Skip to main content
Log in

Classical propagators of quadratic quantum systems

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

A new quantum mechanical formalism based on the probability representation of states is applied to ions in traps and stimulated Raman scattering. Explicit expressions are found for the classical propagators of a free particle, a harmonic oscillator, an ion in the Paul trap, an ion in the Penning trap, and stimulated Raman scattering.

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. S. Mancini, V. I. Man'ko, and P. Tombesi,Phys. Lett. A,213, 1 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. S. Mancini, V. I. Man'ko, and P. Tombesi,Found. Phys.,27, 801 (1997).

    Article  MathSciNet  Google Scholar 

  3. O. V. Manko and V. I. Manko,J. Russ. Laser Res.,18, 407 (1997).

    Article  Google Scholar 

  4. S. Mancini, V. I. Man'ko, and P. Tombesi,Quantum Semiclass. Opt.,7, 615 (1995).

    Article  ADS  Google Scholar 

  5. K. Vogel and H. Risken,Phys. Rev. A,40, 2847 (1989).

    Article  ADS  Google Scholar 

  6. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani,Phys. Rev. Lett.,70, 1244 (1993).

    Article  ADS  Google Scholar 

  7. V. V. Dodonov and V. I. Man'ko,Invariants and Evolution of Nonstationary Quantum Systems (Proc. Lebedev Physical Inst., Vol. 183), Nova Science, New York (1989).

    Google Scholar 

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

    Google Scholar 

  9. O. V. Man'ko,Phys. Lett. A,228, 29 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. P. J. Bardroff, C. Leichte, G. Schrade, and W. P. Schleich,Phys. Rev. Lett.,77, 2198 (1996).

    Article  ADS  Google Scholar 

  11. R. J. Glauber, “The quantum mechanics of particles in time-dependent quadrupole fields,” in:Recent Developments in Quantum Optics (Proc. Intl. Conf. on Quantum Optics, Hyderabad, India, January 1991) (R. Inguva, ed.), Plenum, New York (1993), p. 1.

    Google Scholar 

  12. G. Schrade, V. I. Man'ko, W. P. Schleich, and R. J. Glauber,Quantum Semiclass. Opt.,7, 307 (1995).

    Article  ADS  Google Scholar 

  13. I. A. Malkin and V. I. Man'ko,Phys. Lett. A,32, 243 (1970).

    Article  ADS  Google Scholar 

  14. E. Schrödinger,Sitzunugsber. Preuss. Akad. Wiss.,24, 296 (1930).

    Google Scholar 

  15. V. V. Dodonov, O. V. Man'ko, and V. I. Man'ko,Phys. Rev. A,50, 813 (1994).

    Article  ADS  Google Scholar 

  16. O. V. Man'ko, “Symplectic tomography of nonclassical states of a trapped ion”, Preprint IC/96/39, ICTP, Trieste (1996); Preprint quant-ph/9604018 (1996);J. Russ. Laser Res.,17. 439 (1996); “Symplectic tomography of Schrödinger cat states of a trapped ion”, in:Proc. Second Intl. Symp. on Fundamental Problems in Quantum Mechanics (Oviedo, Spain, July 1996) (M. Ferrero and A. van der Merwe, eds.), Kluwer, Dordrecht (1997), p. 225; “Symplectic tomography of nonlinear Schrödinger cats of a trapped ion”, in:Proc. Fifth Intl. Conf. “Squeezed States and Uncertainty Relations” (Balatonfured, Hungary, May 1997) (D. Han, J. Janszky, Y. S. Kim. and V. I. Man'ko, eds.) (NASA/CP-1998-206855), Goddard Space Flight Center, Greenbelt, Maryland (1998). p. 309.

  17. L. S. Brown and G. Gabrielse,Rev. Mod Phys.,58, 233 (1986).

    Article  ADS  Google Scholar 

  18. O. Castanos, S. Hacyan, R. Lopez-Pena, and V. I. Man'ko,J. Phys. A,31, 1227 (1998).

    Article  MATH  ADS  Google Scholar 

  19. S. Kielich,Progr. Opt.,20, 156 (1983).

    Google Scholar 

  20. M. G. Raymer and I. A. Walmsley,Progr. Opt.,28, 182 (1990).

    Google Scholar 

  21. O. V. Man'ko and N. V. Tcherniega, “Photon distribution function for Stokes wave for stimulated Raman scattering”, Preprint IC/97/35, ICTP, Trieste (1997);J. Russ. Laser Res.,18, 479 (1997).

    Google Scholar 

  22. D. F. Walls,Z. Phys.,237, 224 (1970).

    Article  Google Scholar 

  23. D. F. Walls,Z. Phys.,234, 331 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2, pp. 285–296, November, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Man'ko, O.V. Classical propagators of quadratic quantum systems. Theor Math Phys 121, 1496–1505 (1999). https://doi.org/10.1007/BF02557220

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02557220

Keywords

Navigation