Abstract

A theoretical analysis of light-pressure cooling of a fast ion beam is given. The light-induced velocity changes are compensated by accelerating the ions by an external electric field. By analyzing the Fokker–Planck equation, cooling times and the ultimate temperature of the ions are given. It is argued that the transverse heating and the diffusion to velocities that are not cooled should pose no serious problems in realistic experimental cases. The particular physical conditions in a heavy-ion storage ring are finally discussed.

© 1985 Optical Society of America

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  1. W. Neuhauser, M. Hohenstatt, P. Toschek, H. G. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137–1140 (1980).
    [CrossRef]
  2. D. J. Wineland, W. M. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75–78 (1981).
  3. V. O. Balykin, V. S. Letokhov, A. I. Sidorov, “Intense stationary flow of cold atoms formed by laser deceleration of atomic beam,” Opt. Commun. 49, 248–252 (1984).
    [CrossRef]
  4. J. V. Prodan, W. D. Phillips, H. Metcalf, “Laser production of a very slow monoenergetic atomic beam,” Phys. Rev. Lett. 49, 1149–1153 (1982).
    [CrossRef]
  5. R. Blatt, W. Ertmer, J. L. Hall, “Cooling of an atomic beam with frequency-sweep techniques,” in Laser-Cooled and Trapped Atoms, Vol. 8 of Progress in Quantum Electronics, W. D. Phillips, ed. (Pergamon, London, 1984), pp. 237–248.
  6. L. Moi, “Application of a very long cavity laser to atom slowing down and optical pumping,” Opt. Commun. 50, 349–352 (1984).
    [CrossRef]
  7. V. G. Minogin, “Deceleration and monochromatization of atomic beams by laser radiation pressure,” Opt. Commun. 34, 265–268 (1980).
    [CrossRef]
  8. T. V. Zueva, V. S. Letokhov, V. G. Minogin, “Theory of the deceleration of atomic beams by resonant laser radiation,” Sov. Phys. JETP 54, 38–44 (1981).
  9. V. G. Minogin, Yu. V. Rozhdetsvensky, “Dynamics of a three-level atom in a resonant light field,” Appl. Phys. B 34, 161–166 (1984).
    [CrossRef]
  10. M. Kaivola, U. Nielsen, O. Poulsen, “Laser cooling of fast accelerated ion beams,” CELSIUS-Note 83-17, Uppsala, Sweden (1984).
  11. V. G. Minogin, “Kinetic equation for atoms interacting with laser radiation,” Sov. Phys. JETP 52, 1032–1038 (1980).
  12. R. J. Cook, “Theory of resonance-radiation pressure,” Phys. Rev. A 22, 1078–1098 (1980).
    [CrossRef]
  13. S. Stenholm, “Distribution of photons and atomic momentum in resonance fluorescence,” Phys. Rev. A 27, 2513–2522 (1983).
    [CrossRef]
  14. A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
    [CrossRef]
  15. J. Javanainen, S. Stenholm, “Broad band resonant light pressure. I. Basic equations,” Appl. Phys. 21, 35–45 (1980); “Broad band resonant light pressure. II. Cooling of gases,” Appl. Phys. 21, 163–167 (1980).
    [CrossRef]
  16. R. J. Cook, “Photon number statistics in resonance fluorescence,” Phys. Rev. A 23, 1243–1250 (1981).
    [CrossRef]
  17. J. Javanainen, “Light-induced motion of trapped ions II: arbitrary intensity,” J. Phys. B 14, 4191–4205 (1981).
    [CrossRef]
  18. V. G. Minogin, B. D. Pavlik, “Cooling and capture of atoms and molecules by a resonant light field,” Sov. Phys. JETP 45, 698–705 (1977).
  19. J. Javanainen, “Light-pressure cooling of trapped ions in three dimensions,” Appl. Phys. 23, 175–182 (1980).
    [CrossRef]
  20. R. A. Holt, S. D. Rosner, T. D. Gaily, A. G. Adam, “Lamb-shift and fine-structure measurements in 7Li+,” Phys. Rev. A 22, 1563–1571 (1980).
    [CrossRef]
  21. G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).
  22. M. Bell, J. Chaney, H. Herr, F. Krienen, P. MøAller-Petersen, G. Petrucci, “Electron cooling in ICE at CERN,” Nucl. Instrum. Methods 190, 237–255 (1981).
    [CrossRef]

