Abstract
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.
Similar content being viewed by others
References
D.J.Wineland, H.Dehmelt: Bull. Am. Phys. Soc.20, 637 (1975)
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)
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]
J.Javanainen, S.Stenholm: Appl. Phys.21, 35 (1980);21, 163 (1980)
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)
B.L.Zhelnov, A.P.Kazantsev, G.I.Surdutovich: Sov. J. Quantum Electron.7, 499 (1977)
R.J.Cook: Phys. Rev. A20, 224 (1979);21, 268 (1980); Phys. Rev. Lett.44, 976 (1980)
E.Arimondo, H.Lew, TakeshiOka: Phys. Rev. Lett.43, 753 (1979)
V.I.Balykin, V.S.Letokhov, V.I.Mushin: JETP Lett.29, 560 (1979)
D.J.Wineland, W.M.Itano: Phys. Rev. A20, 1527 (1979)
J.Javanainen, S.Stenholm: Appl. Phys.21, 283 (1980)
S.Stenholm: Invited talk at ICOMP 2 Budapest, April 14–18, 1980 (to appear)
J.Javanainen: Appl. Phys.23, 175 (1980)
L.D.Landau, L.M.Lifshitz:Quantum Mechanics (Pergamon Press, Oxford 1958)
G.N.Watson:Theory of Bessel Functions, 2nd ed. (Cambridge University Press, Cambridge 1958)