Skip to main content
SpringerLink
Log in

Quantum metrology of phase for accelerated two-level atom coupled with electromagnetic field with and without boundary

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We study how to improve the precision of the quantum estimation of phase for an uniformly accelerated atom in fluctuating electromagnetic field by reflecting boundaries. We find that the precision decreases with increases of the acceleration without the boundary. With the presence of a reflecting boundary, the precision depends on the atomic polarization, position and acceleration, which can be effectively enhanced compared to the case without boundary if we choose the appropriate conditions. In particular, with the presence of two parallel reflecting boundaries, we obtain the optimal precision for atomic parallel polarization and the special distance between two boundaries, as if the atom were shielded from the fluctuation.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. Giovannetti, V., Lloyd, S., Maccone, L.: Quantum metrology. Phys. Rev. Lett. 96(1), 010401 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  2. Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011)

    Article  ADS  Google Scholar 

  3. Roy, S.M., Braunstein, S.L.: Exponentially enhanced quantum metrology. Phys. Rev. Lett. 100(22), 220501 (2008)

    Article  ADS  Google Scholar 

  4. Bollinger, J.J., Itano, W.M., Wineland, D.J., Heinzen, D.J.: Optimal frequency measurements with maximally correlated states. Phys. Rev. A 54(6), R4649 (1996)

    Article  ADS  Google Scholar 

  5. Bužek, V., Derka, R., Massar, S.: Optimal quantum clocks. Phys. Rev. Lett. 82(10), 2207 (1999)

    Article  ADS  Google Scholar 

  6. Peters, A., Chung, K.Y., Chu, S.: Measurement of gravitational acceleration by dropping atoms. Nature (London) 400, 849–852 (1999)

    Article  ADS  Google Scholar 

  7. Jozsa, R., Abrams, D.S., Dowling, J.P., Williams, C.P.: Quantum clock synchronization based on shared prior entanglement. Phys. Rev. Lett. 85(9), 2010 (2000)

    Article  ADS  Google Scholar 

  8. Tian, Z.H., Wang, J.C., Fan, H., Jing, J.L.: Relativistic quantum metrology in open system dynamics. Sci. Rep. 5, 7946 (2015)

    Article  ADS  Google Scholar 

  9. Wang, J.C., Tian, Z.H., Jing, J.L.: Quantum metrology and estimation of Unruh effect. Sci. Rep. 4, 7195 (2014)

    Article  ADS  Google Scholar 

  10. Yurke, B., McCall, S.L., Klauder, J.R.: SU (2) and SU (1, 1) interferometers. Phys. Rev. A 33(6), 4033 (1986)

    Article  ADS  Google Scholar 

  11. Dowling, J.P.: Correlated input-port, matter-wave interferometer: quantum-noise limits to the atom-laser gyroscope. Phys. Rev. A 57(6), 4736 (1998)

    Article  ADS  Google Scholar 

  12. Kok, P., Braunstein, S.L., Dowling, J.P.: Quantum lithography, entanglement and Heisenberg-limited parameter estimation. J. Opt. B 6(8), S811 (2004)

    Article  ADS  Google Scholar 

  13. Lucien, J.B.: Measurement of gravity at sea and in the air. Rev. Geophys. 5(4), 477–526 (1967)

    Article  ADS  Google Scholar 

  14. Poli, N., Wang, F.Y., Tarallo, M.G., Alberti, A., Prevedelli, M., Tinox, G.M.: Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter. Phys. Rev. Lett. 106(3), 038501 (2011)

    Article  ADS  Google Scholar 

  15. Wang, J.C., Tian, Z.H., Jing, J.L., Fan, H.: Influence of relativistic effects on satellite-based clock synchronization. Phys. Rev. D 93(6), 065008 (2016)

    Article  ADS  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  17. Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory. Edizioni della Normale, Pisa (1982)

    MATH  Google Scholar 

  18. Hübner, M.: Explicit computation of the Bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  19. Hübner, M.: Computation of Uhlmann’s parallel transport for density matrices and the Bures metric on three-dimensional Hilbert space. Phys. Lett. A 179(4–5), 226–230 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  20. Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72(22), 3439 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D 14(4), 870 (1976)