1984 (3)

V. O. Balykin, V. S. Letokhov, A. I. Sidorov, “Intense stationary flow of cold atoms formed by laser deceleration of atomic beam,” Opt. Commun. 49, 248–252 (1984).
[CrossRef]

L. Moi, “Application of a very long cavity laser to atom slowing down and optical pumping,” Opt. Commun. 50, 349–352 (1984).
[CrossRef]

V. G. Minogin, Yu. V. Rozhdetsvensky, “Dynamics of a three-level atom in a resonant light field,” Appl. Phys. B 34, 161–166 (1984).
[CrossRef]

1983 (1)

S. Stenholm, “Distribution of photons and atomic momentum in resonance fluorescence,” Phys. Rev. A 27, 2513–2522 (1983).
[CrossRef]

1982 (1)

J. V. Prodan, W. D. Phillips, H. Metcalf, “Laser production of a very slow monoenergetic atomic beam,” Phys. Rev. Lett. 49, 1149–1153 (1982).
[CrossRef]

1981 (5)

D. J. Wineland, W. M. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75–78 (1981).

T. V. Zueva, V. S. Letokhov, V. G. Minogin, “Theory of the deceleration of atomic beams by resonant laser radiation,” Sov. Phys. JETP 54, 38–44 (1981).

R. J. Cook, “Photon number statistics in resonance fluorescence,” Phys. Rev. A 23, 1243–1250 (1981).
[CrossRef]

J. Javanainen, “Light-induced motion of trapped ions II: arbitrary intensity,” J. Phys. B 14, 4191–4205 (1981).
[CrossRef]

M. Bell, J. Chaney, H. Herr, F. Krienen, P. MøAller-Petersen, G. Petrucci, “Electron cooling in ICE at CERN,” Nucl. Instrum. Methods 190, 237–255 (1981).
[CrossRef]

1980 (7)

J. Javanainen, “Light-pressure cooling of trapped ions in three dimensions,” Appl. Phys. 23, 175–182 (1980).
[CrossRef]

R. A. Holt, S. D. Rosner, T. D. Gaily, A. G. Adam, “Lamb-shift and fine-structure measurements in 7Li+,” Phys. Rev. A 22, 1563–1571 (1980).
[CrossRef]

J. Javanainen, S. Stenholm, “Broad band resonant light pressure. I. Basic equations,” Appl. Phys. 21, 35–45 (1980); “Broad band resonant light pressure. II. Cooling of gases,” Appl. Phys. 21, 163–167 (1980).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. Toschek, H. G. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137–1140 (1980).
[CrossRef]

V. G. Minogin, “Kinetic equation for atoms interacting with laser radiation,” Sov. Phys. JETP 52, 1032–1038 (1980).

R. J. Cook, “Theory of resonance-radiation pressure,” Phys. Rev. A 22, 1078–1098 (1980).
[CrossRef]

V. G. Minogin, “Deceleration and monochromatization of atomic beams by laser radiation pressure,” Opt. Commun. 34, 265–268 (1980).
[CrossRef]

1977 (1)

V. G. Minogin, B. D. Pavlik, “Cooling and capture of atoms and molecules by a resonant light field,” Sov. Phys. JETP 45, 698–705 (1977).

1976 (1)

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

1970 (1)

A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
[CrossRef]

Adam, A. G.

R. A. Holt, S. D. Rosner, T. D. Gaily, A. G. Adam, “Lamb-shift and fine-structure measurements in 7Li+,” Phys. Rev. A 22, 1563–1571 (1980).
[CrossRef]

Ashkin, A.

A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
[CrossRef]

Balykin, V. O.

V. O. Balykin, V. S. Letokhov, A. I. Sidorov, “Intense stationary flow of cold atoms formed by laser deceleration of atomic beam,” Opt. Commun. 49, 248–252 (1984).
[CrossRef]

Bell, M.

M. Bell, J. Chaney, H. Herr, F. Krienen, P. MøAller-Petersen, G. Petrucci, “Electron cooling in ICE at CERN,” Nucl. Instrum. Methods 190, 237–255 (1981).
[CrossRef]

Blatt, R.

