Skip to main content
SpringerLink
Log in

Nonclassical properties and quantum resources of hierarchical photonic superposition states

  • Atoms, Molecules, Optics
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

We motivate and introduce a class of “hierarchical” quantum superposition states of N coupled quantum oscillators. Unlike other well-known multimode photonic Schrödinger-cat states such as entangled coherent states, the hierarchical superposition states are characterized as two-branch superpositions of tensor products of single-mode Schrödinger-cat states. In addition to analyzing the photon statistics and quasiprobability distributions of prominent examples of these nonclassical states, we consider their usefulness for highprecision quantum metrology of nonlinear optical Hamiltonians and quantify their mode entanglement. We propose two methods for generating hierarchical superpositions in N = 2 coupled microwave cavities, exploiting currently existing quantum optical technology for generating entanglement between spatially separated electromagnetic field modes.

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. D. Greenberger, M. Horne, and A. Zeilinger, in Bell’s Theorem, Quantum Theory, and Conceptions of the Universe (Kluwer, Dordrecht, The Netherlands, 1989), p. 69.

    Book  Google Scholar 

  2. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

    MATH  Google Scholar 

  3. P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezzé, and A. Smerzi, Phys. Rev. A: At., Mol., Opt. Phys. 85, 022321 (2012).

    Article  ADS  Google Scholar 

  4. G. Tuth, Phys. Rev. A: At., Mol., Opt. Phys. 85, 022322 (2012).

    Article  ADS  Google Scholar 

  5. V. Dodonov and V. Man’ko, Theory of Nonclassical States of Light (Taylor and Francis, London, 2003).

    Google Scholar 

  6. B. Sanders, J. Phys. A: Math. Theor. 45, 244002 (2012).

    Article  ADS  Google Scholar 

  7. G. Najarbashi and Y. Maleki, Int. J. Theor. Phys. 50, 2601 (2011).

    Article  MathSciNet  Google Scholar 

  8. P. Munhoz, F. L. Semião, A. Vidiella-Barranco, and J. Roversi, Phys. Lett. A 372, 3580 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  9. T. Ralph, A. Gilchrist, G. Milburn, W. Munro, and S. Glancy, Phys. Rev. A: At., Mol., Opt. Phys. 68, 042319 (2003).

    Article  ADS  Google Scholar 

  10. A. Gilchrist, K. Nemoto, W. Munro, T. Ralph, S. Glancy, S. Braunstein, and G. Milburn, J. Opt. B: Quantum Semiclass. Opt. 6, S828 (2004).

    Article  ADS  Google Scholar 

  11. V. Dodonov, I. Malkin, and V. Man’ko, Physica (Amsterdam) 72, 597 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  12. T. Volkoff and K. Whaley, Phys. Rev. A: At., Mol., Opt. Phys. 91, 012122 (2014).

    Article  ADS  Google Scholar 

  13. D. Trifonov, J. Phys. A: Math. Gen. 31, 5673 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  14. N. Ansari and V. Man’ko, Phys. Rev. A: At., Mol., Opt. Phys. 50, 1942 (1994).

    Article  ADS  Google Scholar 

  15. V. Dodonov and L. de Souza, J. Russ. Laser Res. 28, 453 (2007).

    Article  Google Scholar 

  16. S. van Enk and O. Hirota, Phys. Rev. A: At., Mol., Opt. Phys. 64, 022313 (2001).

    Article  ADS  Google Scholar 

  17. X. Wang, J. Phys. A: Math. Gen. 35, 165 (2002).

    Article  ADS  Google Scholar 

  18. H. Jeong, M. Kim, and J. Lee, Phys. Rev. A: At., Mol., Opt. Phys. 64, 052308 (2001).

    Article  ADS  Google Scholar 

  19. T. Volkoff and K. Whaley, Phys. Rev. A: At., Mol., Opt. Phys. 90, 062122 (2014).

    Article  ADS  Google Scholar 

  20. V. Bužek, J. Mod. Opt. 37, 303 (1990).

    Article  ADS  Google Scholar 

  21. K. Cahill and R. Glauber, Phys. Rev. 177, 1882 (1969).

    Article  ADS  Google Scholar 

  22. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).

