Skip to main content
Log in

Enhancement of photon–phonon entanglement transfer in optomechanics

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this work, we propose a theoretical scheme to enhance stationary entanglement of the mechanical modes of two Fabry–Pérot cavities via broadband squeezed light. We employ the rotating wave approximation, and we consider the adiabatic and nonadiabatic regimes in the situation where a parametric amplifier is placed inside each cavity. The logarithmic negativity is employed to quantify the amount of entanglement. Stationary entanglement is optimal for high value of squeezing parameter and for strong optomechanical coupling. We show that the stationary entanglement is fragile under thermal effects. We show that it is possible to enhance the quantum correlations between the two movable mirrors via tuned parametric amplifier. Besides, we show that the enhancement of the stationary entanglement is deeply related to the gain of the parametric amplifier, the bath temperature of the movable mirrors, the optomechanical cooperativity and the squeezing parameter. We find that the stationary entanglement of two movable mirrors is strong in the adiabatic regime in comparison with the nonadiabatic case.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  2. Schrödinger, E.: Discussion of probability relations between separated systems. Math. Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  ADS  MATH  Google Scholar 

  3. Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)

    Article  MathSciNet  Google Scholar 

  4. Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Scarani, V., Lblisdir, S., Gisin, N., Acin, A.: Quantum cloning. Rev. Mod. Phys. 77, 1225 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  9. Adesso, G., Serafini, A., Illuminati, F.: Determination of continuous variable entanglement by purity measurements. Phys. Rev. Lett. 92, 087901 (2004)

    Article  ADS  Google Scholar 

  10. Tian, L., Wang, H.: Optical wavelength conversion of quantum states with optomechanics. Phys. Rev. A 82, 053806 (2010)

    Article  ADS  Google Scholar 

  11. Wang, Y.-D., Clerk, A.A.: Using interference for high fidelity quantum state transfer in optomechanics. Phys. Rev. Lett. 108, 153603 (2012)

    Article  ADS  Google Scholar 

  12. Tian, L.: Adiabatic state conversion and pulse transmission in optomechanical systems. Phys. Rev. Lett. 108, 153604 (2012)

    Article  ADS  Google Scholar 

  13. Singh, S., Jing, H., Wright, E.M., Meystre, P.: Quantum-state transfer between a Bose–Einstein condensate and an optomechanical mirror. Phys. Rev. A 86, 021801 (2012)

    Article  ADS  Google Scholar 

  14. McGee, S.A., Meiser, D., Regal, C.A., Lehnert, K.W., Holland, M.J.: Mechanical resonators for storage and transfer of electrical and optical quantum states. Phys. Rev. A 87, 053818 (2013)

    Article  ADS  Google Scholar 

  15. Palomaki, T.A., Harlow, J.W., Teufel, J.D., Simmonds, R.W., Lehnert, K.W.: Coherent state transfer between itinerant microwave fields and a mechanical oscillator. Nature 495, 210–214 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Sete, E.A., Eleuch, H., Ooi, C.H.R.: Light-to-matter entanglement transfer in optomechanics. J. Opt. Soc. Am. B 31, 2821 (2014)

    Article  ADS  Google Scholar 

  18. El Qars, J., Daoud, M., Laamara, Ahl: Entanglement versus Gaussian quantum discord in a double-cavity opto-mechanical system. Int. J. Quant. Inf. 13, 1550041 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Amazioug, M., Nassik, M., Habiballah, N.: Entanglement, EPR steering and Gaussian geometric discord in a double cavity optomechanical systems. Eur. Phys. J. D 72, 171 (2018)

    Article  ADS  MATH  Google Scholar 

  20. El Qars, J., Daoud, M., Laamara, Ahl: Controlling stationary one-way steering via thermal effects in optomechanics. Phys. Rev. A 98, 042115 (2018)