R. Blatt, W. Ertmer, J. L. Hall, “Cooling of an atomic beam with frequency-sweep techniques,” in Laser-Cooled and Trapped Atoms, Vol. 8 of Progress in Quantum Electronics, W. D. Phillips, ed. (Pergamon, London, 1984), pp. 237–248.

Budker, G. I.

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

Chaney, J.

M. Bell, J. Chaney, H. Herr, F. Krienen, P. MøAller-Petersen, G. Petrucci, “Electron cooling in ICE at CERN,” Nucl. Instrum. Methods 190, 237–255 (1981).
[CrossRef]

Cook, R. J.

R. J. Cook, “Photon number statistics in resonance fluorescence,” Phys. Rev. A 23, 1243–1250 (1981).
[CrossRef]

R. J. Cook, “Theory of resonance-radiation pressure,” Phys. Rev. A 22, 1078–1098 (1980).
[CrossRef]

Dehmelt, H. G.

W. Neuhauser, M. Hohenstatt, P. Toschek, H. G. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137–1140 (1980).
[CrossRef]

Dikansky, N. S.

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

Ertmer, W.

R. Blatt, W. Ertmer, J. L. Hall, “Cooling of an atomic beam with frequency-sweep techniques,” in Laser-Cooled and Trapped Atoms, Vol. 8 of Progress in Quantum Electronics, W. D. Phillips, ed. (Pergamon, London, 1984), pp. 237–248.

Gaily, T. D.

R. A. Holt, S. D. Rosner, T. D. Gaily, A. G. Adam, “Lamb-shift and fine-structure measurements in 7Li+,” Phys. Rev. A 22, 1563–1571 (1980).
[CrossRef]

Hall, J. L.

R. Blatt, W. Ertmer, J. L. Hall, “Cooling of an atomic beam with frequency-sweep techniques,” in Laser-Cooled and Trapped Atoms, Vol. 8 of Progress in Quantum Electronics, W. D. Phillips, ed. (Pergamon, London, 1984), pp. 237–248.

Herr, H.

M. Bell, J. Chaney, H. Herr, F. Krienen, P. MøAller-Petersen, G. Petrucci, “Electron cooling in ICE at CERN,” Nucl. Instrum. Methods 190, 237–255 (1981).
[CrossRef]

Hohenstatt, M.

W. Neuhauser, M. Hohenstatt, P. Toschek, H. G. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137–1140 (1980).
[CrossRef]

Holt, R. A.

R. A. Holt, S. D. Rosner, T. D. Gaily, A. G. Adam, “Lamb-shift and fine-structure measurements in 7Li+,” Phys. Rev. A 22, 1563–1571 (1980).
[CrossRef]

Itano, W. M.

D. J. Wineland, W. M. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75–78 (1981).

Javanainen, J.

J. Javanainen, “Light-induced motion of trapped ions II: arbitrary intensity,” J. Phys. B 14, 4191–4205 (1981).
[CrossRef]

J. Javanainen, S. Stenholm, “Broad band resonant light pressure. I. Basic equations,” Appl. Phys. 21, 35–45 (1980); “Broad band resonant light pressure. II. Cooling of gases,” Appl. Phys. 21, 163–167 (1980).
[CrossRef]

J. Javanainen, “Light-pressure cooling of trapped ions in three dimensions,” Appl. Phys. 23, 175–182 (1980).
[CrossRef]

Kaivola, M.

M. Kaivola, U. Nielsen, O. Poulsen, “Laser cooling of fast accelerated ion beams,” CELSIUS-Note 83-17, Uppsala, Sweden (1984).

Krienen, F.

M. Bell, J. Chaney, H. Herr, F. Krienen, P. MøAller-Petersen, G. Petrucci, “Electron cooling in ICE at CERN,” Nucl. Instrum. Methods 190, 237–255 (1981).
[CrossRef]

Kudelainen, V. I.

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

Letokhov, V. S.

V. O. Balykin, V. S. Letokhov, A. I. Sidorov, “Intense stationary flow of cold atoms formed by laser deceleration of atomic beam,” Opt. Commun. 49, 248–252 (1984).
[CrossRef]

T. V. Zueva, V. S. Letokhov, V. G. Minogin, “Theory of the deceleration of atomic beams by resonant laser radiation,” Sov. Phys. JETP 54, 38–44 (1981).

