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.
Similar content being viewed by others
References
S. Mancini, V. I. Man'ko, and P. Tombesi,Phys. Lett. A,213, 1 (1996).
S. Mancini, V. I. Man'ko, and P. Tombesi,Found. Phys.,27, 801 (1997).
O. V. Manko and V. I. Manko,J. Russ. Laser Res.,18, 407 (1997).
S. Mancini, V. I. Man'ko, and P. Tombesi,Quantum Semiclass. Opt.,7, 615 (1995).
K. Vogel and H. Risken,Phys. Rev. A,40, 2847 (1989).
D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani,Phys. Rev. Lett.,70, 1244 (1993).
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).
I. A. Malkin and V. I. Man'ko,Dynamic Symmetries and Coherent States of Quantum Systems [in Russian]. Nauka, Moscow (1979).
O. V. Man'ko,Phys. Lett. A,228, 29 (1997).
P. J. Bardroff, C. Leichte, G. Schrade, and W. P. Schleich,Phys. Rev. Lett.,77, 2198 (1996).
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.
G. Schrade, V. I. Man'ko, W. P. Schleich, and R. J. Glauber,Quantum Semiclass. Opt.,7, 307 (1995).
I. A. Malkin and V. I. Man'ko,Phys. Lett. A,32, 243 (1970).
E. Schrödinger,Sitzunugsber. Preuss. Akad. Wiss.,24, 296 (1930).
V. V. Dodonov, O. V. Man'ko, and V. I. Man'ko,Phys. Rev. A,50, 813 (1994).
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.
L. S. Brown and G. Gabrielse,Rev. Mod Phys.,58, 233 (1986).
O. Castanos, S. Hacyan, R. Lopez-Pena, and V. I. Man'ko,J. Phys. A,31, 1227 (1998).
S. Kielich,Progr. Opt.,20, 156 (1983).
M. G. Raymer and I. A. Walmsley,Progr. Opt.,28, 182 (1990).
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).
D. F. Walls,Z. Phys.,237, 224 (1970).
D. F. Walls,Z. Phys.,234, 331 (1970).
Author information
Authors and Affiliations
Additional information
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2, pp. 285–296, November, 1999.
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02557220