Abstract
In quantum simulations and experiments on optomechanical cavities, coherence control is a challenging issue. We propose a scheme of two coupled optomechanical cavities to enhance the intracavity entanglement. Photon hopping is employed to establish couplings between optical modes, while phonon tunneling is utilized to establish couplings between mechanical resonators. Both cavities are driven by classical light. We explore the influences of coupling strengths of the quantum correlations generated inside each cavity using two types of quantum measures: logarithmic negativity and quantum steering. This analysis will reveal the significance of these quantum metrics as well as their various aspects in the Doppler regime. We also investigate stability conditions based on coupling strengths. Therefore, it is possible to quantify the degree of intracavity entanglement. By choosing the appropriate photon and phonon hopping strengths, the generated entanglement can be enhanced. A set of parameters based on the currently available experimental data was used in the calculations.
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References
Aspelmeyer, M., Schwab, K.: . New J. Phys. 10(9), 095001 (2008)
Blencowe, M.: . Phys. Rep. 395(3), 159 (2004)
Genes, C., Mari, A., Vitali, D., Tombesi, P.: . Adv. At. Mol. Opt. Phys. 57, 33 (2009)
Aspelmeyer, M., Gröblacher, S., Hammerer, K., Kiesel, N.: . JOSA B 27(6), A189 (2010)
Clerk, A.A., Marquardt, F.: Basic theory of cavity optomechanics. (2014).https://doi.org/10.1007/978-3-642-55312-7_2
Liu, Y.C., Xiao, Y.F., Chen, Y.L., Yu, X.C., Gong, Q.: Phys. Rev. Lett. 111(8), 083601 (2013)
Yan, Y., Gu, W., Li, G.: SCIENCE CHINA Physics. Mech Astron 58(5), 1 (2015)
Yan, X.B., Deng, Z.J., Tian, X.D., Wu, J.H.: . Opt Express 27(17), 24393 (2019)
LSC, L.: The laser interferometer gravitational-wave observatory. Tech. rep. LIGO-p070082-01 (2007)
Purdy, T.P., Peterson, R.W., Regal, C.: . Science 339(6121), 801 (2013)
jae Lee, H., Namgung, W., Ahn, D.: . Phys. Lett. A 338(3-5), 192 (2005). https://doi.org/10.1016/j.physleta.2005.03.010
Bougouffa, S., Ficek, Z.: Phys. Scr. 2012(T147), 014005 (2012)
Bougouffa, S., Ficek, Z.: .. In: Conference on Coherence and Quantum Optics (Optical Society of America), pp. M6–53 (2013)
Sete, E.A., Eleuch, H., Ooi, C.H.R.: . J. Opt. Soc. Am. B 31 (11), 2821 (2014). https://doi.org/10.1364/JOSAB.31.002821
Sete, E.A., Eleuch, H.: . Phys. Rev. A 91(3), 032309 (2015)
Nielson, M.A., Chuang, I.L.: Quant. Comput. Quantum Inf. (2000)
Acín, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., Scarani, V.: . Phys. Rev. Lett. 98(23), 230501 (2007)
Giovannetti, V., Lloyd, S., Maccone, L.: . Nature photonics 5(4), 222 (2011)
Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: . Rev. Mod. Phys. 84(4), 1655 (2012)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: . Rev. Mod. Phys. 81(2), 865 (2009)
Schrödinger, E.: Math. Proc. Cambridge Philos. Soc., vol. 31 (Cambridge University Press, 1935), vol. 31, pp. 555-563 (1935)
Skrzypczyk, P., Navascués, M., Cavalcanti, D.: . Phys. Rev. Lett. 112(18), 180404 (2014)
