Skip to main content
Log in

Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

We consider dynamic symmetry, quantum control, and dynamic chaos of atoms moving in high-quality cavities. We review the group-theoretical approach to solve the evolution equations in the cavity quantum electrodynamics and control the quantum evolution in a micromaser device. Taking into account the photon recoil effect, we study nonlinear dynamics of the fundamental interactions between two-level atoms and a quantized cavity field. The strongly coupled atom–field system is treated as a quantum–classical hybrid with dynamically coupled quantum and classical degrees of freedom. Interaction of the purely quantum atom–field system with the classical translational atomic degree of freedom results in emergence of classical dynamic chaos from quantum electrodynamics. That chaos is shown to manifest itself in some ranges of the control parameters in the exponential sensitivity of quantum atomic variables to small variations in the initial conditions and in the appearance of dynamic atomic fractals. We discuss how to observe this effect in real experiments. Our findings establish a quantum–classical correspondence in the cavity quantum electrodynamics.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. L. Berman (Ed.), Cavity Quantum Electrodynamics, Academic Press, Boston (1994).

    Google Scholar 

  2. E. T. Jaynes and E. W. Cummings, Proc. IEEE, 51, 89 (1963).

    Article  Google Scholar 

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

    Google Scholar 

  4. V. P. Karassiov and L. A. Shelepin, Proceedings of the Lebedev Physical Institute [in Russian], Nauka, Moscow (1982), Vol. 144, p. 124.

    Google Scholar 

  5. V. P. Karassiov and L. A. Shelepin, Izv. Akad. Nauk SSSR, Ser. Fiz., 46, 997 (1982).

  6. F. T. Hioe and C. E. Carroll, Phys. Rev. A, 32, 1541 (1985).

    Article  ADS  Google Scholar 

  7. V. V. Dodonov, V. I. Man’ko, and S. M. Chumakov, Proceedings of the Lebedev Physical Institute [in Russian], Nauka, Moscow (1986), Vol. 176, p. 57.

    MathSciNet  Google Scholar 

  8. V. V. Dodonov and V. I. Man’ko, Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the Lebedev Physical Institute, Nova Science, Commack, New York (1987), Vol. 183.

  9. S. V. Prants, J. Phys. A: Math. Gen., 19, 3457 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  10. S. V. Prants and L. S. Yacoupova, Zh. ´ Eksp. Teor. Fiz., 97, 1140 (1990).

  11. S. V. Prants, Phys. Lett. A, 144, 225 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  12. S. V. Prants and L. S. Yacoupova, J. Mod. Opt., 39, 961 (1992).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. L. E. Kon’kov and S. V. Prants, J. Math. Phys., 37, 1204 (1996).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. S. V. Prants, J. Russ. Laser Res., 17, 539 (1996).