    Book  Google Scholar 

  23. V. Bargmann, Commun. Pure Appl. Math. 14, 187 (1961).

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  25. A. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, The Netherlands, 1982).

    MATH  Google Scholar 

  26. M. Paris, Int. J. Quant. Inf. 7, 125 (2009).

    Article  Google Scholar 

  27. F. Fröwis and W. Dür, New J. Phys. 14, 093039 (2012).

    Article  Google Scholar 

  28. V. Bužek and P. Knight, in Progress in Optics: XXXIV (Elsevier, Amsterdam, The Netherlands, 1995), p. 1.

    Google Scholar 

  29. M. Genoni, M. Paris, G. Adesso, H. Nha, P. Knight, and M. Kim, Phys. Rev. A: At., Mol., Opt. Phys. 87, 012107 (2013).

    Article  ADS  Google Scholar 

  30. G. Chiribella, G. D’Ariano, and M. Sacchi, Phys. Rev. A: At., Mol., Opt. Phys. 73, 062103 (2006).

    Article  ADS  Google Scholar 

  31. C. Brif, Ann. Phys. (N. Y.) 251, 180 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  32. F. Lastra, G. Romero, C. Lupez, N. Zagury, and J. Retamal, Opt. Comm. 283, 3825 (2010).

    Article  ADS  Google Scholar 

  33. H. Jeong and M. Kim, arXiv:0111015v2.

  34. M. S. Kim, W. Son, V. Bužek, and P. L. Knight, Phys. Rev. A: At., Mol., Opt. Phys. 65, 032323 (2002).

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  36. E. Feld’man and M. Yurishchev, JETP Lett. 90, 70 (2009).

    Article  ADS  Google Scholar 

  37. S. Barnett and P. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, New York, 1997).

    MATH  Google Scholar 

  38. A. Ourjoumtsev, F. Ferreyrol, R. Tualle-Brouri, and P. Grangier, Nat. Phys. 5, 189 (2009).

    Article  Google Scholar 

  39. B. Vlastakis, G. Kirchmair, Z. Leghtas, S. Nigg, L. Frunzio, S. Girvin, M. Mirrahimi, M. Devoret, and R. Schoelkopf, Science (Washington) 342, 607 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  40. S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, Nature (London) 455, 510 (2008).

    Article  ADS  Google Scholar 

  41. P. Milman, A. Auffeves, F. Yamaguchi, M. Brune, J. Raimond, and S. Haroche, Eur. Phys. J. D 32, 233 (2005).

    Article  ADS  Google Scholar 

  42. V. Albert, S. Krastanov, C. Shen, R.-B. Liu, R. Schoelkopf, M. Mirrahimi, M. Devoret, and L. Jiang, arXiv:1503.00194v2.

  43. A. Holevo, Quantum Systems, Channels, Information: A Mathematical Introduction (De Gruyter, Berlin, 2012).

    Book  MATH  Google Scholar 

  44. M. Sasaki, T. Usuda, O. Hirota, and A. Holevo, PPhys. Rev. A: At., Mol., Opt. Phys. 53, 1273 (1996).

    Article  ADS  Google Scholar 

  45. Q.-P. Su, C.-P. Yang, and S.-B. Zheng, PSci. Rep. 4, 3898 (2014).

    ADS  Google Scholar 

  46. F. Fröwis and W. Dür, Phys. Rev. Lett. 106, 110402 (2011).

    Article  ADS  Google Scholar 

  47. F. Fröwis and W. Dür, Phys. Rev. Lett. 85, 052329 (2012).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, University of California, Berkeley, California, 94720, USA

    T. J. Volkoff

Authors
  1. T. J. Volkoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. J. Volkoff.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Volkoff, T.J. Nonclassical properties and quantum resources of hierarchical photonic superposition states. J. Exp. Theor. Phys. 121, 770–784 (2015). https://doi.org/10.1134/S1063776115110187

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776115110187

Keywords

Search

Navigation