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Bipartite Entanglement in Optomechanical Cavities Driven by Squeezed Light

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Abstract

We investigate the stationary bipartite entanglement in a useful hybrid optomechanical system, which is constituted of two coupled-cavity optomechanics through a photon hopping process and both are driven by squeezed light. The transfer of correlations from an entangled light source to optomechanical cavities is explored. It is found that the generation of bipartite entanglement and entanglement transfer depend strongly on photon hopping strength and the matching of the input squeezed modes to the cavity modes. It is revealed that the generated stationary bipartite entanglement due to squeezed light that drives the cavities is robust against the thermal fluctuations. The fidelity of a coherent state of the optical modes is explored and it is shown that it offered interesting conditions on the stability of the system, which are the same for entanglement generation.

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References

  1. Aspelmeyer, M., Schwab, K.: Focus on mechanical systems at the quantum limit. New, J. Phys. 10(9), 095001 (2008)

    Article  ADS  Google Scholar 

  2. Blencowe, M.: Quantum electromechanical systems. Phys. Rep. 395(3), 159 (2004)

    Article  ADS  Google Scholar 

  3. Genes, C., Mari, A., Vitali, D., Tombesi, P.: Quantum effects in optomechanical systems. Adv. At. Mol. Opt. Phys. 57, 33 (2009)

    Article  ADS  Google Scholar 

  4. Aspelmeyer, M., Gröblacher, S., Hammerer, K., Kiesel N.: Quantum optomechanics–throwing a glance. JOSA B 27(6), A189 (2010)

    Article  ADS  Google Scholar 

  5. Clerk, A.A., Marquardt, F.: Basic theory of cavity optomechanics. https://doi.org/10.1007/978-3-642-55312-7_2 (2014)

  6. Vitali, D., Gigan, S., Ferreira, A., Böhm, H., 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 

  7. LSC, L.: The laser interferometer gravitational-wave observatory. Tech. rep., LIGO-P070082-01 (2007)

  8. Oo, T., Dong, C., Fiore, V., Wang, H.: Evanescently coupled optomechanical system with sin nanomechanical oscillator and deformed silica microsphere. Appl. Phys. Lett. 103(3), 031116 (2013)

    Article  ADS  Google Scholar 

  9. Liu, Y.C., Xiao, Y.F., Chen, Y.L., Yu, X.C., Gong, Q.: Parametric down-conversion and polariton pair generation in optomechanical systems. Phys. Rev. Lett. 111(8), 083601 (2013)

    Article  ADS  Google Scholar 

  10. Yan, Y., Gu, W., Li, G.: Entanglement transfer from two-mode squeezed vacuum light to spatially separated mechanical oscillators via dissipative optomechanical coupling. Sci. China Phys. Mech. Astron. 58(5), 1 (2015)

    Article  Google Scholar 

  11. Yan, X.B., Deng, Z.J., Tian, X.D., Wu, J.H.: Entanglement optimization of filtered output fields in cavity optomechanics. Opt. Express 27(17), 24393 (2019)

    Article  ADS  Google Scholar 

  12. Braunstein, S.L., Kimble, H.J.: Teleportation of continuous quantum variables. Phys. Rev. Lett. 80(4), 869 (1998). https://doi.org/10.1103/physrevlett.80.869

    Article  ADS  Google Scholar 

  13. Vedral, V.: Entanglement, computation and quantum measurements. https://doi.org/10.1093/acprof:oso/9780199215706.003.00012 (2006)

  14. Sun, F., Mao, D., Dai, Y., Ficek, Z., He, Q., Gong, Q.: Phase control of entanglement and quantum steering in a three-mode optomechanical system. New, J. Phys. 19(12), 123039 (2017)

    Article  ADS  Google Scholar 

  15. Adesso, G., Serafini, A., Illuminati, F.: Quantification and scaling of multipartite entanglement in continuous variable systems. Phys. Rev. Lett. 93, 22 (2004). https://doi.org/10.1103/physrevlett.93.220504