Meshkov, I. N.

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

Metcalf, H.

J. V. Prodan, W. D. Phillips, H. Metcalf, “Laser production of a very slow monoenergetic atomic beam,” Phys. Rev. Lett. 49, 1149–1153 (1982).
[CrossRef]

Minogin, V. G.

V. G. Minogin, Yu. V. Rozhdetsvensky, “Dynamics of a three-level atom in a resonant light field,” Appl. Phys. B 34, 161–166 (1984).
[CrossRef]

T. V. Zueva, V. S. Letokhov, V. G. Minogin, “Theory of the deceleration of atomic beams by resonant laser radiation,” Sov. Phys. JETP 54, 38–44 (1981).

V. G. Minogin, “Kinetic equation for atoms interacting with laser radiation,” Sov. Phys. JETP 52, 1032–1038 (1980).

V. G. Minogin, “Deceleration and monochromatization of atomic beams by laser radiation pressure,” Opt. Commun. 34, 265–268 (1980).
[CrossRef]

V. G. Minogin, B. D. Pavlik, “Cooling and capture of atoms and molecules by a resonant light field,” Sov. Phys. JETP 45, 698–705 (1977).

MøAller-Petersen, P.

M. Bell, J. Chaney, H. Herr, F. Krienen, P. MøAller-Petersen, G. Petrucci, “Electron cooling in ICE at CERN,” Nucl. Instrum. Methods 190, 237–255 (1981).
[CrossRef]

Moi, L.

L. Moi, “Application of a very long cavity laser to atom slowing down and optical pumping,” Opt. Commun. 50, 349–352 (1984).
[CrossRef]

Neuhauser, W.

W. Neuhauser, M. Hohenstatt, P. Toschek, H. G. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137–1140 (1980).
[CrossRef]

Nielsen, U.

M. Kaivola, U. Nielsen, O. Poulsen, “Laser cooling of fast accelerated ion beams,” CELSIUS-Note 83-17, Uppsala, Sweden (1984).

Parchomchuk, V. V.

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

Pavlik, B. D.

V. G. Minogin, B. D. Pavlik, “Cooling and capture of atoms and molecules by a resonant light field,” Sov. Phys. JETP 45, 698–705 (1977).

Pestrikov, D. V.

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

Petrucci, G.

M. Bell, J. Chaney, H. Herr, F. Krienen, P. MøAller-Petersen, G. Petrucci, “Electron cooling in ICE at CERN,” Nucl. Instrum. Methods 190, 237–255 (1981).
[CrossRef]

Phillips, W. D.

J. V. Prodan, W. D. Phillips, H. Metcalf, “Laser production of a very slow monoenergetic atomic beam,” Phys. Rev. Lett. 49, 1149–1153 (1982).
[CrossRef]

Poulsen, O.

M. Kaivola, U. Nielsen, O. Poulsen, “Laser cooling of fast accelerated ion beams,” CELSIUS-Note 83-17, Uppsala, Sweden (1984).

Prodan, J. V.

J. V. Prodan, W. D. Phillips, H. Metcalf, “Laser production of a very slow monoenergetic atomic beam,” Phys. Rev. Lett. 49, 1149–1153 (1982).
[CrossRef]

Rosner, S. D.

R. A. Holt, S. D. Rosner, T. D. Gaily, A. G. Adam, “Lamb-shift and fine-structure measurements in 7Li+,” Phys. Rev. A 22, 1563–1571 (1980).
[CrossRef]

Rozhdetsvensky, Yu. V.

V. G. Minogin, Yu. V. Rozhdetsvensky, “Dynamics of a three-level atom in a resonant light field,” Appl. Phys. B 34, 161–166 (1984).
[CrossRef]

Sidorov, A. I.

V. O. Balykin, V. S. Letokhov, A. I. Sidorov, “Intense stationary flow of cold atoms formed by laser deceleration of atomic beam,” Opt. Commun. 49, 248–252 (1984).
[CrossRef]

Skrinsky, A. N.

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

Stenholm, S.