    Article  ADS  Google Scholar 

  22. Birrel, N.D., Davis, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982)

    Book  Google Scholar 

  23. Crispino, L.C.B., Higuchi, A., Matsas, G.E.A.: The Unruh effect and its applications. Rev. Mod. Phys. 80(3), 787 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Tian, Z.H., Jing, J.L.: Measurement-induced-nonlocality via the Unruh effect. Ann. Phys. 333, 76–89 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Jia, L.J., Tian, Z.H., Jing, J.L.: Entropic uncertainty relation in de Sitter space. Ann. Phys. 353, 37–47 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Jin, Y., Yu, H.: Electromagnetic shielding in quantum metrology. Phy. Rev. A 91(2), 022120 (2015)

    Article  ADS  Google Scholar 

  27. Liu, X.B., Tian, Z.H., Wang, J.C., Jing, J.L.: Inhibiting decoherence of two-level atom in thermal bath by presence of boundaries. Quantum Inf. Process. 15(9), 3677–3694 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Liu, X.B., Tian, Z.H., Wang, J.C., Jing, J.L.: Protecting quantum coherence of two-level atoms from vacuum fluctuations of electromagnetic field. Ann. Phys. 366, 102–112 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Wang, J.C., Jing, J.L.: Quantum decoherence in noninertial frames. Phys. Rev. A 82(3), 032324 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Tian, Z.H., Jing, J.L.: How the Unruh effect affects transition between classical and quantum decoherences. Phys. Lett. B 707(2), 264–271 (2012)

    Article  ADS  Google Scholar 

  31. Wang, J. C., Tian, Z. H., Jing, J. L., Fan, H.: Irreversible degradation of quantum coherence under relativistic motion. arXiv: 1601.03238

  32. Rosenkranz, M., Jaksch, D.: Parameter estimation with cluster states. Phys. Rev. A 79(2), 022103 (2009)

    Article  ADS  Google Scholar 

  33. Huelga, S.F., Macchiavello, C., Pellizzari, T., Ekert, A.K., Plenio, M.B., Cirac, J.I.: Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79(20), 3865 (1997)

    Article  ADS  Google Scholar 

  34. Ulam-Orgikh, D., Kitagawa, M.: Spin squeezing and decoherence limit in Ramsey spectroscopy. Phys. Rev. A 64(5), 052106 (2001)

    Article  ADS  Google Scholar 

  35. Knysh, S., Smelyanskiy, V.N., Durkin, G.A.: Scaling laws for precision in quantum interferometry and the bifurcation landscape of the optimal state. Phys. Rev. A 83(2), 021804 (2011)

    Article  ADS  Google Scholar 

  36. Kołodynński, J., Demkowicz-Dobrzanski, R.: Phase estimation without a priori phase knowledge in the presence of loss. Phys. Rev. A 82(5), 053804 (2010)

    Article  ADS  Google Scholar 

  37. Tian, Z.H., Wang, J.C., Fan, H., Jing, J.L.: Relativistic quantum metrology in open system dynamics. Sci. Rep. 5, 7946 (2015)

    Article  ADS  Google Scholar 

  38. Tian, Z.H., Jing, J.L.: Dynamics and quantum entanglement of two-level atoms in de Sitter spacetime. Ann. Phys. 350, 1–13 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Zhong, W., Sun, Z., Ma, J., Wang, X., Nori, F.: Fisher information under decoherence in Bloch representation. Phys. Rev. A 87(2), 022337 (2013)

    Article  ADS  Google Scholar 

  40. Compagno, G., Passante, R., Persico, F.: Atom-Field Interactions and Dressed Atoms. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  41. Zanardi, P., Paris, M.G.A., C, L.: Quantum criticality as a resource for quantum estimation. Phys. Rev. A 78(4), 042105 (2008)

    Article  ADS  Google Scholar 

  42. Gorini, V., Kossakowski, A., Surdarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys 17, 821 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  43. Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. Greiner, W., Reinhardt, J.: Field Quantization. Springer, Berlin (1996)

    Book  MATH  Google Scholar 

  45. Brown, L.S., Maclay, G.J.: Vacuum stress between conducting plates: an image solution. Phys. Rev. 184(5), 1272 (1969)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos. 11475061 and 11305058. X. Liu was supported by the Hunan Provincial Innovation Foundation For Postgraduate under Grant No. CX2017B175.

Author information

Authors and Affiliations

  1. Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Ying Yang, Xiaobao Liu, Jieci Wang & Jiliang Jing

Authors
  1. Ying Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaobao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jieci Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiliang Jing
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiliang Jing.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Y., Liu, X., Wang, J. et al. Quantum metrology of phase for accelerated two-level atom coupled with electromagnetic field with and without boundary. Quantum Inf Process 17, 54 (2018). https://doi.org/10.1007/s11128-018-1815-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1815-z

Keywords

Search

Navigation