    Article  Google Scholar 

  16. Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65(3), 032314 (2002). https://doi.org/10.1103/physreva.65.032314

    Article  ADS  Google Scholar 

  17. Lee, H.J., Namgung, W., Ahn, D.: Entanglement generates entanglement: entanglement transfer by interaction. Phys. Lett. A 338(3-5), 192 (2005). https://doi.org/10.1016/j.physleta.2005.03.010

    Article  ADS  MATH  Google Scholar 

  18. Bougouffa, S., Ficek, Z.: Entanglement transfer between bipartite systems. Phys. Scr. 2012(t147)(t147), 014005 (2012)

    Article  Google Scholar 

  19. Bougouffa, S., Ficek, Z.: .. In: Conference on Coherence and Quantum Optics, pp M6–53. Optical Society of America (2013)

  20. Sete, E.A., Eleuch, H., Ooi, C.H.R.: Light-to-matter entanglement transfer in optomechanics. J. Opt. Soc. Am. B 31(11), 2821 (2014). https://doi.org/10.1364/JOSAB.31.002821

    Article  ADS  Google Scholar 

  21. Sete, E.A., Eleuch, H.: High-efficiency quantum state transfer and quantum memory using a mechanical oscillator. Phys. Rev. A 91(3), 032309 (2015)

    Article  ADS  Google Scholar 

  22. Zhou, L., Han, Y., Jing, J., Zhang, W.: Entanglement of nanomechanical oscillators and two-mode fields induced by atomic coherence. Phys. Rev. A 83(5), 052117 (2011)

    Article  ADS  Google Scholar 

  23. Nunnenkamp, A., Børkje, K., Girvin, S.M.: Single-photon optomechanics. Phys. Rev. Lett. 107(6), 063602 (2011)

    Article  ADS  Google Scholar 

  24. Purdy, T.P., Peterson, R.W., Regal, C.A.: Observation of radiation pressure shot noise on a macroscopic object. Science 339(6121), 801–804 (2013)

    Article  ADS  Google Scholar 

  25. Bai, C.H., Wang, D.Y., Wang, H.F., Zhu, A.D., Zhang, S.: Robust entanglement between a movable mirror and atomic ensemble and entanglement transfer in coupled optomechanical system. Sci. Rep. 6(1). https://doi.org/10.1038/srep33404(2016)

  26. Bougouffa, S., Ficek, Z.: Evidence of indistinguishability and entanglement determined by the energy-time uncertainty principle in a system of two strongly coupled bosonic modes. Phys. Rev. A 93(6), 063848 (2016)

    Article  ADS  Google Scholar 

  27. Liang, X., 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(1), 58 (2019). https://doi.org/10.1007/s10773-018-3909-x

    Article  MATH  Google Scholar 

  28. Ge, W., Al-Amri, M., Nha, H., Zubairy, M.S.: Entanglement of movable mirrors in a correlated emission laser via cascade-driven coherence. Phys. Rev. A 88 (5), 052301 (2013)

    Article  ADS  Google Scholar 

  29. Ge, W., Zubairy, M.S.: Macroscopic optomechanical superposition via periodic qubit flipping. Phys. Rev. A 91(1), 013842 (2015)

    Article  ADS  Google Scholar 

  30. Ge, W., Zubairy, M.S.: Entanglement of two movable mirrors with a single photon superposition state. Phys. Scr. 90(7), 074015 (2015)

    Article  ADS  Google Scholar 

  31. Si, L.G., Xiong, H., Zubairy, M.S., Wu, Y.: Optomechanically induced opacity and amplification in a quadratically coupled optomechanical system. Phys. Rev. A 95(3), 033803 (2017)

    Article  ADS  Google Scholar 

  32. Asiri, S., Liao, Z., Zubairy, M.S.: Reconstruction of quantum state of mechanical mirror via polariton-phonon coupling. Phys. Scr. 93(12), 124002 (2018)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. Genes, C., Mari, A., Tombesi, P., Vitali, D.: Robust entanglement of a micromechanical resonator with output optical fields. Phys. Rev. A 78(3). https://doi.org/10.1103/physreva.78.032316 (2008)