S. Stenholm, “Distribution of photons and atomic momentum in resonance fluorescence,” Phys. Rev. A 27, 2513–2522 (1983).
[CrossRef]

J. Javanainen, S. Stenholm, “Broad band resonant light pressure. I. Basic equations,” Appl. Phys. 21, 35–45 (1980); “Broad band resonant light pressure. II. Cooling of gases,” Appl. Phys. 21, 163–167 (1980).
[CrossRef]

Sukhina, B. N.

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

Toschek, P.

W. Neuhauser, M. Hohenstatt, P. Toschek, H. G. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137–1140 (1980).
[CrossRef]

Wineland, D. J.

D. J. Wineland, W. M. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75–78 (1981).

Zueva, T. V.

T. V. Zueva, V. S. Letokhov, V. G. Minogin, “Theory of the deceleration of atomic beams by resonant laser radiation,” Sov. Phys. JETP 54, 38–44 (1981).

Appl. Phys. (2)

J. Javanainen, S. Stenholm, “Broad band resonant light pressure. I. Basic equations,” Appl. Phys. 21, 35–45 (1980); “Broad band resonant light pressure. II. Cooling of gases,” Appl. Phys. 21, 163–167 (1980).
[CrossRef]

J. Javanainen, “Light-pressure cooling of trapped ions in three dimensions,” Appl. Phys. 23, 175–182 (1980).
[CrossRef]

Appl. Phys. B (1)

V. G. Minogin, Yu. V. Rozhdetsvensky, “Dynamics of a three-level atom in a resonant light field,” Appl. Phys. B 34, 161–166 (1984).
[CrossRef]

J. Phys. B (1)

J. Javanainen, “Light-induced motion of trapped ions II: arbitrary intensity,” J. Phys. B 14, 4191–4205 (1981).
[CrossRef]

Nucl. Instrum. Methods (1)

M. Bell, J. Chaney, H. Herr, F. Krienen, P. MøAller-Petersen, G. Petrucci, “Electron cooling in ICE at CERN,” Nucl. Instrum. Methods 190, 237–255 (1981).
[CrossRef]

Opt. Commun. (3)

L. Moi, “Application of a very long cavity laser to atom slowing down and optical pumping,” Opt. Commun. 50, 349–352 (1984).
[CrossRef]

V. G. Minogin, “Deceleration and monochromatization of atomic beams by laser radiation pressure,” Opt. Commun. 34, 265–268 (1980).
[CrossRef]

V. O. Balykin, V. S. Letokhov, A. I. Sidorov, “Intense stationary flow of cold atoms formed by laser deceleration of atomic beam,” Opt. Commun. 49, 248–252 (1984).
[CrossRef]

Part. Accel. (1)

G. I. Budker, N. S. Dikansky, V. I. Kudelainen, I. N. Meshkov, V. V. Parchomchuk, D. V. Pestrikov, A. N. Skrinsky, B. N. Sukhina, “Experimental studies of electron cooling,” Part. Accel. 7, 197–211 (1976).

Phys. Lett. (1)

D. J. Wineland, W. M. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75–78 (1981).

Phys. Rev. A (5)

W. Neuhauser, M. Hohenstatt, P. Toschek, H. G. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137–1140 (1980).
[CrossRef]

R. A. Holt, S. D. Rosner, T. D. Gaily, A. G. Adam, “Lamb-shift and fine-structure measurements in 7Li+,” Phys. Rev. A 22, 1563–1571 (1980).
[CrossRef]

R. J. Cook, “Photon number statistics in resonance fluorescence,” Phys. Rev. A 23, 1243–1250 (1981).
[CrossRef]

R. J. Cook, “Theory of resonance-radiation pressure,” Phys. Rev. A 22, 1078–1098 (1980).
[CrossRef]

S. Stenholm, “Distribution of photons and atomic momentum in resonance fluorescence,” Phys. Rev. A 27, 2513–2522 (1983).
[CrossRef]

Phys. Rev. Lett. (2)

A. Ashkin, “Atomic-beam deflection by resonance-radiation pressure,” Phys. Rev. Lett. 25, 1321–1324 (1970).
[CrossRef]

J. V. Prodan, W. D. Phillips, H. Metcalf, “Laser production of a very slow monoenergetic atomic beam,” Phys. Rev. Lett. 49, 1149–1153 (1982).
[CrossRef]

Sov. Phys. JETP (3)

T. V. Zueva, V. S. Letokhov, V. G. Minogin, “Theory of the deceleration of atomic beams by resonant laser radiation,” Sov. Phys. JETP 54, 38–44 (1981).

