Skip to main content
Log in

Schrödinger Picture Analysis of the Beam Splitter: an Application of the Janszky Representation

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

The Janszky representation constructs quantum states of a field mode as a superposition of coherent states on a line in the complex plane. We show that this provides a natural Schrödinger picture description of the interference between a pair of modes at a beam splitter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. Grangier, G. Roger, and A. Aspect, Europhys. Lett., 1, 173 (1986).

    Article  ADS  Google Scholar 

  2. R. E. Slusher, L. W. Hollberg, B. Yurke, et al., Phys. Rev. Lett., 55, 2409 (1985).

    Article  ADS  Google Scholar 

  3. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, et al., Phys. Rev. Lett., 57, 691 (1986).

    Article  ADS  Google Scholar 

  4. L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, Phys. Rev. Lett., 57, 2520 (1986).

    Article  ADS  Google Scholar 

  5. R. Loudon and P. L. Knight, J. Mod. Opt., 34, 709 (1987).

    Article  ADS  Google Scholar 

  6. H.-A. Bachor, A Guide to Experiments in Quantum Optics, Wiley-VCH, Weinhem (1998).

    MATH  Google Scholar 

  7. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett., 59, 2044 (1987).

    Article  ADS  Google Scholar 

  8. H. Fearn and R. Loudon, J. Opt. Soc. Am. B, 6, 917 (1989).

    Article  ADS  Google Scholar 

  9. H. Fearn and R. Loudon, Opt. Commun., 64, 485 (1987).

    Article  ADS  Google Scholar 

  10. R. Loudon, The Quantum Theory of Light, Oxford University Press (2000).

  11. S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics, Oxford University Press (1997).

  12. R. J. Glauber, Phys. Rev. Lett., 10, 84 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  13. E. C. G. Sudarshan, Phys. Rev. Lett., 10, 277 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  14. R. J. Glauber, Phys. Rev., 130, 2529 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  15. R. J. Glauber, Phys. Rev., 131, 2766 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  16. J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics, Benjamin, New York (1968).

    Google Scholar 

  17. H. M. Nussenzveig, Introduction to Quantum Optics, Gordon & Breach, London (1973).

    Google Scholar 

  18. R. J. Glauber, Quantum Theory of Optical Coherence, Wiley-VCH, Weinheim (2007).

    Google Scholar 

  19. J. Janszky and A. Vinogradov, Phys. Rev. Lett., 64, 2771 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  20. M. Orszag, R. Ramĺrez, J. C. Retamal, and S. Saavedra, Phys. Rev. Lett., 68, 3815 (1992).

    Article  ADS  Google Scholar 

  21. J. Janszky, P. Adam, and A. Vinogradov, Phys. Rev. Lett., 68, 3816 (1992).

    Article  ADS  Google Scholar 

  22. J. Jansky, P. Domokos, and P. Adam, Phys. Rev. A, 48, 2213 (1993).

    Article  ADS  Google Scholar 

  23. P. Domokos, P. Adam, and J. Janszky, Phys. Rev. A, 50, 4293 (1994).

    Article  ADS  Google Scholar 

  24. J. Janszky, P. Domokos, S. Szabo, and P. Adam, Phys. Rev. A, 51, 4193 (1995).

    Article  ADS  Google Scholar 

  25. B. R. Mollow, Phys. Rev. A, 12, 1919 (1975).

    Article  ADS  Google Scholar 

  26. D. T. Pegg, in: D. F. Walls and J. D. Harvey (Eds.), Laser Physics, Academic, New York (1980).

  27. P. L. Knight and P. M. Radmore, Phys. Rev. A, 26, 676 (1982).

    Article  ADS  Google Scholar 

  28. E. Knill, R. Laflamme, and G. J. Milburn, Nature, 409, 46 (2001).

    Article  ADS  Google Scholar 

  29. I. Białynicki-Birula, in: F. Haake, L. M. Narducci, and D. F. Walls (Eds.), Coherence, Cooperation and Fluctuations, Cambridge University Press (1986).

  30. I. Białynicki-Birula and J. Mycielski, Phys. Scr., 20, 539 (1979).

    Article  ADS  Google Scholar 

  31. Fan Hong-Yi, Phys. Rev. A, 41, 1526 (1990).

    Article  ADS  Google Scholar 

  32. G. Yeoman and S. M. Barnett, J. Mod. Opt., 40, 1479 (1993).

    Article  Google Scholar 

  33. S. M. Barnett and S. J. D. Phoenix, Phys. Rev. A, 40, 2404 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  34. S. Haroche and J.-M. Raimond, Exploring the Quantum, Oxford University Press (2006) and references therein.

  35. W. H. Zurek, Nature, 412, 712 (2001).

    Article  ADS  Google Scholar 

  36. M. Ringbauer, T. J. Wienhold, L. A. Howard, et al., New J. Phys., 20, 053042 (2018).

    Article  ADS  Google Scholar 

  37. D. T. Pegg and S. M. Barnett, Europhys. Lett., 6, 483 (1988).

    Article  ADS  Google Scholar 

  38. D. T. Pegg and S. M. Barnett, Phys. Rev. A, 39, 1665 (1989).

    Article  ADS  Google Scholar 

  39. S. M. Barnett and D. T. Pegg, J. Mod. Opt., 36, 7 (1989).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stephen M. Barnett.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barnett, S.M. Schrödinger Picture Analysis of the Beam Splitter: an Application of the Janszky Representation. J Russ Laser Res 39, 340–348 (2018). https://doi.org/10.1007/s10946-018-9727-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10946-018-9727-z

Keywords

Navigation