Zhou, L., Han, Y., Jing, J., Zhang, W.: . Phys. Rev. A 83 (5), 052117 (2011)
Nunnenkamp, A., Børkje, K., Girvin, S.M.: . Phys. Rev. Lett. 107(6), 063602 (2011)
Purdy, T.: . Science 339, 801 (2013)
Bai, C.H., Wang, D.Y., Wang, H.F., Zhu, A.D., Zhang, S.: Sci. Rep. 6(1) (2016). https://doi.org/10.1038/srep33404
Bougouffa, S., Ficek, Z.: Phys. Rev. A. 93(6), 063848 (2016)
Liang, X., Guo, Q., Yuan, W.: . Int. J. Theor. Phys. 58(1), 58 (2019). https://doi.org/10.1007/s10773-018-3909-x
Ge, W., Al-Amri, M., Nha, H., Zubairy, M.S.: . Phys. Rev. A 88(5), 052301 (2013)
Ge, W., Zubairy, M.S.: . Phys. Rev. A 91(1), 013842 (2015)
Ge, W., Zubairy, M.S.: . Phys. Scr. 90(7), 074015 (2015)
Si, L.G., Xiong, H., Zubairy, M.S., Wu, Y.: . Phys. Rev. A 95(3), 033803 (2017)
Asiri, S., Liao, Z., Zubairy, M.S.: . Phys. Scr. 93(12), 124002 (2018)
Sete, E.A., Eleuch, H.: . Phys. Rev. A 85, 043824 (2012). https://doi.org/10.1103/PhysRevA.85.043824
El Qars, J., Daoud, M., Laamara, R.A.: . Eur. Phys. J. D 71 (5), 122 (2017)
Kronwald, A., Marquardt, F., Clerk, A.A.: . New J. Phys. 16 (6), 063058 (2014). https://doi.org/10.1088/1367-2630/16/6/063058
Yousif, T., Zhou, W., Zhou, L.: . J. Mod. Opt. 61(14), 1180 (2014). https://doi.org/10.1080/09500340.2014.927016
Liao, C.G., Shang, X., Xie, H., Lin, X.M.: . Opt Express 30(7), 10306 (2022)
Lin, W., Liao, C.G.: . Eur. Phys. J. Plus 136(3), 1 (2021)
Ameri, V., Eghbali-Arani, M., Rafiee, M.: 18. https://doi.org/10.1007/s11128-019-2465-5 (2019)
Qiao, G.J., Gao, H.X., Liu, H.D., Yi, X.X.: . Sci. Rep. 8 (1), 1 (2018). https://doi.org/10.1038/s41598-018-33903-z
Marchese, M.M., Belenchia, A., Pirandola, S., Paternostro, M.: . New J. Phys. 23(4), 043022 (2021)
Li, W., Li, C., Song, H.: Quant. Inf. Process. 16 (2017). https://doi.org/10.1007/s11128-017-1517-y
Paule, G.M.: Transient synchronization and quantum correlations. Springer (2018). https://doi.org/10.1007/978-3-319-93964-3_4
Jähne, K., Genes, C., Hammerer, K., Wallquist, M., Polzik, E.S., Zoller, P.: . Phys. Rev. A 79(6), 063819 (2009)
Jurcevic, P., Javadi-Abhari, A., Bishop, L.S., Lauer, I., Bogorin, D.F., Brink, M., Capelluto, L., Günlük, O., Itoko, T., Kanazawa, N., et al.: . Quantum Sci. Technol. 6(2), 025020 (2021)
Asjad, M., Tombesi, P., Vitali, D.: . Phys. Rev. A 94(5), 052312 (2016)
Plenio, M.B.: . Phys. Rev. Lett. 95(9), 090503 (2005). https://doi.org/10.1103/physrevlett.95.090503
Ludwig, M., Marquardt, F.: . Phys. Rev. Lett. 111(7), 073603 (2013)
Giovannetti, V., Vitali, D.: . Phys. Rev. A 63(2), 023812 (2001)
Rehaily, A.A., Bougouffa, S.: . Int. J. Theor. Phys. 56(5), 1399 (2017). https://doi.org/10.1007/s10773-017-3280-3
Gardiner, C.W.: . Phys. Rev. Lett. 56(18), 1917 (1986). https://doi.org/10.1103/physrevlett.56.1917
Benguria, R., Kac, M.: . Phys. Rev. Lett. 46(1), 1 (1981). https://doi.org/10.1103/physrevlett.46.1
Zhang, Q., Zhang, X., Liu, L.: Phys. Rev. A 96(4) (2017). https://doi.org/10.1103/physreva.96.042320
Gao, B., xiang Li, G., Ficek, Z.: Phys. Rev. A 94(3). https://doi.org/10.1103/physreva.94.033854 (2016)
Parkins, A.: . Phys. Rev. A 42(11), 6873 (1990)