V. G. Minogin, B. D. Pavlik, “Cooling and capture of atoms and molecules by a resonant light field,” Sov. Phys. JETP 45, 698–705 (1977).

V. G. Minogin, “Kinetic equation for atoms interacting with laser radiation,” Sov. Phys. JETP 52, 1032–1038 (1980).

Other (2)

M. Kaivola, U. Nielsen, O. Poulsen, “Laser cooling of fast accelerated ion beams,” CELSIUS-Note 83-17, Uppsala, Sweden (1984).

R. Blatt, W. Ertmer, J. L. Hall, “Cooling of an atomic beam with frequency-sweep techniques,” in Laser-Cooled and Trapped Atoms, Vol. 8 of Progress in Quantum Electronics, W. D. Phillips, ed. (Pergamon, London, 1984), pp. 237–248.

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Figures (3)

Fig. 1
Fig. 1

The ions interact over a distance l with a counterrunning laser beam. The ions are also accelerated by a constant electric field .

Fig. 2
Fig. 2

A combined process of absorption and spontaneous emission. (a) The ion in the lower state moves to the right at the velocity v0. A photon with momentum ħq is coming in. (b) The ion has absorbed the photon and its momentum; hence its velocity is v0 + vr. (c) Spontaneous emission takes place. (d) Since spontaneous emission is invariant under inversion, the average recoil kick acquired by the ion is zero. Therefore, the average change in the velocity of the ion in the cycle (a)–(d) is −vr. The average change of the velocity is ascribed to the light-pressure force, and the fluctuations due to the random directions of the spontaneous photons contribute to the stochastic diffusion.

Fig. 3
Fig. 3

The acceleration that is due to the light-pressure force and the auxiliary accelerating field, ϕ, as a function of the velocity ν (solid line). The zeros of the acceleration ϕ are ν and ν+; the former is a stable and the latter is an unstable fixed point of Eq. (3.3). In the figure the value corresponding to the optimum has been chosen for the auxiliary acceleration, a = am = Γκ2vr/2γ2. For comparison, a Gaussian initial distribution is also shown (dashed line). The tail of the distribution extending beyond ν+ describes ions that are not cooled. The center velocity ν1 = δ/q is used in Subsection 4.C.

Tables (1)

Tables Icon

Table 1 Parameters for Laser Cooling of a 100-keV Beam of 7Li+ with Circularly Polarized Light That Drives the Transition with the Wavelength λ = 548.4 nma

Equations (54)