  35. Liao, J.Q., Wu, Q.Q., Nori, F.: Entangling two macroscopic mechanical mirrors in a two-cavity optomechanical system. Phys. Rev. A 89(1), 014302 (2014)

    Article  ADS  Google Scholar 

  36. Barzanjeh, S., Vitali, D., Tombesi, P., Milburn, G.J.: Entangling optical and microwave cavity modes by means of a nanomechanical resonator. Phys. Rev. A 84(4), 042342 (2011). https://doi.org/10.1103/physreva.84.042342

    Article  ADS  Google Scholar 

  37. Barzanjeh, S., Redchenko, E., Peruzzo, M., Wulf, M., Lewis, D., Fink, J.: Stationary entangled radiation from micromechanical motion. arXiv:1809.05865 (2018)

  38. 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 

  39. Huang, S., Agarwal, G.: Entangling nanomechanical oscillators in a ring cavity by feeding squeezed light. New, J. Phys. 11(10), 103044 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  41. Frisk Kockum, A., Miranowicz, A., De Liberato, S., Savasta, S., Nori, F.: Ultrastrong coupling between light and matter. Nat. Rev. Phys. 1(1), 19 (2019). 10.1038/s42254-018-0006-2

    Article  Google Scholar 

  42. Riedinger, R., Wallucks, A., Marinković, I., Löschnauer, C., Aspelmeyer, M., Hong, S., Gröblacher, S.: Remote quantum entanglement between two micromechanical oscillators. Nature 556(7702), 473 (2018)

    Article  ADS  Google Scholar 

  43. Hofer, S.G., Wieczorek, W., Aspelmeyer, M., Hammerer, K.: Quantum entanglement and teleportation in pulsed cavity optomechanics. Phys. Rev. A 84(5), 052327 (2011)

    Article  ADS  Google Scholar 

  44. Pirandola, S., Mancini, S., Vitali, D., Tombesi, P.: Continuous-variable entanglement and quantum-state teleportation between optical and macroscopic vibrational modes through radiation pressure. Phys. Rev. A 68(6), 062317 (2003)

    Article  ADS  Google Scholar 

  45. Mancini, S., Vitali, D., Tombesi, P.: Scheme for teleportation of quantum states onto a mechanical resonator. Phys. Rev. Lett. 90(13), 137901 (2003)

    Article  ADS  Google Scholar 

  46. Asjad, M., Tombesi, P., Vitali, D.: Feedback control of two-mode output entanglement and steering in cavity optomechanics. Phys. Rev. A 94(5), 052312 (2016)

    Article  ADS  Google Scholar 

  47. Sete, E.A., Eleuch, H.: Controllable nonlinear effects in an optomechanical resonator containing a quantum well. Phys. Rev. A 85, 043824 (2012). https://doi.org/10.1103/PhysRevA.85.043824

    Article  ADS  Google Scholar 

  48. El Qars, J., Daoud, M., Laamara, R.A.: Dynamical gaussian quantum steering in optomechanics. Eur. Phys. J. D 71(5), 122 (2017)

    Article  ADS  Google Scholar 

  49. Kronwald, A., Marquardt, F., Clerk, A.A.: Dissipative optomechanical squeezing of light. New, J. Phys. 6(6), 063058 (2014). https://doi.org/10.1088/1367-2630/16/6/063058

    Article  Google Scholar 

  50. Yousif, T., Zhou, W., Zhou, L.: State transfer and entanglement of two mechanical oscillators in coupled cavity optomechanical system. J. Mod. Opt. 61(14), 1180 (2014). https://doi.org/10.1080/09500340.2014.927016

    Article  ADS  Google Scholar 

  51. Guo, Y., Li, K., Nie, W., Li, Y.: Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system. Phys. Rev. A 90(5), 053841 (2014)

    Article  ADS  Google Scholar 

  52. Liao, J.Q., Law, C., Kuang, L.M., Nori, F.: Enhancement of mechanical effects of single photons in modulated two-mode optomechanics. Phys. Rev. A 92(1), 013822 (2015)