Sun, F., Mao, D., Dai, Y., Ficek, Z., He, Q., Gong, Q.: . New J. Phys. 19(12), 123039 (2017)
Li, W., Li, C., Song, H.: . Phys. Rev. E 93(6), 062221 (2016)
Braunstein, S.L., Pati, A.K.: Quantum information with continuous variables (Springer Science & Business Media) (2012)
Li, W., Li, C., Song, H.: 48, 035503 (2015). https://doi.org/10.1088/0953-4075/48/3/035503
Genes, C., Vitali, D., Tombesi, P., Gigan, S., Aspelmeyer, M.: Phys. Rev. A 77(3). https://doi.org/10.1103/physreva.77.033804 (2008)
Vitali, D., Gigan, S., Ferreira, A., Böhm, H., Tombesi, P., Guerreiro, A., Vedral, V., Zeilinger, A., Aspelmeyer, M.: . Phys. Rev. Lett. 98(3), 030405 (2007)
Mari, A., Vitali, D.: ., vol. 78 (2008). https://doi.org/10.1103/physreva.78.062340
Du, L., Fan, C.H., Zhang, H.X., Wu, J.H.: . Scient. Rep. 7(1), 1 (2017)
Li, W., Li, C., Song, H.: . J. Phys. B: At. Mol. Opt. Phys. 48 (3), 035503 (2015)
Mari, A., Eisert, J.: . New J. Phys. 14(7), 075014 (2012)
Peres, A.: . Phys. Rev. Lett. 77(8), 1413 (1996)
Guo, Y., Li, K., Nie, W., Li, Y.: . Phys. Rev. A 90(5), 053841 (2014)
Sheng, J., Yang, C., Wu, H.: . Sci. Adv. 7(50), eabl7740 (2021)
Ockeloen-Korppi, C., Damskägg, E., Paraoanu, G.S., Massel, F., Sillanpää, M.: . Phys. Rev. Lett. 121(24), 243601 (2018)
Chille, V., Quinn, N., Peuntinger, C., Croal, C., Mišta, L., Marquardt, C. Jr., Leuchs, G., Korolkova, N.: Phys Rev A 91(5) (2015). https://doi.org/10.1103/PhysRevA.91.050301
Bougouffa, S.: . Opt. Commun. 283(14), 2989 (2010)
Plenio, M.B.: Phys. Rev. Lett. 95(9) (2005). https://doi.org/10.1103/PhysRevLett.95.090503
Vidal, G., Werner, R.F.: . Phys. Rev. A Rev. A 65(3), 032314 (2002). https://doi.org/10.1103/physreva.65.032314
Hartmann, M.J., Plenio, M.B.: . Phys. Rev. Lett. 101(20), 200503 (2008)
Bougouffa, S., Ficek, Z.: . Phys. Rev. A 102(2020), 043720 (2020). https://doi.org/10.1103/PhysRevA.102.043720
Al-Awfi, S., Al-Hmoud, M., Bougouffa, S.: . EPL (Europhysics Lett.) 123(1), 14005 (2018). https://doi.org/10.1209/0295-5075/123/14005
Kogias, I., Lee, A.R., Ragy, S., Adesso, G.: . Phys. Rev. Lett. 114(6), 060403 (2015)
Renyi, A.: .. In: Proceedings of the fourth berkeley symposium on mathematical statistics and probability, pp. 547-561 (Univ of California Press), (1961)
Wilde, M.M.: Quantum information theory (Cambridge University Press) (2013)
Adesso, G., Girolami, D., Serafini, A.: . Phys. Rev. Lett. 109 (19), 190502 (2012)
Händchen, V., Eberle, T., Steinlechner, S., Samblowski, A., Franz, T., Werner, R.F., Schnabel, R.: . Nat Photonics 6(9), 596 (2012)
Sun, L., Shi, J., Zhang, K., Gu, W., Ficek, Z., Yang, W.: . Alexandria Eng. J. 61(12), 9297 (2022)
Acknowledgements
This research was supported by the Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University, Saudi Arabia, Grant No. (20-13-12-004). We thank Z. Ficek for the valuable discussions.
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Bougouffa, S., Al-Hmoud, M. & Hakami, J.W. Probing Quantum Correlations in a Hybrid Optomechanical System. Int J Theor Phys 61, 190 (2022). https://doi.org/10.1007/s10773-022-05175-x
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DOI: https://doi.org/10.1007/s10773-022-05175-x