Skip to main content
SpringerLink
Log in

Optimal estimation of a classical force with a damped oscillator in the non-Markovian bath

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We derive the optimal quantum limit of probing a classical force by a damped harmonic oscillator initially prepared in the factorized squeezed state. The memory effects of the thermal bath on the oscillator evolution are investigated. We show that the optimal force sensitivity obtained by the quantum estimation theory approaches to zero for the non-Markovian bath, whereas approaches to a finite non-zero value for the Markovian bath as the mean energy of the oscillator goes to infinity.

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. C.A. Regal, J.D. Teufel, K.W. Lehnert, Nat. Phys. 4, 555 (2008)

    Article  Google Scholar 

  2. R. Maiwald, D. Leibfried, J. Britton, J.C. Bergquist, G. Leuchs, D.J. Wineland, Nat. Phys. 5, 551 (2009)

    Article  Google Scholar 

  3. J.D. Teufel, T. Donner, M.A. Castellanos-Beltran, J.W. Harlow, K.W. Lehnert, Nat. Nanotechnol. 4, 820 (2009)

    Article  ADS  Google Scholar 

  4. M.J. Biercuk, H. Uys, J.W. Britton, A.P. VanDevender, J.J. Bollinger, Nat. Nanotechnol. 5, 646 (2010)

    Article  ADS  Google Scholar 

  5. The LIGO Scientific Collaboration, Nat. Phys. 7, 962 (2011)

    Article  Google Scholar 

  6. M. Kacprowicz, R. Demkowicz-Dobrzanski, W. Wasilewski, K. Banaszek, I.A. Walmsley, Nat. Photon. 4, 357 (2010)

    Article  ADS  Google Scholar 

  7. V. Giovannetti, S. Lloyd, L. Maccone, Science 306, 1330 (2004)

    Article  ADS  Google Scholar 

  8. V. Giovannetti, S. Lloyd, L. Maccone, Phys. Rev. Lett. 96, 010401 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  9. V. Giovannetti, S. Lloyd, L. Maccone, Nat. Photon. 5, 222 (2011)

    Article  ADS  Google Scholar 

  10. H.P. Breuer, F. Petruccione, Open Quantum Systems (Oxford University Press, Oxford, 2002)

  11. A. Monras, M.G.A. Paris, Phys. Rev. Lett. 98, 160401 (2007)

    Article  ADS  Google Scholar 

  12. M. Aspachs, G. Adesso, I. Fuentes, Phys. Rev. Lett. 105, 151301 (2010)

    Article  ADS  Google Scholar 

  13. Y. Matsuzaki, S.C. Benjamin, J. Fitzsimons, Phys. Rev. A 84, 012103 (2011)

    Article  ADS  Google Scholar 

  14. A.W. Chin, S.F. Huelga, M.B. Plenio, Phys. Rev. Lett. 109, 233601 (2012)

    Article  ADS  Google Scholar 

  15. M. Tsang, H.M. Wiseman, C.M. Caves, Phys. Rev. Lett. 106, 090401 (2011)

    Article  ADS  Google Scholar 

  16. V.B. Braginsky, Y.I. Vorontsov, K.S. Thorne, Science 209, 547 (1980)

    Article  ADS  Google Scholar 

  17. V.B. Braginsky, F.Y. Khalili, Quantum Measurement (Cambridge University Press, 1992)

  18. C.M. Caves, K.S. Thorne, R.W.P. Drever, V.D. Sandberg, M. Zimmerman, Rev. Mod. Phys. 52, 341 (1980)

    Article  ADS  Google Scholar 

  19. C.W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976)

  20. A.S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdan, 1982)

  21. S.L. Braunstein, C.M. Caves, Phys. Rev. Lett. 72, 3439 (1994)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  22. C.L. Latune, B.M. Escher, R.L. de Matos Filho, L. Davidovich, Phys. Rev. A 88, 042112 (2013)

    Article  ADS  Google Scholar 

  23. B.M. Escher, R.L. de Matos Filho, L. Davidovich, Nat. Phys. 7, 406 (2011)

    Article  Google Scholar 

  24. F. Haake, R. Reibold, Phys. Rev. A 32, 2462 (1985)

    Article  ADS  Google Scholar 

  25. B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  26. R. Karrlein, H. Grabert, Phys. Rev. E 55, 153 (1997)

    Article  ADS  Google Scholar 

  27. G.W. Ford, R.F. O’Connell, Phys. Rev. D 64, 105020 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  28. C.H. Fleming, A. Roura, B.L. Hu, Ann. Phys. 326, 1207 (2011)

    Article  MathSciNet  MATH  ADS  Google Scholar 

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

  30. V. Hakim, V. Ambegaokar, Phys. Rev. A 32, 423 (1985)

    Article  ADS  Google Scholar 

  31. E. Pollak, J. Shao, D.H. Zhang, Phys. Rev. E 77, 021107 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  32. H. Scutaru, J. Phys. A 31, 3659 (1998)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  33. W.N. Plick, P.M. Anisimov, J.P. Dowling, H. Lee, G.S. Agarwal, New J. Phys. 12, 113025 (2010)

    Article  ADS  Google Scholar 

  34. W.J. Munro, K. Nemoto, G.J. Milburn, S.L. Braunstein, Phys. Rev. A 66, 023819 (2002)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Xinyang Normal University, Xinyang, Henan, 464000, P.R. China

    Yang Gao & Yong Lei Jia

  2. Hearne Institute for Theoretical Physics and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, 70803, LA, USA

    Hwang Lee

Authors
  1. Yang Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hwang Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Lei Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang Gao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, Y., Lee, H. & Jia, Y.L. Optimal estimation of a classical force with a damped oscillator in the non-Markovian bath. Eur. Phys. J. D 68, 321 (2014). https://doi.org/10.1140/epjd/e2014-50505-8

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2014-50505-8

Keywords

Search

Navigation