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Laser cooling of trapped particles II

The fast particle limit

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We consider cooling of a trapped particle in the limit when the position and velocity variables do not change adiabatically. The slowly varying quantity in a harmonic trap is then the energy, and a representation based on oscillator eigenstates is used. For large excitation, fast particles, a Fokker-Planck expansion is obtained which is valid when our adiabatic description breaks down. Estimates of the initial cooling rate are given and compared with earlier results. Our treatment requires a large number of oscillator states to be coupled by each one-photon process, and in this limit the diffusion will make the expansion invalid towards the end of the cooling; our physical interpretation is that particles leak out of the trap. The opposite case, the Lamb-Dicke regime, is advantageous for cooling experiments, and then a difference equation replaces the Fokker-Planck equation of the present paper.

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  1. 1.

    D.J.Wineland, H.Dehmelt: Bull. Am. Phys. Soc.20, 637 (1975)

  2. 2.

    D.J.Wineland, R.E.Drullinger, F.L.Walls: Phys. Rev. Lett.40, 1639 (1978); R.E.Drullinger, D.J.Wineland: InLaser Spectroscopy IV, ed. by H.Walther and K.W.Rothe, Springer Ser. Opt. Sci.21 (Springer, Berlin, Heidelberg, New York 1979)

  3. 3.

    W.Neuhauser, M.Hohenstatt, P.Toschek, H.Dehmelt: Phys. Rev. Lett.41, 321 (1978); Appl. Phys.17, 123 (1978); and inLaser Spectroscopy IV, see [2]

  4. 4.

    J.Javanainen, S.Stenholm: Appl. Phys.21, 35 (1980);21, 163 (1980)

  5. 5.

    V.S.Letokhov, V.G.Minogin, B.D.Pavlik: Sov. Phys. JETP45, 698 (1977); V.S.Letokhov, V.G.Minogin: Sov. Phys. JETP47, 690 (1978)

  6. 6.

    B.L.Zhelnov, A.P.Kazantsev, G.I.Surdutovich: Sov. J. Quantum Electron.7, 499 (1977)

  7. 7.

    R.J.Cook: Phys. Rev. A20, 224 (1979);21, 268 (1980); Phys. Rev. Lett.44, 976 (1980)

  8. 8.

    E.Arimondo, H.Lew, TakeshiOka: Phys. Rev. Lett.43, 753 (1979)

  9. 9.

    V.I.Balykin, V.S.Letokhov, V.I.Mushin: JETP Lett.29, 560 (1979)

  10. 10.

    D.J.Wineland, W.M.Itano: Phys. Rev. A20, 1527 (1979)

  11. 11.

    J.Javanainen, S.Stenholm: Appl. Phys.21, 283 (1980)

  12. 12.

    S.Stenholm: Invited talk at ICOMP 2 Budapest, April 14–18, 1980 (to appear)

  13. 13.

    J.Javanainen: Appl. Phys.23, 175 (1980)

  14. 14.

    L.D.Landau, L.M.Lifshitz:Quantum Mechanics (Pergamon Press, Oxford 1958)

  15. 15.

    G.N.Watson:Theory of Bessel Functions, 2nd ed. (Cambridge University Press, Cambridge 1958)

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Javanainen, J., Stenholm, S. Laser cooling of trapped particles II. Appl. Phys. 24, 71–84 (1981). https://doi.org/10.1007/BF00900402

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