Skip to main content
SpringerLink
Log in

Quantum phase estimations with spin coherent states superposition

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

Abstract

The quantum metrological performance of spin coherent states superposition is considered, and conditions for measurements with the Heisenberg-limit (HL) precision are identified. It is demonstrated that the choice of the parameter-generating operator can lead to physically different estimation outcomes. In particular, closed-form analytical descriptions for the performance of spin cat states are derived. These findings show the routes to careful control of parameters necessary for achieving HL precision and provide insightful information on the geometry of the specific coherent state superposition and its relevance to the performance of the states for parameter estimations.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. V. Giovannetti, S. Lloyd, L. Maccone, Advances in quantum metrology. Nature Photonic 5, 222 (2011)

    Article  ADS  Google Scholar 

  2. P.R. Bevington, D.K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 2003)

    Google Scholar 

  3. M. Holland, K. Burnett, Interferometric detection of optical phase shifts at the heisenberg limit. Phys. Rev. Lett. 71, 1355 (1993)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. S. Pirandola, B.R. Bardhan, T. Gehring, C. Weedbrook, S. Lloyd, Advances in photonic quantum sensing. Nature Photon. 12, 724–733 (2018)

    Article  ADS  Google Scholar 

  6. B.P. Abbott et al., Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016)

  7. T. Ono, R. Okamoto, S. Takeuchi, An entanglement-enhanced microscope. Nature Commun. 4, 3426 (2013)

    Google Scholar 

  8. P. Cappellaro, J. Emerson, N. Boulant, C. Ramanathan, S. Lloyd, D.G. Cory, Entanglement assisted metrology. Phys. Rev. Lett. 94, 020502 (2005)

  9. Y. Maleki, A.M. Zheltikov, Recovery of maximally entangled quantum states by weak-measurement reversal. Laser Physics Letters 15, 056201 (2018)

  10. G.Y. Xiang, B.L. Higgins, D.W. Berry, H.M. Wiseman, G.J. Pryde, Entanglement-enhanced measurement of a completely unknown optical phase. Nature Photonic 5, 43–47 (2011)

    Article  ADS  Google Scholar 

  11. A.N. Boto, P. Kok, D.S. Abrams, S.L. Braunstein, C.P. Williams, J.P. Dowling, Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit. Phys. Rev. Lett. 85, 2733–2736 (2000)

    Article  ADS  Google Scholar 

  12. J.P. Dowling, Quantum optical metrology—the lowdown on high-N00N states. Contemp. Phys. 49, 125–143 (2008)

    Article  ADS  Google Scholar 

  13. I. Afek, O. Ambar, Y. Silberberg, High-NOON states by mixing quantum and classical light. Science 328, 879 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  14. Y. Maleki, A.M. Zheltikov, Generating maximally-path-entangled number states in two spin ensembles coupled to a superconducting flux qubit. Phys. Rev. A 97, 012312 (2018)

  15. Y. Maleki, A.M. Zheltikov, A high-N00N output of harmonically driven cavity QED. Sci. Rep. 9, 16780 (2019)

    Article  ADS  Google Scholar 

  16. B.C. Sanders, C.C. Gerry, Connection between the NOON state and a superposition of SU(2) coherent states. Phys. Rev. A 90, 045804 (2014)

  17. J. Huang, M. Zhuang, B. Lu, Y. Ke, C. Lee, Achieving Heisenberg-limited metrology with spin cat states via interaction-based readout. Phys. Rev. A 98, 012129 (2018)

  18. J. Huang, X. Qin, H. Zhong, Y. Ke, C. Lee, Quantum metrology with spin cat states under dissipation. Sci. Rep. 5, 17894 (2015)

    Article  ADS  Google Scholar 

  19. Y. Maleki, A.M. Zheltikov, A spin cat-state family for Heisenberg-limit metrology. JOSA B 37, 1021–1026 (2020)

    Article  ADS  Google Scholar 

  20. G.S. Agarwal, R.R. Puri, R.P. Singh, Atomic Schrodinger cat states. Phys. Rev. A 56, 2249 (1997)

    Article  ADS  Google Scholar 

  21. B. Lücke et al., Twin matter waves for interferometry beyond the classical limit. Science 334, 773–776 (2011)

    Article  ADS  Google Scholar 

  22. H. Strobel et al., Fisher information and entanglement of non-Gaussian spin states. Science 345, 424–427 (2014)

    Article  ADS  Google Scholar 

  23. C. Sommer, G. Pupillo, N. Takei, S. Takeda, A. Tanaka, K. Ohmori, C. Genes, Time-domain Ramsey interferometry with interacting Rydberg atoms. Phys. Rev. A 94, 053607 (2016)

  24. C. Sturm, D. Tanese, H.S. Nguyen, H. Flayac, E. Galopin, A. Lematre, I. Sagnes, D. Solnyshkov, A. Amo, G. Malpuech, J. Bloch, All-optical phase modulation in a cavity-polariton mach-Zehnder interferometer. Nat. Commun. 5, 3278 (2014)

    Article  ADS  Google Scholar 

  25. G. S. Agarwal, Quantum Optics (Cambridge University Press, 2013)

  26. Y. Maleki, A. Maleki, Entangled multi-mode spin coherent states of trapped ions. J. Opt. Soc. Am. B 35, 1211–1217 (2018)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, Texas A&M University, College Station, Texas, 77843-4242, USA

    Yusef Maleki

Authors
  1. Yusef Maleki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yusef Maleki.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maleki, Y. Quantum phase estimations with spin coherent states superposition. Eur. Phys. J. Plus 136, 1028 (2021). https://doi.org/10.1140/epjp/s13360-021-02020-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-02020-8

Search

Navigation