Enhancing estimation precision of parameter for a two-level atom with circular motion

  • Ying Yang
  • Jiliang JingEmail author
  • Zixu Zhao


We find a way to improve the estimation precision of parameter by enhancing the quantum Fisher information (QFI) of parameter by investigating the dynamics of a two-level atom with circular motion which is coupled to the scalar field in open quantum system. Our results illustrate that the QFI of phase decreases with the increase in centripetal acceleration and the evolution of time. However, in contrast to the unbounded case, we find that the QFI of phase decreases slowly with a boundary. Especially, the QFI tends to 1 when the atom is very close to the boundary, which implies that the atom is shielded from the influence of the vacuum fluctuation with a boundary. Therefore, we can enhance the estimation precision of the parameter by choosing an appropriate position.


Precision of parameter estimation Quantum Fisher information Quantum metrology Boundary 



This work was supported by the National Natural Science Foundation of China under Grant Nos. 11875025 and 11705144, and the Scientific Research Program of Education Department of Shaanxi Provincial Government (17JK0706).


  1. 1.
    Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976)zbMATHGoogle Scholar
  2. 2.
    Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory [M]. Springer Science & Business Media, Moscow (2011)CrossRefGoogle Scholar
  3. 3.
    Giovanetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330 (2004)ADSCrossRefGoogle Scholar
  4. 4.
    Giovannetti, V., Lloyd, S., Maccone, L.: Quantum metrology. Phys. Rev. Lett. 96(1), 010401 (2006)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photonics 5, 222–229 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    Yao, Y., Xiao, X., Ge, Li, Wang, X.g, Sun, C.p: Quantum Fisher information in noninertial frames. Phys. Rev. A. 89, 042336 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    Li, N., Luo, S.: Entanglement detection via quantum Fisher information. Phys. Rev. A 88, 014301 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    Bužek, V., Derka, R., Massar, S.: Optimal quantum clocks. Phys. Rev. Lett. 82(10), 2207 (1999)ADSCrossRefGoogle Scholar
  9. 9.
    Lucien, J.B.: Measurement of gravity at sea and in the air. Rev. Geophis. 5(4), 477–526 (1967)ADSCrossRefGoogle Scholar
  10. 10.
    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)ADSCrossRefGoogle Scholar
  11. 11.
    Liu, P., Wang, P., Yang, W., Jin, G.R., Sun, C.P.: Fisher information of a squeezed-state interferometer with a finite photon-number resolution. Phys. Rev. A 95, 023824 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    Liu, P., Jin, G.R.: Ultimate phase estimation in a squeezed-state interferometer using photon counters with a finite number resolution. J. Phys. A: Math. Theor. 50(40), 405303 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Zhang, Y.M., Li, X.W., Yang, W., Jin, G.R.: Quantum Fisher information of entangled coherent states in the presence of photon loss. Phys. Rev. A 88(4), 043832 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    Wang, T.L., Wu, L.N., Yang, W.: Quantum Fisher information as a signature of the superradiant quantum phase transition. New J. Phys. 16(16), 063039 (2014)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439 (1994)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Vittorio, G., Seth, L., Lorenzo, M.: Advances in quantum metrology. Nat. Photonics 5(4), 222 (2011)CrossRefGoogle Scholar
  17. 17.
    Pezzé, L., Smerzi, A.: Entanglement, nonlinear dynamics, and the Heisenberg limit. Phys. Rev. Lett. 102, 100401 (2009)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Hyllus, P., Laskowski, W., Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Pezzé, L., Smerzi, A.: Fisher information and multiparticle entanglement. Phys. Rev. A 85, 022321 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    Tóth, G.: Multipartite entanglement and high-precision metrology. Phys. Rev. A 85, 022322 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Hyllus, P., Pezzé, L., Smerzi, A.: Useful multiparticle entanglement and sub-shot-noise sensitivity in experimental phase estimation. Phys. Rev. Lett. 107, 080504 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    Strobel, H., Muessel, W., Linnemann, D., Zibold, T., Hume, D.B., Pezze, L., Smerzi, A., Oberthaler, M.K.: Fisher information and entanglement of non-Gaussian spin states. Science 345, 424 (2014)ADSCrossRefGoogle Scholar