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v 0 = ( 2 Q V / M ) 1 / 2 .
f 0 ( v ) = ( 1 / 2 π u 0 ) exp [ - ( v - v 0 ) 2 / 2 u 0 2 ] ,
γ = ( γ 2 2 + 2 κ 2 ) 1 / 2 .
( t + v z ) f = v ( - ϕ f ) + 2 v 2 ( d f ) ;
ϕ = - Γ κ 2 v r ( Δ - q v ) 2 + γ 2 ,
d = 1 2 Γ κ 2 v r 2 ( Δ - q v ) 2 + γ 2 × { ( 1 + α ) - 2 κ 2 [ 3 γ 2 2 - ( Δ - q v ) 2 ] [ ( Δ - q v ) 2 + γ 2 ] 2 } .
t + v z t + v 0 z .
ξ = z - t v 0 ,             ν = v - v 0 ,             τ = z / v 0 .
f τ = ν ( - ϕ f ) + 2 ν 2 ( d f ) .
f ( ξ , ν , τ = 0 ) = f 0 ( ν ) = 1 2 π u 0 exp [ - ( ν / 2 u 0 ) 2 ] .
ϕ = - Γ κ 2 v r ( δ - q ν ) 2 + γ 2 + a ,
δ = Δ - q v 0 .
d = 1 2 Γ κ 2 v r 2 ( δ + q ν ) 2 + γ 2 ( 1 + α ) .
0 < a < Γ κ 2 v r γ 2 .
ν ± = [ δ ± ( v r Γ κ 2 a - γ 2 ) 1 / 2 ] / q
d ν d τ = ϕ ( ν ) = - Γ κ 2 v r ( δ - q ν ) 2 + γ 2 + a ,
a q τ = q ( ν - ν 0 ) + v r Γ κ 2 a q ( ν + - ν - ) ln | ( ν + - ν ) ( ν - - ν 0 ) ( ν + - ν 0 ) ( ν - - ν ) | .
ν ( τ ) = ν - - ν - - ν 0 ν + - ν 0 ( ν + - ν - ) exp [ - a 2 q 2 ( ν + - ν - ) v r Γ κ 2 τ ] ,             τ .
1 / τ e = 2 Γ κ 2 v r q ( δ - q ν - ) [ ( δ - q ν - ) 2 + γ 2 ] 2 .
f ( ν , τ ) = ϕ ( ν ) ϕ [ ν 0 ( ν , τ ) ] f 0 [ ν 0 ( ν , τ ) ] .
τ c = u 0 / a .
ϕ = - ( ν - ν - ) ϕ 1 ,
ϕ 1 = 2 Γ κ 2 v r q ( δ - q ν - ) [ ( δ - q ν - ) 2 + γ 2 ] 2 = 1 / τ e ,
d = d 0 ,
d 0 = ½ Γ κ 2 v r 2 δ 2 + γ 2 ( 1 + α ) .
f τ = ν [ ϕ 1 ( ν - ν - ) f ] + 2 ν 2 ( d 0 f ) .
f ( ν , τ = 0 ) = δ ( ν - ν 0 ) .
g ( ν , τ ; ν 0 , 0 ) = 1 2 π u ( τ ) exp { - [ ν - ν ( τ ) ] 2 2 u 2 ( τ ) } ,
u 2 ( τ ) = u 2 [ 1 - exp ( - 2 τ / τ e ) ] ,
ν ( τ ) = ν - + ( ν 0 - ν - ) exp ( - τ / τ e ) ,
u 2 = d 0 / ϕ 1 = γ 4 M ( δ - q ν - γ + γ δ - q ν - ) ( 1 + α ) .
f ( ν , τ ) = g ( ν , τ ; ν 0 , 0 ) f 0 ( ν 0 ) d ν 0 ,
f ( ν ) = 1 2 π u exp [ - ( ν - ν - ) 2 2 u 2 ] .
u = [ γ 4 M ( δ - q ν - γ + γ δ - q ν - ) ( 1 + α ) ] 1 / 2 ,
T = M u 2 k B = γ 4 k B ( δ - q ν - γ + γ δ - q ν - ) ( 1 + α ) .
u , m = [ γ 2 M ( 1 + α ) ] 1 / 2 ,
T m = γ 2 k B ( 1 + α ) .
a m = Γ κ 2 v r 2 γ 2 Γ v r 4 ,
τ c , m 4 u 0 / Γ v r .
τ e , m = ( γ 3 Γ κ 2 ) / r ,
r = q v r / 2.
τ e , g = 2 / r ,
Γ = d 2 ω 3 3 π 0 c 3 ,
γ = γ 2 ( 1 + 2 I / I s ) 1 / 2 .
V X = M v 0 X / e .
V x = M v 0 x / q e .
j d ( ν ) = - d 0 f ( ν ) ν .
j d ( ν l ) 1 τ e ν l - ν u exp [ - ( ν l - ν - ) 2 2 u 2 ] .
τ l 1 j d ( ν l ) τ e u ν l - ν l exp [ ( ν l - ν - ) 2 2 u 2 ] .
f ( ν x , ν y , τ ) τ = ½ Γ κ 2 v r 2 ( δ - q ν - ) 2 + γ 2 × ( α x 2 ν x 2 + α y 2 ν y 2 ) f ( ν x , ν y , τ ) .
α + α x + α y = 1.
g ( ν x , ν y , τ ; ν x 0 , ν y 0 , 0 ) = 1 2 π [ u x ( τ ) u y ( τ ) ] 1 / 2 × exp [ - ( ν x - ν x 0 ) 2 2 u x 2 ( τ ) - ( ν y - ν y 0 ) 2 2 u x 2 ( τ ) ] ,
u x , y 2 ( τ ) = τ 2 Γ κ 2 v r 2 ( δ - q ν - ) 2 + γ 2 α x , y .
u x , y ( τ c ) 4 m / sec .

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