Coherent States in Modern Physics

  • Robert Gilmore
Conference paper

Abstract

In the preceding work [1] a number of algebraic techniques have been used to construct and label the symmetrized states describing an ensemble of N identical two-level atoms. Under certain physically attainable circumstances, such states evolve into “coherent atomic states” under a classical driving field. The properties of the atomic coherent states were stated and compared with the properties of the field coherent states. The atomic and field coherent states were found to be related by a group contraction process.

Keywords

Coherence Convolution Tate Mandel 

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References

  1. 1.
    F. T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, this volume p. 191. See also the paper by the same authors to be published.Google Scholar
  2. 2.
    S. Helgason, Differential Geometry and Symmetric Spaces (Academic Press, New York, 1962 ). N. Jacobson, Lie Algebras ( Wiley-Interscience, New York, 1962 ).MATHGoogle Scholar
  3. 3.
    H. Weyl, The Theory of Groups and Quantum Mechanics ( Dover Publications, New York, 1931 ).MATHGoogle Scholar
  4. 4.
    H. Weyl, The Classical Groups (Princeton University Press, Princeton, New Jersey, 1946 ).MATHGoogle Scholar
  5. 5.
    I. M. Gel’fand, M. L. Tsetlein, Doklady Akad. Nauk SSSR 71, 825–828 (1950).MathSciNetMATHGoogle Scholar
  6. 6.
    I. M. Gel’fand, M. L. Tsetlein, Doklady Akad. Nauk SSSR 71, 1017–1020 (1950).MathSciNetMATHGoogle Scholar
  7. 7.
    R. Gilmore, J. Math. Phys. 11, 3420–3427 (1970).ADSMATHCrossRefGoogle Scholar
  8. 8.
    R. Gilmore, Ann. Phys. New York (to be published).Google Scholar
  9. 9.
    M. F. Perrin, Ann. Scient. L’Ecole Normale Sup. 45, 1–51 (1928).MathSciNetGoogle Scholar
  10. 10.
    E. B. Dynkin, Am. Math. Soc. Transl. (2) 72, 203–228 (1968).Google Scholar
  11. 11.
    J. Bardeen, D. Pines, Phys. Rev. 99, 1140–1150 (1955).ADSMATHCrossRefGoogle Scholar
  12. 12.
    D. Pines, Phys. Rev. 109, 280–287 (1958).ADSMATHCrossRefGoogle Scholar
  13. 13.
    P. W. Anderson, Phys. Rev. 112, 1900–1916 (1958).MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    J. Bardeen, L. N. Cooper, J. R. Schrieffer, Phys. Rev. 106, 162–164 (1957); J. Bardeen, L. N. Cooper, J. R. Schrieffer, Phys. Rev. 108, 1175–1204 (1957).MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    N. N. Bogoliubov, I. Sov. Phys. JETP 34(7), 41–46 (1958); II. Sov, Phys. JETP 34 (7), 51–55 (1958).MathSciNetGoogle Scholar
  16. 16.
    W. H. Bassichis, L. L. Foldy, Phys. Rev. 133A, 935–943 (1964).ADSCrossRefGoogle Scholar
  17. 17.
    A. J. Solomon, J. Math. Phys. 12, 390–394 (1971).ADSCrossRefGoogle Scholar
  18. 18.
    W. Miller, On Lie Algebras and Some Special Functions of Mathematical Physics, Memoirs of the American Mathematical Society #50 (Am. Math. Soc., Providence, R. I. 1964 ).Google Scholar
  19. 19.
    W. Miller, Lie Theory and Special Functions ( Academic Press, New York, 1968 ).MATHGoogle Scholar
  20. 20.
    A. Feldman, A. H. Kahn, Phys. Rev. (3) B1, 4584–4589 (1970).Google Scholar
  21. 21.
    I. A. Malkin, V. I. Man’ko, Sov. Phys. JETP 28, 527–532 (1969).ADSGoogle Scholar
  22. 22.
    I. A. Malkin, V. I. Man’ko, Sov. J. Nucl. Phys. 8, 731–735 (1969).Google Scholar
  23. 23.
    I. A. Malkin, V. I. Man’ko, D. A. Trifonov, Sov. Phys. JETP 31, 386–390 (1970).ADSGoogle Scholar
  24. 24.
    I. A. Malkin, V. I. Man’ko, D. A. Trifonov, Phys. Lett. 30 A, 30A, 414 (1969).CrossRefGoogle Scholar
  25. 25.
    I. A. Malkin, V. I. Man’ko, Sov. Phys. JETP 32, 949–953 (1971).ADSGoogle Scholar
  26. 26.
    I. A. Malkin, V. I. Man’ko, Phys. Lett. 32A, 243–244 (1970).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • Robert Gilmore
    • 1
  1. 1.University of South FloridaTampaUSA

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