Skip to main content
SpringerLink
Log in

Generating large steady-state optomechanical entanglement by the action of Casimir force

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

In this paper, we study an optomechanical device consisting of a Fabry-Pérot cavity with two dielectric nanospheres trapped near the cavity mirrors by an external driving laser. In the condition where the distances between the nanospheres and cavity mirrors are small enough, the Casimir force helps the optomechanical coupling to induce a steady-state optomechanical entanglement of the mechanical and optical modes in a certain regime of parameters. We investigate in detail the dependence of the steady-state optomechanical entanglement on external control parameters of the system, i.e., the effective detuning, the pump powers of the cavity, the cavity decay rate and the wavelength of the driving field. It is found that the large steady-state optomechanical entanglement, i.e. E N = 5.76, can be generated with experimentally feasible parameters, i.e. the pump power P = 18.2 μW, the cavity decay rate κ = 0.5 MHz and the wavelength of the laser λL=1064 nm, which should be checked by optical measurement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kippenberg T J, Vahala K J. Cavity opto-mechanics. Opt Express, 2007, 15: 17172–17205

    Article  ADS  Google Scholar 

  2. Kippenberg T J, Vahala K J. Cavity optomechanics: Back-action at the mesoscale. Science, 2008, 321: 1172–1176

    Article  ADS  Google Scholar 

  3. Marquardt F, Girvin S M. Trend: Optomechanics. Physics, 2009, 2: 40

    Article  Google Scholar 

  4. Aspelmeyer M, Gröblacher S, Hammerer K, et al. Quantum optomechanics-throwing a glance [Invited]. J Opt Soc Am B, 2010, 27: A189–A197

    Article  ADS  Google Scholar 

  5. Aspelmeyer M, Meystre P, Schwab K. Quantum optomechanics. Phys Tod, 2012, 65: 29

    Article  ADS  Google Scholar 

  6. Wilson-Rae I, Nooshi N, Zwerger W, et al. Theory of ground state cooling of a mechanical oscillator using dynamical backaction. Phys Rev Lett, 2007, 99: 093901

    Article  ADS  Google Scholar 

  7. Marquardt F, Chen J P, Clerk A A, et al. Quantum theory of cavity-assisted sideband cooling of mechanical motion. Phys Rev Lett, 2007, 99: 093902

    Article  ADS  Google Scholar 

  8. Vitali D, Gigan S, Ferreira A, et al. Optomechanical entanglement between a movable mirror and a cavity field. Phys Rev Lett, 2007, 98: 030405

    Article  ADS  Google Scholar 

  9. Phelps G A, Meystre P. Laser phase noise effects on the dynamics of optomechanical resonators. Phys Rev A, 2011, 83: 063838

    Article  ADS  Google Scholar 

  10. Bhattacharya M, Meystre P. Trapping and cooling a mirror to its quantum mechanical ground state. Phys Rev Lett, 2007, 99: 073601

    Article  ADS  Google Scholar 

  11. Hartmann M J, Plenio M B. Steady state entanglement in the mechanical vibrations of two dielectric membranes. Phys Rev Lett, 2008, 101: 200503

    Article  ADS  Google Scholar 

  12. Cheung H K, Law C K. Nonadiabatic optomechanical Hamiltonian of a moving dielectric membrane in a cavity. Phys Rev A, 2011, 84: 023812

    Article  ADS  Google Scholar 

  13. Thompson J D, Zwickl B M, Jayich A M, et al. Strong dispersive coupling of a high finesse cavity to a micromechanical membrane. Nature, 2008, 452: 72

    Article  ADS  Google Scholar 

  14. Li Y, Wu L A, Wang Z D. Fast ground-state cooling of mechanical resonators with time-dependent optical cavities. Phys Rev A, 2011, 83: 043804

    Article  ADS  Google Scholar 

  15. Xu XW, Zhao Y J, Liu Y X. Entangled-state engineering of vibrational modes in a multimembrane optomechanical system. Phys Rev A, 2013, 88: 022325

    Article  ADS  Google Scholar 

  16. Sun Q, Hu X H, Liu W M, et al. Effect on cavity optomechanics of the interaction between a cavity field and a one-dimensional interacting bosonic gas. Phys Rev A, 2011, 84: 023822

    Article  ADS  Google Scholar 

  17. Kumar T, Bhattacherjee A B, Man Mohan. Dynamics of a movable micromirror in a nonlinear optical cavity. Phys Rev A, 2010, 81: 013835