    Article  ADS  Google Scholar 

  53. Clerk, A., Marquardt, F., Jacobs, K.: Back-action evasion and squeezing of a mechanical resonator using a cavity detector. New, J. Phys. 10(9), 095010 (2008)

    Article  ADS  Google Scholar 

  54. Tanas, R.: Squeezing and squeezing-like terms in the master equation for a two-level atom in strong fields. J. Opt. B: Quantum Semiclassical Opt. 4(3), S142 (2002)

    Article  ADS  Google Scholar 

  55. Messikh, A., Wahiddin, M., Pah, C., Ficek, Z.: The effect of finite bandwidth squeezed light on entanglement creation in the Dicke model. J. Opt. B: Quantum Semiclassical Opt. 6(7), 289 (2004)

    Article  ADS  Google Scholar 

  56. Gao, B., xiang Li, G., Ficek, Z.: Engineering a squeezed phonon reservoir with a bichromatic driving of a quantum dot. Phys. Rev. A 94(3). https://doi.org/10.1103/physreva.94.033854 (2016)

  57. Gardiner, C.: Inhibition of atomic phase decays by squeezed light: a direct effect of squeezing. Phys. Rev. Lett. 56(18), 1917 (1986)

    Article  ADS  Google Scholar 

  58. Carmichael, H., Lane, A., Walls, D.: Resonance fluorescence from an atom in a squeezed vacuum. Phys. Rev. Lett. 58(24), 2539 (1987)

    Article  ADS  Google Scholar 

  59. Carmichael, H., Lane, A., Walls, D.: Resonance fluorescence in a squeezed vacuum. J. Mod. Opt. 34(6–7), 821 (1987)

    Article  ADS  Google Scholar 

  60. Parkins, A.: Resonance fluorescence of a two-level atom in a two-mode squeezed vacuum. Phys. Rev. A 42(11), 6873 (1990)

    Article  ADS  Google Scholar 

  61. Dalton, B., Ficek, Z., Swain, S.: Atoms in squeezed light fields. J. Mod. Opt. 46(3), 379 (1999)

    Article  ADS  Google Scholar 

  62. Giovannetti, V., Vitali, D.: Phase-noise measurement in a cavity with a movable mirror undergoing quantum brownian motion. Phys. Rev. A 63(2), 023812 (2001)

    Article  ADS  Google Scholar 

  63. Rehaily, A.A., Bougouffa, S.: Entanglement generation between two mechanical resonators in two optomechanical cavities. Int. J. Theor. Phys. 56(5), 1399 (2017). https://doi.org/10.1007/s10773-017-3280-3

    Article  MathSciNet  MATH  Google Scholar 

  64. Gardiner, C.W.: Inhibition of atomic phase decays by squeezed light: a direct effect of squeezing. Phys. Rev. Lett. 56(18), 1917 (1986). https://doi.org/10.1103/physrevlett.56.1917

    Article  ADS  Google Scholar 

  65. Benguria, R., Kac, M.: Quantum langevin equation. Phys. Rev. Lett. 46(1), 1 (1981). https://doi.org/10.1103/physrevlett.46.1

    Article  ADS  MathSciNet  Google Scholar 

  66. Zhang, Q., Zhang, X., Liu, L.: Transfer and preservation of entanglement in a hybrid optomechanical system. Phys. Rev. A 96(4). https://doi.org/10.1103/physreva.96.042320 (2017)

  67. Braunstein, S.L., Pati, A.K.: Quantum Information with Continuous Variables. Springer Science & Business Media, Berlin (2012)

    MATH  Google Scholar 

  68. Aloufi, K., Bougouffa, S., Ficek, Z.: Dynamics of entangled states in a correlated reservoir. Phys. Scr. 90(7), 074020 (2015)

