Photon-phonon squeezing and entanglement in a cavity optomechanical system with a flying atom

Abstract

We study the quadrature squeezing and entanglement in a cavity optomechanical system (COMS). In our model, a flying atom sequentially passes through and interacts with the COMS and a Ramsey pulse zone, and subsequently the atomic state is detected. In this way, the photon-phonon squeezing and entanglement can be generated. The dynamic evolution of the squeezing and entanglement in the presence of losses are examined by using the master equation method.

Keywords

optomechanics / squeezing / entanglement

References

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

[2] T. J. Kippenberg and K. J. Vahala, Cavity optomechanics: Back-action at the mesoscale, Science 321(5893), 1172 (2008)

[3] D. P. DiVincenzo, Quantum computation, Science 270(5234), 255 (1995)

[4] V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics 5(4), 222 (2011)

[5] J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, Parametric normal-mode splitting in cavity optomechanics, Phys. Rev. Lett. 101(26), 263602 (2008)

[6] Z. R. Gong, H. Ian, Y. X. Liu, C. P. Sun, and F. Nori, Effective Hamiltonian approach to the Kerr nonlinearity in an optomechanical system, Phys. Rev. A 80(6), 065801 (2009)

[7] R. Ghobadi, A. R. Bahrampour, and C. Simon, Quantum optomechanics in the bistable regime, Phys. Rev. A 84(3), 033846 (2011)

[8] A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. Chang, and O. Painter, Electromagnetically induced transparency and slow light with optomechanics, Nature 472(7341), 69 (2011)

[9] Y. C. Liu, B. B. Li, and Y. F. Xiao, Electromagnetically induced transparency in optical microcavities, Nanophotonics 6(5), 789 (2017)

[10] X. B. Yan, W. Z. Jia, Y. Li, J. H. Wu, X. L. Li, and H. W. Mu, Optomechanically induced amplification and perfect transparency in double-cavity optomechanics, Front. Phys. 10(3), 351 (2015)

[11] Y. C. Liu, Y. F. Xiao, X. Luan, Q. H. Gong, and C. W. Wong, Coupled cavities for motional ground-state cooling and strong optomechanical coupling, Phys. Rev. A 91(3), 033818 (2015)

[12] X. Chen, Y. C. Liu, P. Peng, Y. Zhi, and Y. F. Xiao, Cooling of macroscopic mechanical resonators in hybrid atomoptomechanical systems, Phys. Rev. A 92(3), 033841 (2015)

[13] K. Y. Zhang, L. Zhou, G. J. Dong, and W. P. Zhang, Cavity optomechanics with cold atomic gas, Front. Phys. 6(3), 237 (2011)

[14] S. Bose, K. Jacobs, and P. L. Knight, Preparation of nonclassical states in cavities with a moving mirror, Phys. Rev. A 56(5), 4175 (1997)

[15] T. S. Yin, X. Y. Lü, L. L. Zheng, M. Wang, S. Li, and Y. Wu, Nonlinear effects in modulated quantum optomechanics, Phys. Rev. A 95(5), 053861 (2017)

[16] W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, Towards quantum superpositions of a mirror, Phys. Rev. Lett. 91(13), 130401 (2003)

[17] 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(3), 030405 (2007)

[18] T. P. Purdy, P. L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, Strong optomechanical squeezing of light, Phys. Rev. X 3(3), 031012 (2013)

[19] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81(2), 865 (2009)

[20] S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Entangling macroscopic oscillators exploiting radiation pressure, Phys. Rev. Lett. 88(12), 120401 (2002)

[21] X. W. Xu, Y. J. Zhao, and Y. X. Liu, Entangled-state engineering of vibrational modes in a multimembrane optomechanical system,Phys. Rev. A 88(2), 022325 (2013)

[22] M. Wang, X. Y. Lü, Y. D. Wang, J. Q. You, and Y. Wu, Macroscopic quantum entanglement in modulated optomechanics, Phys. Rev. A 94(5), 053807 (2016)

[23] X. Y. Lü, G. L. Zhu, L. L. Zheng, and Y. Wu, Entanglement and quantum superposition induced by a single photon, Phys. Rev. A 97(3), 033807 (2018)

[24] P. D. Drummond and Z. Ficek, Quantum squeezing, Springer Science & Business Media, 2013

[25] Y. W. Hu, Y. F. Xiao, Y. C. Liu, and Q. Gong, Optomechanical sensing with on-chip microcavities, Front. Phys. 8(5), 475 (2013)

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

[27] J. Q. Liao and C. K. Law, Parametric generation of quadrature squeezing of mirrors in cavity optomechanics, Phys. Rev. A 83(3), 033820 (2011)

[28] X. Y. Lü, J. Q. Liao, L. Tian, and F. Nori, Steady-state mechanical squeezing in an optomechanical system via Duffing nonlinearity, Phys. Rev. A 91(1), 013834 (2015)

[29] R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, Noise squeezing in a nanomechanical duffing resonator, Phys. Rev. Lett. 98(7), 078103 (2007)

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

[31] W. C. Ge and M. S. Zubairy, Macroscopic optomechanical superposition via periodic qubit flipping, Phys. Rev. A 91(1), 013842 (2015)

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

[33] J. M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73(3), 565 (2001)

[34] D. F. V. James and J. Jerke, Effective Hamiltonian theory and its applications in quantum information, Can. J. Phys. 85(6), 625 (2007)

[35] W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80(10), 2245 (1998)

[36] A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, Resolved-sideband cooling of a micromechanical oscillator, Nat. Phys. 4(5), 415 (2008)

[37] A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg, Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit, Nat. Phys. 5(7), 509 (2009)

[38] J. Q. Liao, J. F. Huang, L. Tian, L. M. Kuang, and C. P. Sun, Generalized ultrastrong optomechanics, arXiv: 1802.09254

[39] A. Xuereb, C. Genes, and A. Dantan, Strong coupling and long-range collective interactions in optomechanical arrays, Phys. Rev. Lett. 109(22), 223601 (2012)

[40] M. A. Lemonde, N. Didier, and A. A. Clerk, Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification, Nat. Commun. 7, 11338 (2016)

[41] P. B. Li, H. R. Li, and F. L. Li, Enhanced electromechanical coupling of a nanomechanical resonator to coupled superconducting cavities, Sci. Rep. 6(1), 19065 (2016)

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