  22. 22.
    Huber, S., Konig, R., Vershynina, A.: Geometric inequalities from phase space translations. J. Math. Phys. 58, 012206 (2017)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Datta, N., Pautrat, Y., Rouz, C.: Contractivity properties of a quantum diffusion semigroup. J. Math. Phys. 58, 012205 (2017)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Augusiak, R., Kołodyński, J., Streltsov, A., Bera, M.N., Acín, A., Lewenstein, M.: Asymptotic role of entanglement in quantum metrology. Phys. Rev. A 94, 012339 (2016)ADSCrossRefGoogle Scholar
  25. 25.
    Kim, S.K., Soh, K.S., Yee, J.H.: Zero-point field in a circular-motion frame. Phys. Rev. D 35, 557 (1987)ADSCrossRefGoogle Scholar
  26. 26.
    Bell, J.S., Leinaas, J.M.: The Unruh effect and quantum fluctuations of electrons in storage rings. Nuclear Phys. B 284, 488–508 (1987)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Jackson, J.D.: On understanding spin-flip synchrotron radiation and the transverse polarization of electrons in storage rings. Rev. Mod. Phys. 48, 417 (1976)ADSCrossRefGoogle Scholar
  28. 28.
    Derbenev, Y.S., Kondratenko, A.M.: Polarization kinetics of particles in storage rings. Sov. Phys. JETP 37, 968 (1973)ADSGoogle Scholar
  29. 29.
    Barber, D.P., Mane, S.R.: Calculations of Bell and Leinaas and Derbenev and Kondratenko for radiative electron polarization. Phys. Rev. A 37, 456 (1988)ADSCrossRefGoogle Scholar
  30. 30.
    Akhmedov, E.T., Singleton, D.: On the relation between Unruh and Sokolov–Ternov effects. Int. J. Mod. Phys. A 22(26), 4797–4823 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    Dalibard, J., Dupont-Roc, J., Cohen-Tannoudji, C.: Vacuum fluctuations and radiation reaction: identification of their respective contributions. J. Phys. 43, 1617–1638 (1982)CrossRefGoogle Scholar
  32. 32.
    Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge university press, Cambridge (1984)zbMATHGoogle Scholar
  33. 33.
    Tian, Z.H., Jing, J.L.: Measurement-induced-nonlocality via the Unruh effect. Ann. Phys. 333, 76–89 (2013)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Jia, L.J., Tian, Z.H., Jing, J.L.: Entropic uncertainty relation in de Sitter space. Ann. Phys. 353, 37–47 (2015)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    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, 3677–3694 (2016)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Yang, Y., Liu, X., Wang, J., Jing, J.: Quantum metrology of phase for accelerated two-level atom coupled with electromagnetic field with and without boundary. Quantum Inf. Process. 17(3), 54 (2018)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    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)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    Compagno, G., Passante, R., Persico, F.: Atom-Field Interactions and Dressed Atoms. Cambridge University Press, Cambridge (1995)CrossRefGoogle Scholar
  39. 39.
    Cramér, H.: Mathematical Methods of Statistics. Princeton University, Princeton (1946)zbMATHGoogle Scholar
  40. 40.
    Gorini, V., Andrzej, K., Ennackal, C.G.S.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821–825 (1976)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Benatti, F., Floreanini, R.: Controlling entanglement generation in external quantum fields. J. Opt. B: Quantum Semiclassical Opt. 7, S429 (2005)ADSCrossRefGoogle Scholar
  42. 42.
    Benatti, F., Floreanini, R., Piani, M.: Environment induced entanglement in Markovian dissipative dynamics. Phys. Rev. Lett. 91, 070402 (2003)ADSCrossRefGoogle Scholar
  43. 43.
    Bell, J.S., Leinaas, J.M.: Electrons as accelerated thermometers. Nuclear Phys. B 212, 131–150 (1983)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 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 ApplicationsHunan Normal UniversityChangshaPeople’s Republic of China
  2. 2.School of ScienceXi’an University of Posts and TelecommunicationsXi’anPeople’s Republic of China

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