    Article  ADS  Google Scholar 

  69. Bougouffa, S., Ficek, Z.: Atoms versus photons as carriers of quantum states. Phys. Rev. A 88(2), 022317 (2013)

    Article  ADS  Google Scholar 

  70. Plenio, M.B.: Logarithmic negativity: a full entanglement monotone that is not convex. Phys. Rev, Lett. 95(9), 090503 (2005). https://doi.org/10.1103/physrevlett.95.090503

    Article  ADS  Google Scholar 

  71. Adesso, G., Serafini, A., Illuminati, F.: Extremal entanglement and mixedness in continuous variable systems. Phys. Rev. A 70(2), 022318 (2004). https://doi.org/10.1103/physreva.70.022318

    Article  ADS  Google Scholar 

  72. Sete, E.A., Eleuch, H., Das, S.: Semiconductor cavity qed with squeezed light: nonlinear regime. Phys. Rev. A 84, 053817 (2011). https://doi.org/10.1103/PhysRevA.84.053817

    Article  ADS  Google Scholar 

  73. Ludwig, M., Hammerer, K., Marquardt, F.: Entanglement of mechanical oscillators coupled to a nonequilibrium environment. Phys. Rev A 82(1) (2010)

  74. Sete, E.A., Eleuch, H.: Anomalous optical bistability and robust entanglement of mechanical oscillators using two-photon coherence. J. Opt, Soci. Am. B 32(5), 971 (2015). https://doi.org/10.1364/josab.32.000971

    Article  ADS  Google Scholar 

  75. Sete, E.A., Eleuch, H.: High-efficiency quantum state transfer and quantum memory using a mechanical oscillator. Phys. Rev. A 91(3). https://doi.org/10.1103/physreva.91.032309 (2015)

  76. Gröblacher, 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). https://doi.org/10.1038/nature08171

    Article  ADS  Google Scholar 

  77. Schliesser, A., Arcizet, O., Rivière, R., Anetsberger, G., Kippenberg, T.J.: Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit. Nat. Phys. 5(7), 509 (2009). https://doi.org/10.1038/nphys1304

    Article  Google Scholar 

  78. Fainstein, A., Lanzillotti-Kimura, N.D., Jusserand, B., Perrin, B.: Strong optical-mechanical coupling in a vertical gaas/alas microcavity for subterahertz phonons and near-infrared light. Phys. Rev. Lett. 110(3). https://doi.org/10.1103/physrevlett.110.037403 (2013)

  79. Kleckner, D., Marshall, W., de Dood, M.J.A., Dinyari, K.N., Pors, B.J., Irvine, W.T.M., Bouwmeester, D.: High finesse opto-mechanical cavity with a movable thirty-micron-size mirror. Phys. Rev. Lett. 96(17). https://doi.org/10.1103/physrevlett.96.173901 (2006)

  80. Gigan, S., Böhm, H. R., Paternostro, M., Blaser, F., Langer, G., Hertzberg, J.B., Schwab, K.C., Bäuerle, D., Aspelmeyer, M., Zeilinger, A.: Self-cooling of a micromirror by radiation pressure. Nature 444(7115), 67 (2006). https://doi.org/10.1038/nature05273

    Article  ADS  Google Scholar 

  81. Gröblacher, S., Gigan, S., Böhm, H. R., Zeilinger, A., Aspelmeyer, M.: Radiation-pressure self-cooling of a micromirror in a cryogenic environment. EPL (Europhys Lett) 81(5), 54003 (2008). https://doi.org/10.1209/0295-5075/81/54003

    Article  ADS  Google Scholar 

  82. Heidmann, A., Arcizet, O., Molinelli, C., Briant, T., Cohadon, P.F.: Radiation-pressure effects upon a micromirror in a high-finesse optical cavity. https://doi.org/10.1117/12.763214 (2008)

  83. 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). https://doi.org/10.1038/nature05244

    Article  ADS  Google Scholar 

  84. Arcizet, O., Schliesser, A, Kippenberg, T.: Controlling light propagation via radiation pressure optomechanical coupling. https://doi.org/10.1364/iqec.2009.iwe2(2009)

