Nonclassical Properties of Intelligent SU(1,1) States for Two Modes

  • Christopher C. Gerry
  • Rainer Grobe
Conference paper


Intelligent states are those states which equalize an uncertainty relation. The ordinary coherent states1 equalize the usual uncertainty relation between the canonical position and momentum variables while exhibiting the noise of the vacuum in each. On the other hand, a squeezed state may also equalize the uncertainty relation while exhibiting less noise than the vacuum in one of the variables with a corresponding enhancement of noise in the other variable2. Other kinds of intelligent states have been constructed on the basis of Lie algebras associated with important symmetry or dynamical groups such as SU(2)3 and SU(1,1)4. It turns out that for a single mode field, the su(1,1) Lie algebra is related to the square of the field amplitude and the corresponding SU(1,1) squeezing is the squeezing of the quadratures of the squared field5. The intelligent states associated with this algebra have been shown to possess a number of nonclassical properties such as squeezing and oscillations of the photocount probabilities6,7. Also a method for generating such states7 has been proposed.


Coherent State Uncertainty Relation Field Amplitude Momentum Variable Nonclassical Property 


  1. 1.
    R.J. Glauber, Phys. Rev. 131, 2766 (1963)MathSciNetCrossRefGoogle Scholar
  2. 2.
    H.P.Yuen, Phys. Rev. A 13, 2226 (1976)CrossRefGoogle Scholar
  3. 3.
    C. Aragone, E. Chabaud and S. Salamo, J. Math. Phys. 17, 1963 (1976)CrossRefGoogle Scholar
  4. 4.
    G. Vanden Bergh and H. DeMeyer, J. Phys. A 11, 1569 (1978)MathSciNetCrossRefGoogle Scholar
  5. 5.
    M. Hillery, Phys. Rev. A 36, 3796 (1987)CrossRefGoogle Scholar
  6. 6.
    D. Yu and M. Hillery, Quantum Opt. 6, 37 (1994)CrossRefGoogle Scholar
  7. 7.
    G.S. Prakash and G.S. Agarwal, Phys. Rev. A 50, 4258 (1994)CrossRefGoogle Scholar
  8. 8.
    M. Hillery, Phys. Rev. A 40, 3174 (1989)MathSciNetCrossRefGoogle Scholar
  9. 9.
    C.C. Gerry and R. Grobe, Phys. Rev. A 51, 4123 (1995)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Christopher C. Gerry
    • 1
    • 2
  • Rainer Grobe
    • 1
    • 3
  1. 1.Department of Physics and AstronomyUniversity of RochesterRochesterUSA
  2. 2.Department of PhysicsAmherst CollegeAmherstUSA
  3. 3.Department of PhysicsIllinois State UniversityNormalUSA

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