    Article  ADS  Google Scholar 

  21. Teufel, J., Donner, T., Li, D., Harlow, J., Allman, M., Cicak, K., Sirois, A., Whittaker, J., Lehnert, K., Simmonds, R.: Sideband cooling of micromechanical motion to the quantum ground state. Nature 475(7356), 359 (2011)

    Article  ADS  Google Scholar 

  22. Machnes, S., Cerrillo, J., Aspelmeyer, M., Wieczorek, W., Plenio, M.B., Retzker, A.: Pulsed laser cooling for cavity optomechanical resonators. Phys. Rev. Lett. 108(15), 153601 (2012)

    Article  ADS  Google Scholar 

  23. Chan, J., Alegre, T.P.M., Naeini, A.H.Safavi, Hill, J.T., Krause, A., Gröblacher, S., Aspelmeyer, M., Painter, O.: Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478(7367), 89 (2011)

    Article  ADS  Google Scholar 

  24. Bhattacharya, M., Meystre, P.: Trapping and cooling a mirror to its quantum mechanical ground state. Phys. Rev. Lett. 99(7), 073601 (2007)

    Article  ADS  Google Scholar 

  25. Liao, J.Q., Tian, L.: Macroscopic quantum superposition in cavity optomechanics. Phys. Rev. Lett. 116(16), 163602 (2016)

    Article  ADS  Google Scholar 

  26. Mancini, S., Giovannetti, V., Vitali, D., Tombesi, P.: Entangling macroscopic oscillators exploiting radiation pressure. Phys. Rev. Lett. 88, 120401 (2002)

    Article  ADS  Google Scholar 

  27. 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 

  28. Vitali, D., Gigan, S., Ferreira, A., Bohm, H.R., 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 

  29. Liu, Z.-X., Wang, B., Kong, C., Si, L.-G., Xiong, H., Wu, Y.: A proposed method to measure weak magnetic field based on a hybrid optomechanical system. Sci. Rep. 7, 12521 (2017)

    Article  ADS  Google Scholar 

  30. Xiong, H., Si, L.G., Wu, Y.: Precision measurement of electrical charges in an optomechanical system beyond linearized dynamics. Appl. Phys. Lett. 110, 171102 (2017)

    Article  ADS  Google Scholar 

  31. Xiong, H., Liu, Z.X., Wu, Y.: Highly sensitive optical sensor for precision measurement of electrical charges based on optomechanically induced difference-sideband generation. Opt. Lett. 42, 3630 (2017)

    Article  ADS  Google Scholar 

  32. Caves, C.M.: Quantum-mechanical radiation-pressure fluctuations in an interferometer. Phys. Rev. Lett. 45, 75 (1980)

    Article  ADS  Google Scholar 

  33. Abramovici, A., Althouse, W.E., Drever, R.W.P., Gürsel, Y., Kawamura, S., Raab, F.J., Shoemaker, D., Sievers, L., Spero, R.E., Thorne, K.S., Vogt, R.E., Weiss, R., Whitcomb, S.E., Zucker, M.E.: LIGO: the laser interferometer gravitational-wave observatory. Science 256, 325 (1992)

    Article  ADS  Google Scholar 

  34. Braginsky, V., Vyatchanin, S.P.: Low quantum noise tranquilizer for Fabry–Perot interferometer. Phys. Lett. A 293, 228 (2002)

    Article  ADS  MATH  Google Scholar 

  35. Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. AlQasimi, A., James, D.F.V.: Sudden death of entanglement at finite temperature. Phys. Rev. A 77, 012117 (2008)

    Article  ADS  Google Scholar 

  37. Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)

    Article  ADS  Google Scholar 

  38. Yu, T., Eberly, J.H.: Sudden death of entanglement: classical noise effects. Opt. Commun. 264, 393 (2006)

    Article  ADS  Google Scholar 

  39. Yu, T., Eberly, J.H.: Quantum open system theory: bipartite aspects. Phys. Rev. Lett. 97, 140403 (2006)

    Article  ADS  Google Scholar 

  40. Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323, 598 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Almeida, M.P., et al.: Environment-Induced sudden death of entanglement. Science 316, 579 (2007)