    Article  ADS  Google Scholar 

  18. Dalafi A, Naderi M H, Soltanolkotabi M, et al. Nonlinear effects of atomic collisions on the optomechanical properties of a Bose-Einstein condensate in an optical cavity. Phys Rev A, 2013, 87: 013417

    Article  ADS  Google Scholar 

  19. Zheng Q, Li S C, Zhang X P, et al. Controllable optical bistability of Bose-Einstein condensate in an optical cavity with Kerr medium. Chin Phys B, 2012, 21: 093702

    Article  ADS  Google Scholar 

  20. Kanamoto R, Meystre P. Optomechanics of a quantum-degenerate Fermi gas. Phys Rev Lett, 2010, 104: 063601

    Article  ADS  Google Scholar 

  21. Verhagenn E, Deleglise S, Weis S, et al. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature, 2012, 482: 63–67

    Article  ADS  Google Scholar 

  22. Weis S, Rivire R, Delglise S, et al. Optomechanically induced transparency. Science, 2010, 330: 1520–1523

    Article  ADS  Google Scholar 

  23. Kim K H, Bahl G, Lee W, et al. Cavity optomechanics on a microfluidic resonator with water and viscous liquids. Light Sci Appl, 2013, 2: e110

    Article  Google Scholar 

  24. Li Y, Wang Y D, Xue F, et al. Quantum theory of transmission line resonator-assisted cooling of a micromechanical resonator. Phys Rev B, 2008, 78: 134301

    Article  ADS  Google Scholar 

  25. Xue F, Liu Y X, Sun C P, et al. Two-mode squeezed states and entangled states of two mechanical resonators. Phys Rev B, 2007, 76: 064305

    Article  ADS  Google Scholar 

  26. Kleckner D, Bouwmeester D. Sub-kelvin optical cooling of a micromechanical resonator. Nature, 2006, 444: 75–78

    Article  ADS  Google Scholar 

  27. Xia K, Evers J. Ground state cooling of a nanomechanical resonator in the nonresolved regime via quantum interference. Phys Rev Lett, 2009, 103: 227203

    Article  ADS  Google Scholar 

  28. Liu Y C, Xiao Y F, Luan X, et al. Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics. Phys Rev Lett, 2013, 110: 153606

    Article  ADS  Google Scholar 

  29. Liu Y C, Hu Y W, Wong C W, et al. Review of cavity optomechanical cooling. Chin Phys B, 2013, 22: 114213

    Article  ADS  Google Scholar 

  30. Wang Y D, Clerk A A. Reservoir-engineered entanglement in optomechanical systems. Phys Rev Lett, 2013, 110: 253601

    Article  ADS  Google Scholar 

  31. Vitali D, Tombesi P, Woolley M J. Entangling a nanomechanical resonator and a superconducting microwave cavity. Phys Rev A, 2007, 76: 042336

    Article  ADS  Google Scholar 

  32. Abdi M, Pirandola S, Tombesi P, et al. Entanglement swapping with local certification: Application to remote micromechanical resonators. Phys Rev Lett, 2012, 109: 143601

    Article  ADS  Google Scholar 

  33. Kuzyk M C, van Enk S J, Wang H. Generating robust optical entanglement in weak-coupling optomechanical systems. Phys Rev A, 2013, 88: 062341

    Article  ADS  Google Scholar 

  34. Wang C, He L Y, Zhang Y, et al. Complete entanglement analysis on electron spins using quantum dot and microcavity coupled system. Sci China-Phys Mech Astron, 2013, 56: 2054–2058

    Article  ADS  MathSciNet  Google Scholar 

  35. Liu Y M. Virtual-photon-induced entanglement with two nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity. Sci China-Phys Mech Astron, 2013, 56: 2138–2142

    Article  ADS  Google Scholar 

  36. Mancini S, Giovannetti V, Vitali D, et al. Entangling macroscopic oscillators exploiting radiation pressure. Phys Rev Lett, 2002, 88: 120401

    Article  ADS  Google Scholar 

  37. Pinard M, Dantan A, Vitali D, et al. Entangling movable mirrors in a double-cavity system. Europhys Lett, 2005, 72: 747–753

    Article  ADS  Google Scholar 

  38. Niedenzu W, Sandner R M, Genes C, et al. Quantum-correlated motion and heralded entanglement of distant optomechanically coupled objects. J Phys B-At Mol Opt Phys, 2012, 45: 245501