    Article  Google Scholar 

  15. S. V. Prants, J. Russ. Laser Res., 18, 69 (1997).

    Article  Google Scholar 

  16. M. Ban, Phys. Rev. A, 47, 5093 (1993).

    Article  MathSciNet  ADS  Google Scholar 

  17. S. V. Prants, J. Phys. A: Math. Theor., 44, 265101 (2011).

    Article  ADS  Google Scholar 

  18. L. E. Kon’kov and S. V. Prants, JETP Lett., 65, 833 (1997) [Pis’ma Zh´ETF, 65, 801 (1997)].

  19. S. V. Prants, L. E. Kon’kov, and I. L. Kirilyuk, Phys. Rev. E, 60, 335 (1999).

    Article  ADS  Google Scholar 

  20. S. V. Prants, Phys. Rev. E, 61, 1386 (2000).

    Article  ADS  Google Scholar 

  21. S. V. Prants and L. E. Kon’kov, Phys. Rev. E, 61, 3632 (2000).

    Article  ADS  Google Scholar 

  22. S. V. Prants and L. E. Kon’kov, JETP Lett., 73, 180 (2001) [Pis’ma Zh´ETF, 73, 200 (2001)].

  23. S. V. Prants, JETP Lett., 75, 651 (2002) [Pis’ma Zh´ETF, 75, 777 (2002)].

  24. S. V. Prants and V. Yu. Sirotkin, Phys. Rev. A, 64, 033412 (2001).

    Article  ADS  Google Scholar 

  25. V. Yu. Argonov and S. V. Prants, J. Exp. Theor. Phys., 96, 832 (2003) [Zh. ´ Eksp. Teor. Fiz., 123, 946 (2003)].

  26. V. Yu. Argonov and S. V. Prants, J. Russ. Laser Res., 27, 360 (2006).

  27. V. Yu. Argonov and S. V. Prants, Phys. Rev. A, 75, 063428 (2007).

  28. V. Yu. Argonov and S. V. Prants, Phys. Rev. A, 78, 043413 (2008).

  29. A. Draght, J. Opt. Soc. Am, 72, 372 (1982).

    Article  ADS  Google Scholar 

  30. V. I. Man’ko, in: J. Sanchez and K.-B. Wolf (Eds.), Lie Methods in Optics., Lecture Notes in Physics, Springer, New York (1985), Vol. 250.

  31. S. V. Prants, Mod. Phys. Lett.A, 8, 2671 (1993).

  32. S. V. Prants, Zh. Éksp. Teor. Fiz., 104, 2590 (1993).

    Google Scholar 

  33. B. V. Chirikov, Phys. Rep., 52, 263 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  34. G. M. Zaslavsky, Phys. Rep., 80, 157 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  35. D. V. Makarov, M. Yu. Uleysky, and S. V. Prants, Chaos, 14, 79 (2004).

    Article  ADS  Google Scholar 

  36. A. L. Virovlyansky, D. V. Makarov, and S. V. Prants, Phys.-Usp., 55, 18 (2012).

  37. J. Wei and E. Norman, J. Math. Phys., 4, 576 (1963).

    MathSciNet  ADS  Google Scholar 

  38. A. I. Maltsev, Dokl. Acad. Sci. USSR, 36, 42 (1942).

    Google Scholar 

  39. L. Landau, Phys. Zh. Sowjun., 2, 46 (1932).

    Google Scholar 

  40. C. Zener, Proc. Roy. Soc. London A, 137, 696 (1932).

    Article  ADS  Google Scholar 

  41. S. V. Prants and L. S. Yakoupova, Opt. Spektrosk., 69, 964 (1990).

    Google Scholar 

  42. S. V. Prants, Opt. Comm., 125, 222 (1996).

    Article  ADS  Google Scholar 

  43. S. V. Prants, Opt. Spektrosk., 77, 173 (1994).

    Google Scholar 

  44. M. Uleysky, L. Kon’kov, and S. Prants, Commun. Nonlinear Sci. Numer. Simul., 8, 329 (2003).

    Article  ADS  MATH  Google Scholar 

  45. M. V. Budyansky, M. Yu. Uleysky, and S. V. Prants, J. Exp. Theor. Phys., 99, 1018 (2004) [Zh. ´ Eksp. Teor. Fiz., 126, 1167 (2004)].

  46. M. V. Budyansky, M. Yu. Uleysky, and S. V. Prants, Physica D, 195, 369 (2004).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. S. V. Prants, M. V. Budyansky, V. I. Ponomarev, and M. Yu. Uleysky, Ocean Modell., 38, 114 (2011).

    Article  ADS  Google Scholar 

  48. S. V. Prants and M. Yu. Uleysky, Phys. Lett. A, 309, 357 (2003).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. S. V. Prants, M. Yu. Uleysky, and V. Yu. Argonov, Phys. Rev. A, 73, 023807 (2006).

    Article  ADS  Google Scholar 

  50. S. V. Prants, Commun. Nonlinear Sci. Numer. Simul., 12, 19 (2007).

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sergey V. Prants.

Additional information

Manuscript submitted by the author in English on April 26, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prants, S.V. Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities. J Russ Laser Res 36, 211–227 (2015). https://doi.org/10.1007/s10946-015-9494-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10946-015-9494-z

Keywords

Navigation