    Article  ADS  Google Scholar 

  42. Ficek, Z., Tanaś, R.: Dark periods and revivals of entanglement in a two-qubit system. Phys. Rev. A 74, 024304 (2006)

    Article  ADS  Google Scholar 

  43. Mann, A., Sanders, B.C., Munro, W.J.: Bell’s inequality for an entanglement of nonorthogonal states. Phys. Rev. A 51, 989 (1995)

    Article  ADS  Google Scholar 

  44. El Qars, J., Daoud, M., Laamara, Ahl: Nonclassical correlations in a two-mode optomechanical system. Int. J. Quant. Inf. 30, 1650134 (2016)

    MathSciNet  MATH  Google Scholar 

  45. Amazioug, M., Nassik, M., Habiballah, N.: Gaussian quantum discord and EPR steering in optomechanical system. Opt. Int. J. Light Elect. Opt. 158, 1186–1193 (2018)

    Article  MATH  Google Scholar 

  46. Amazioug, M., Nassik, M., Habiballah, N.: Entanglement and Gaussian interferometric power dynamics in an optomechanical system with radiation pressure. Chin. J. Phys. 58, 1–7 (2019)

    Article  Google Scholar 

  47. Amazioug, M., Nassik, M.: Control of atom-mirror entanglement versus Gaussian geometric discord with RWA. Int. J. Quant. Inf. 17, 1950045 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  48. Agarwal, G.S., Huang, S.: Strong mechanical squeezing and its detection. Phys. Rev. A 93, 043844 (2016)

    Article  ADS  Google Scholar 

  49. Walls, D.F., Milburn, G.J.: Quantum Optics. Springer, Berlin (1994)

    Book  MATH  Google Scholar 

  50. Wu, L.A., Kimble, H.J., Hall, J.L., Wu, H.: Generation of squeezed states by parametric down conversion. Phys. Rev. Lett. 57, 2520 (1986)

    Article  ADS  Google Scholar 

  51. Aspelmeyer, M., Kippenberg, T.J., Marquardt, F.: Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  53. Gardiner, C.W., Zoller, P.: Quantum Noise, p. 71. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  55. Wang, Y.D., Chesi, S., Clerk, A.A.: Bipartite and tripartite output entanglement in three-mode optomechanical systems. Phys. Rev. A 91, 013807 (2015)

    Article  ADS  Google Scholar 

  56. Pinard, M., Dantan, A., Vitali, D., Arcizet, O., Briant, T., Heidmann, A.: Entangling movable mirrors in a double-cavity system. Europhys. Lett. 72, 747–753 (2005)

    Article  ADS  Google Scholar 

  57. Mari, A., Eisert, J.: Gently modulating optomechanical systems. Phys. Rev. Lett. 103, 213603 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  59. Parks, P.C., Hahn, V.: Stability Theory. Prentice Hall, New York (1993)

    MATH  Google Scholar 

  60. Amazioug, M., Nassik, M., Habiballah, N.: Measure of general quantum correlations in optomechanics. Int. J. Quant. Inf. 16, 1850043 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  61. Simon, R.: Criterion for continuous variable systems. Phys. Rev. Lett. 84, 2726 (2000)

    Article  ADS  Google Scholar 

  62. Gröblacher, S., Hammerer, K., Vanner, M.R., Aspelmeyer, M.: Observation of strong coupling between a micromechanical resonator and an optical cavity field. Nature (London) 460, 724 (2009)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Amazioug.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Amazioug, M., Maroufi, B. & Daoud, M. Enhancement of photon–phonon entanglement transfer in optomechanics. Quantum Inf Process 19, 160 (2020). https://doi.org/10.1007/s11128-020-02655-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02655-z

Keywords

Navigation