    Article  ADS  Google Scholar 

  39. Dobrindt J M, Wilson-Rae I, Kippenberg T J. Parametric normal-mode splitting in cavity optomechanics. Phys Rev Lett, 2008, 101: 263602

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  41. Woolley M J, Doherty A C, Milburn G J, et al. Nanomechanical squeezing with detection via a microwave cavity. Phys Rev A, 2008, 78: 062303

    Article  ADS  Google Scholar 

  42. Safavi-Naeini A H, Groeblacher S, Hill J T, et al. Squeezed light from a silicon micromechanical resonator. Nature, 2013, 500: 185–189

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. Ghobadi R, Bahrampour A R, Simon C. Quantum optomechanics in the bistable regime. Phys Rev A, 2011, 84: 033846

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  46. Fu C B, Yan X B, Gu K H, et al. Steady-state solutions of a hybrid system involving atom-light and optomechanical interactions: Beyond the weak-cavity-field approximation. Phys Rev A, 2013, 87: 053841

    Article  ADS  Google Scholar 

  47. Agarwal G S, Huang S. Electromagnetically induced transparency in mechanical effects of light. Phys Rev A, 2010, 81: 041803

    Article  ADS  Google Scholar 

  48. Zhang L, Song Z D. Modification on static responses of a nanooscillator by quadratic optomechanical couplings. Sci China-Phys Mech Astron, 2014, 57: 880–886

    Article  ADS  Google Scholar 

  49. Wang H, Sun H C, Zhang J, et al. Transparency and amplification in hybrid system of the mechanical resonator and circuit QED. Sci China-Phys Mech Astron, 2012, 55: 2264–2272

    Article  ADS  MathSciNet  Google Scholar 

  50. Abramovici A, Althouse WE, Drever RWP, et al. LIGO: The laser interferometer gravitational-wave observatory. Science, 1992, 256: 325–333

    Article  ADS  Google Scholar 

  51. Vitali D, Mancini S, Tombesi P. Optomechanical scheme for the detection of weak impulsive forces. Phys Rev A, 2001, 64: 051401

    Article  ADS  Google Scholar 

  52. Stannigel K, Rabl P, Sorensen A S, et al. Optomechanical transducers for long-distance quantum communication. Phys Rev Lett, 2010, 105: 220501

    Article  ADS  Google Scholar 

  53. Liu Y C, Xiao Y F, Chen Y L, et al. Parametric down-conversion and polariton pair generation in optomechanical systems. Phys Rev Lett, 2013, 111: 083601

    Article  ADS  Google Scholar 

  54. Romero-Isart O, Pflanzer A C, Juan M L, et al. Optically levitating dielectrics in the quantum regime: Theory and protocols. Phys Rev A, 2011, 83: 013803

    Article  ADS  Google Scholar 

  55. Chang D E, Regal C A, Papp S B, et al. Cavity opto-mechanics using an optically levitated nanosphere. Proc Natl Acad Sci USA, 2010, 107: 1005–1010

    Article  ADS  Google Scholar 

  56. Pender G A T, Barker P F, Marquardt F, et al. Optomechanical cooling of levitated spheres with doubly resonant fields. Phys Rev A, 2012, 85: 021802

    Article  ADS  Google Scholar 

  57. Arvanitaki A, Geraci A A. Detecting high-frequency gravitational waves with optically levitated sensors. Phys Rev Lett, 2013, 110: 071105

    Article  ADS  Google Scholar 

  58. Li T, Kheifets S, Medellin D, et al. Measurement of the instantaneous velocity of a Brownian particle. Science, 2010, 328: 1673–1675

    Article  ADS  Google Scholar 

  59. Li T, Kheifets S, Raizen M G. Millikelvin cooling of an optically trapped microsphere in vacuum. Nat Phys, 2011, 7: 527–530

    Article  Google Scholar 

  60. Yin Z Q. Phase noise and laser-cooling limits of optomechanical oscillators. Phys Rev A, 2009, 80: 033821

    Article  ADS  Google Scholar 

  61. Yin Z Q, Geraci A A, Li T. Optomechanics of levitated dielectric particles. Int J Mod Phys B, 2013, 27: 1330018

    Article  ADS  MathSciNet  Google Scholar 

  62. Geraci A A, Papp S B, Kitching J. Short-range force detection using optically cooled levitated microspheres. Phys Rev Lett, 2010, 105: 101101

