Skip to main content
SpringerLink
Log in

Invariant-algebraic approach to problems of quantum optics

  • Published:
Journal of Soviet Laser Research Aims and scope

Abstract

A general approach is formulated for analyzing algebraic models of quantum composite systems with an internal symmetry described by group G. The case G = SU(2) is examined in detail as applied to the analysis of polarization invariance in quantum optics. A new class of fully depolarizable quantum states of light (scalar biphotons) is defined and investigated. Certain interactions of scalar biphoton light with material media are considered in the context of Dicke and Jaynes-Cummings models.

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

Literature Cited

  1. R. H. Dicke, Phys. Rev.,93, No. 1, 99–110 (1954).

    Google Scholar 

  2. I. A. Malkin and V. I. Man'ko, Dynamic Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  3. A. M. Perelomov, Generalized Coherent States and Their Applications [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  4. V. V. Dodonov and V. I. Man'ko, “Invariants and evolution of nonstationary quantum systems,” Trudy FIAN,183, Nauka, Moscow (1987).

    Google Scholar 

  5. V. P. Karasev and L. A. Shelepin, Trudy FIAN,144, 124–140 (1984).

    Google Scholar 

  6. V. P. Karasev, Trudy FIAN,191, 120–132 (1989).

    Google Scholar 

  7. V. V. Dodonov, V. I. Man'ko, and S. M. Chumakov, Trudy FIAN,176, 57–95 (1986).

    Google Scholar 

  8. V. P. Karassiov, S. V. Prants, and V. I. Puzyrevsky, in: Interaction of the Electromag. Rad. with Con. Matter, World Science, Singapore (1990).

    Google Scholar 

  9. M. G. Kozerovskii and S. M. Chumakov, Trudy FIAN,191, 150–170 (1989).

    Google Scholar 

  10. G. Dattoli and A. Torre, J. Math. Phys.,28, No. 3, 618–621 (1987).

    Google Scholar 

  11. C. Buzano, M. G. Rasetti, and M. L. Rastello, Phys. Rev. Lett.,62, No. 2, 137–139 (1989).

    Google Scholar 

  12. L. C. Biedenharn, J. Phys.,A22, No. 18, L873-L878 (1989).

    Google Scholar 

  13. H. C. Myung and A. Sagle, Hadronic J.,10, No. 1, 35–51 (1987).

    Google Scholar 

  14. K. B. Wolf, Ann. Phys. (N.Y.),172, No. 1, 1–25 (1986).

    Google Scholar 

  15. C. Aragone and F. Zypman, J. Phys.,A19, No. 12, 2267–2279 (1986).

    Google Scholar 

  16. V. P. Karasev, Kratk. Soobshch. Fiz. FIAN, No. 9, 3–6 (1988).

    Google Scholar 

  17. V. P. Karassiov, in: Topological Phases in Quantum Theory, World Science, Singapore (1989), pp. 400–408.

    Google Scholar 

  18. V. P. Karassiov, J. Phys.,A20, No. 15, 5061–5069 (1987).

    Google Scholar 

  19. R. A. Brandt and O. W. Greenberg, J. Math. Phys.,10, No. 5, 1168–1176 (1969).

    Google Scholar 

  20. Y. Ohnuki and S. Kamefuchi, Quantum Field Theory and Para-statistics, University Press, Tokyo (1982).

    Google Scholar 

  21. B. I. Spasskii and A. V. Moskovskii, Usp. Fiz. Nauk,142, No. 4, 599–617 (1984).

    Google Scholar 

  22. V. I. Strazhev and P. L. Shkol'nikov, Izv. Vyssh. Uchebn. Zaved., Fiz.,25, No. 7, 77–80 (1982).

    Google Scholar 

  23. V. P. Karasev and V. I. Puzyrevsky, J. Sov. Laser Res.,10, 229–241 (1990).

    Google Scholar 

  24. H. Weyl, Classical Groups, Princeton Univ. Press (1939).

  25. V. P. Karasev, in: Group-Theoretical Methods in Fundamental and Applied Physics [in Russian], Nauka, Moscow (1988), pp. 54–72.

    Google Scholar 

  26. G. G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley (1972).

  27. Yu. A. Bakhturin, Identities in Lie Algebra [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  28. A. Barut and R. Raczka, Theory of Group Representations and Its Applications [Russian translation], Mir, Moscow (1980).

    Google Scholar 

  29. K. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw (1980).

  30. R. Le Blanc and D. J. Rowe, J. Math. Phys.,28, No. 6, 1231–1236 (1987).

    Google Scholar 

  31. J. Deenen and C. Quesne, J. Math. Phys.,25, No. 8, 2354–2366 (1984).

    Google Scholar 

  32. E. S. Fradkin and G. A. Vilkovisky, Phys. Lett., Vol. B%%, No. 2, 224–226 (1975).

    Google Scholar 

  33. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics, Pergamon (in press).

  34. D. N. Klyshko, Usp. Fiz. Nauk,154, No. 1, 133–152 (1988).

    Google Scholar 

  35. J. Perina, Quantum Statistics of Linear and Nonlinear Optical Phenomena [Russian translation], Mir (1987).

  36. S. Ya. Kilin, Quantum Optics [in Russian], Nauka i Tekhnika, Minsk (1990).

    Google Scholar 

  37. R. Simon and N. Mukunda, Phys. Lett.,A143, 165–169 (1990).

    Google Scholar 

  38. P. Roman, Nuovo Cim.,13, No. 5, 974–982 (1959).

    Google Scholar 

  39. H. Fearn and R. Loudon, Opt. Commun.,64, No. 6, 485–490 (1987).

    Google Scholar 

  40. H. P. Yuen, Phys. Lett.,A51, No. 1, 1–22 (1975).

    Google Scholar 

  41. B. Yurke, S. McCall, and J. R. Klauder, Phys. Rev.,A33, No. 6, 4033–4054 (1986).

    Google Scholar 

  42. D. Yu. Kuznetsov, Kratk. Soobshch. Fiz. FIAN, No. 12, 31–32 (1989).

    Google Scholar 

  43. Y. Ahronov and J. M. Knight, Phys. Rev. Lett.,54, No. 15, 1920–1923 (1980).

    Google Scholar 

  44. Y. Yamamoto and H. A. Haus, Rev. Mod. Phys.,58, No. 4, 1001–1020 (1986).

    Google Scholar 

  45. G. M. D'Ariano and N. Sterpi, Phys. Rev.,A39, No. 4, 1860–1868 (1989).

    Google Scholar 

Download references

Authors
  1. V. P. Karasev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Landsberg Optics Division, Lebedev Physics Institute. Translated from Preprint No. 137 of the Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karasev, V.P. Invariant-algebraic approach to problems of quantum optics. J Russ Laser Res 12, 147–164 (1991). https://doi.org/10.1007/BF01126635

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01126635

Keywords

Search

Navigation