  85. Han, K., Kim, J., Bahl, G.: Radiation-driven optomechanical pressure sensor. https://doi.org/10.1364/fio.2013.ftu4c.3 (2013)

  86. Ockeloen-Korppi, C., Damskägg, E., Paraoanu, G.S., Massel, F., Sillanpää, M.: Revealing hidden quantum correlations in an electromechanical measurement. Phys. Rev. Lett. 121(24), 243601 (2018)

    Article  ADS  Google Scholar 

  87. Pirkkalainen, J.M., Cho, S., Li, J., Paraoanu, G., Hakonen, P., Sillanpää, M.: Hybrid circuit cavity quantum electrodynamics with a micromechanical resonator. Nature 494(7436), 211 (2013)

    Article  ADS  Google Scholar 

  88. Kuzyk, M.C., Wang, H.: Generating robust optical entanglement via optomechanical coupling. https://doi.org/10.1364/cleo_qels.2013.qm3c.6 (2013)

  89. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series and Poducts. Academic Press, New York (2014)

    Google Scholar 

  90. Dorsel, A., McCullen, J.D., Meystre, P., Vignes, E., Walther, H.: Optical bistability and mirror confinement induced by radiation pressure. Phys. Rev. Lett. 51 (17), 1550 (1983)

    Article  ADS  Google Scholar 

  91. Gozzini, A., Maccarrone, F., Mango, F., Longo, I., Barbarino, S.: Light-pressure bistability at microwave frequencies. JOSA B 2(11), 1841 (1985)

    Article  ADS  Google Scholar 

  92. Marquardt, F., Harris, J., Girvin, S.M.: Dynamical multistability induced by radiation pressure in high-finesse micromechanical optical cavities. Phys. Rev. Lett. 96(10), 103901 (2006)

    Article  ADS  Google Scholar 

  93. Jähne, K., Genes, C., Hammerer, K., Wallquist, M., Polzik, E.S., Zoller, P.: Cavity-assisted squeezing of a mechanical oscillator. Phys. Rev. A 79(6), 063819 (2009)

    Article  ADS  Google Scholar 

  94. Milburn, G., Braunstein, S.L.: Quantum teleportation with squeezed vacuum states. Phys. Rev. A 60(2), 937 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  95. Hou, P.Y., Huang, Y.Y., Yuan, X.X., Chang, X.Y., Zu, C., He, L., Duan, L.M.: Quantum teleportation from light beams to vibrational states of a macroscopic diamond. Nat. Commun. 7, 11736 (2016)

    Article  ADS  Google Scholar 

  96. Rueda, A., Hease, W., Barzanjeh, S., Fink, J.M.: Electro-optic entanglement source for microwave to telecom quantum state transfer. npj Quantum Inf. 5(1), 1 (2019)

    Article  Google Scholar 

  97. Barbosa, F.A.S., de Faria, A.J., Coelho, A.S., Cassemiro, K.N., Villar, A.S., Nussenzveig, P., Martinelli, M.: Disentanglement in bipartite continuous-variable systems. Phys. Rev. A 84(5), 052330 (2011). https://doi.org/10.1103/physreva.84.052330

    Article  ADS  Google Scholar 

  98. Barzanjeh, S., Abdi, M., Milburn, G.J., Tombesi, P., Vitali, D.: Reversible optical-to-microwave quantum interface. Phys. Rev. Lett. 109(13), 130503 (2012). https://doi.org/10.1103/physrevlett.109.130503

    Article  ADS  Google Scholar 

  99. Mari, A., Vitali, D.: Optimal fidelity of teleportation of coherent states and entanglement. Phys. Rev. A 78(6), 062340 (2008). https://doi.org/10.1103/physreva.78.062340

    Article  ADS  Google Scholar 

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Acknowledgements

The researchers acknowledge the deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi Arabia, for financing this project under grant no. (381213)

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Bougouffa, S., Al-Hmoud, M. Bipartite Entanglement in Optomechanical Cavities Driven by Squeezed Light. Int J Theor Phys 59, 1699–1716 (2020). https://doi.org/10.1007/s10773-020-04437-w

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