    Article  ADS  Google Scholar 

  63. Nie W J, Lan Y H, Li Y, et al. Effect of the Casimir force on the entanglement between a levitated nanosphere and cavity modes. Phys Rev A, 2012, 86: 063809

    Article  ADS  Google Scholar 

  64. Nie W J, Lan Y H, Li Y, et al. Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction. Phys Rev A, 2013, 88: 063849

    Article  ADS  Google Scholar 

  65. Gieseler J, Deutsch B, Quidant R, et al. Subkelvin parametric feedback cooling of a laser-trapped nanoparticle. Phys Rev Lett, 2012, 109: 103603

    Article  ADS  Google Scholar 

  66. Xuereb A, Paternostro M. Selectable linear or quadratic coupling in an optomechanical system. Phys Rev A, 2013, 87: 023830

    Article  ADS  Google Scholar 

  67. Romero-Isart O, Juan M L, Quidant R, et al. Toward quantum superposition of living organisms. New J Phys, 2010 12: 033015

    Article  Google Scholar 

  68. Nie W J, Lan Y H, Zhu S Y. Casimir force between topological insulator slabs. Phys Rev B, 2013, 88: 085421

    Article  ADS  Google Scholar 

  69. Yin Z Q, Li T, Feng M. Three-dimensional cooling and detection of a nanosphere with a single cavity. Phys Rev A, 2011, 83: 013816

    Article  ADS  Google Scholar 

  70. Romero-Isart Q, Pflanzer A C, Blaser F, et al. Large quantum superpositions and interference of massive nanometer-sized objects. Phys Rev Lett, 2011, 107: 020405

    Article  ADS  Google Scholar 

  71. Romero-Isart Q. Quantum superposition of massive objects and collapse models. Phys Rev A, 2011, 84: 052121

    Article  ADS  Google Scholar 

  72. Casimir H B G. On the attraction between two perfectly conducting plates. Proc K Ned Akad Wet Ser B, 1948, 51: 793–795

    MATH  Google Scholar 

  73. Derjaguin B V, Abrikosova I I, Lifshitz E M. Direct measurement of molecular attraction between solids separated by a narrow gap. Q Rev Chem Soc, 1956, 10: 295–329

    Article  Google Scholar 

  74. Bordag M, Mohideen U, Mostepanenko V M. New developments in the Casimir effect. Phys Rep, 2001, 1: 1–205

    Article  ADS  MathSciNet  Google Scholar 

  75. Canaguier-Durand A, Maia Neto P A, Cavero-Pelaez I, et al. Casimir interaction between plane and spherical metallic surfaces. Phys Rev Lett, 2009, 102: 230404

    Article  ADS  Google Scholar 

  76. Bimonte G, Emig T. Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere-sphere and sphere-plane geometry. Phys Rev Lett, 2012, 109: 160403

    Article  ADS  Google Scholar 

  77. Lambrecht A, Reynaud S. Casimir force between metallic mirrors. Eur Phys J D, 2000, 8: 309–318

    Article  ADS  Google Scholar 

  78. Scardicchio A, Jaffe R L. Casimir effects: An optical approach I. Foundations and examples. Nucl Phys B, 2005, 704: 552–582

    Article  ADS  MATH  MathSciNet  Google Scholar 

  79. Butera S, Passante R. Field fluctuations in a one-dimensional cavity with a mobile wall. Phys Rev Lett, 2013, 111: 060403

    Article  ADS  Google Scholar 

  80. DeJesus E X, Kaufman C. Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations. Phys Rev A, 1987, 35: 5288–5290

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Tsinghua University, Beijing, 100084, China

    WenJie Nie & YueHeng Lan

  2. Beijing Computational Science Research Center, Beijing, 100084, China

    WenJie Nie, Yong Li & ShiYao Zhu

  3. Department of Applied Physics East China Jiaotong University, Nanchang, 330013, China

    WenJie Nie

Authors
  1. WenJie Nie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. YueHeng Lan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. ShiYao Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to WenJie Nie or Yong Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nie, W., Lan, Y., Li, Y. et al. Generating large steady-state optomechanical entanglement by the action of Casimir force. Sci. China Phys. Mech. Astron. 57, 2276–2284 (2014). https://doi.org/10.1007/s11433-014-5580-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-014-5580-4

Keywords

Search

Navigation