADSCrossRefGoogle Scholar
  26. 26.
    Lvovsky, A.I., Mlynek, J.: Quantum-optical catalysis: generating Nonclassical states of light by means of linear optics. Phys. Rev. Lett. 88, 250401 (2002)ADSCrossRefGoogle Scholar
  27. 27.
    Li, H.M., Xu, X.X., Wang, Z., Wan, Z.L., Xu, Y.J.: Quantum-catalyzed squeezed vacuum state with single-photon measurement and its nonclassicality. Int. J. Theor. Phys. 57, 2892 (2018)zbMATHCrossRefGoogle Scholar
  28. 28.
    Xu, X.X.: Enhancing quantum entanglement and quantum teleportation for two-mode squeezed vacuum state by local quantum-optical catalysis. Phys. Rev. A 92, 012318 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    Bartley, T.J., Donati, G., Spring, J.B., Jin, X.M., Barbieri, M., Datta, A., Smith, B.J., Walmsley, I.A.: Multiphoton state engineering by heralded interference between single photons and coherent states. Phys. Rev. A 86, 043820 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    Hu, L.Y., Liao, Z.Y., Zubairy, M.S.: Continuous-variable entanglement via multiphoton catalysis. Phys. Rev. A 95, 012310 (2017)ADSCrossRefGoogle Scholar
  31. 31.
    Wang, S., Hou, L.L., Chen, X.F., Xu, X.F.: Continuous-variable quantum teleportation with non Gaussian entangled states generated via multiple-photon subtraction and addition. Phys. Rev. A 91, 063832 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    Birrittella, R.J., Baz, M.E., Gerry, C.C.: Photon catalysis and quantum state engineering. J. Opt. Soc. Am. B 35, 1514 (2018)ADSCrossRefGoogle Scholar
  33. 33.
    Zhang, S.L., Zhang, X.D.: Photon catalysis acting as noiseless linear amplification and its application. Phys. Rev. A 97, 043830 (2018)ADSCrossRefGoogle Scholar
  34. 34.
    Mancini, S., Man’ko, V.I., Tombesi, P.: Ponderomotive control of quantum macroscopic coherence. Phys. Rev. A 55, 3042 (1997)ADSCrossRefGoogle Scholar
  35. 35.
    Rai, A., Agarwal, G.S.: Quantum optical spring. Phys. Rev. A 78, 013831 (2008)ADSCrossRefGoogle Scholar
  36. 36.
    Sekatski, P., Aspelmeyer, M., Sangouard, N.: Macroscopic optomechanics from displaced single-photon entanglement. Phys. Rev. Lett. 112, 080502 (2014)ADSCrossRefGoogle Scholar
  37. 37.
    Jiang, L.Y., Guo, Q., Xu, X.X., Cai, M., Yuan, W., Duan, Z.L.: Dynamics and nonclassical properties of an opto-mechanical system prepared in four-headed cat state and number state. Opt. Commun. 369, 179 (2016)ADSCrossRefGoogle Scholar
  38. 38.
    Liang, X.Y., Guo, Q., Yuan, W.: Nonclassical properties of an opto-Mechanical system Initially prepared in N-headed cat state and number state. Int. J. Theor. Phys. 58, 58 (2019)zbMATHCrossRefGoogle Scholar
  39. 39.
    Zurek, W.H., Habib, S., Paz, J.P.: Coherent states via decoherence. Phys. Rev. Lett. 70, 1187 (1993)ADSCrossRefGoogle Scholar
  40. 40.
    Marek, P., Jeong, H., Kim, M.S.: Generating “squeezed” superpositions of coherent states using photon addition and subtraction. Phys. Rev. A 78, 063811 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    Hu, L.Y., Xu, X.X., Wang, Z.S., Xu, X.F.: Photon-subtracted squeezed thermal state: nonclassicality and decoherence. Phys. Rev. A 82, 043842 (2010)ADSCrossRefGoogle Scholar
  42. 42.
    de Oliveira, F.A.M., Kim, M.S., Knight, P.L., Buek, V.: Properties of displaced number states. Phys. Rev. A 41, 2645 (1990)ADSCrossRefGoogle Scholar
  43. 43.
    Mandel, L.: Sub-poissonian photon statistics in resonance fluorescence. Opt. Lett. 4, 205 (1979)ADSCrossRefGoogle Scholar
  44. 44.
    Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)CrossRefGoogle Scholar
  45. 45.
    Meng, X.G., Goan, H.S., Wang, J.S., Zhang, R.: Nonclassical thermal-state superpositions: analytical evolution law and decoherence behavior. Opt. Commun. 411, 15 (2018)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ji-Zhu Peng
    • 1
  • Meng-Ran Chen
    • 1
  • Bing Liu
    • 1
  • Ye-Jun Xu
    • 1
    Email author
  1. 1.Interdisciplinary Research Center of Quantum and Photoelectric InformationChizhou UniversityChizhouChina

Personalised recommendations