Abstract

An ion, atom, molecule or macro-particle in a trap can exhibit large motional oscillations due to the Doppler-affected radiation pressure by a laser, blue-detuned from an absorption line of a particle. This oscillator can be nearly thresholdless, but under certain conditions it may exhibit huge hysteretic excitation. Feasible applications include a “Foucault pendulum” in a trap, a rotation sensor, single atom spectroscopy, isotope separation, etc.

© 2009 Optical Society of America

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  1. See e. g. N. Minorsky, Nonlinear Oscillations, Princeton, NJ, Van Nostrand, 1962.
  2. D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
    [CrossRef] [PubMed]
  3. K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser - a laser with one-atom in an optical-resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
    [CrossRef] [PubMed]
  4. P. Filipowicz, J. Javanainen, and P. Meystre, "Theory of a microscopic maser," Phys. Rev. A 34, 3077-3087 (1986).
    [CrossRef] [PubMed]
  5. For reviews on trapping/cooling see e. g. Laser manipulations of atoms and ions, Eds. E. Arimondo, W. D. Phillips, and S. Strumia (N.-Holland, Amst., 1992) and Refs. [6-9] below.
  6. H. Metcalf and P. van der Straten, "Cooling and trapping of neutral atoms," Phys. Rep. 244, 203-286 (1994).
    [CrossRef]
  7. S. Chu, "The manipulation of neutral particles," Rev. Mod. Phys. 70, 685-706 (1998).
    [CrossRef]
  8. C. N. Cohen-Tannoudji, "Manipulating atoms with photons," Rev. Mod. Phys. 70, 707-719 (1998).
    [CrossRef]
  9. W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
    [CrossRef]
  10. For review on coherent quantum-state manipulation of trapped ions see e. g. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, "Experimental issues in coherent quantum-state manipulation of trapped atomic ions," J. of Research of the NIST,  103, 259-328 (1998).
  11. For reviews on particle trapping by gradient forces, see A. Ashkin, "Applications of laser-radiation pressure," Science  210, 1081-1088 (1980) and Refs. [12-15] below.
    [PubMed]
  12. A. Ashkin, "Optical trapping and manipulation of neutral particles using lasers," Proc. Natl. Acad. Sci. USA,  94, 4853-4860 (1997).
    [CrossRef] [PubMed]
  13. S. Chu, J. B. Bjorkholm, A. Ashkin, and A. Cable, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
    [CrossRef] [PubMed]
  14. A. Ashkin and J. M. Dziedzic, "Observation of radiation-pressure trapping of particles by alternating lightbeams," Phys. Rev. Lett. 54, 1245-1248 (1985).
    [CrossRef] [PubMed]
  15. J. B. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, "Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure," Phys. Rev. Lett. 41, 1361-1364 (1978).
    [CrossRef]
  16. T. W. Hänsch and A. L. Schawlow, "Cooling of gasses by laser radiation," Opt. Comm. 13, 68-69 (1975).
    [CrossRef]
  17. V. S. Letokhov, V. G. Minogin, and B. D. Pavlik, "Cooling and trapping of atoms and molecules by a resonant laser field," Opt. Comm. 19, 72-75 (1976).
    [CrossRef]
  18. W. Neuhauser,M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, "Optical-sideband cooling of visible atom cloud confined in parabolic well," Phys. Rev. Lett. 41, 233-236 (1978).
    [CrossRef]
  19. D. J. Wineland and W. M. Itano, "Laser cooling of atoms," Phys. Rev. A 20, 1521-1540 (1979).
  20. S. Chu, L. Hollberg, J. B. Bjorkholm, A. Cable, and A. Ashkin, "3-dimensional viscosous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48-51 (1985).
    [CrossRef] [PubMed]
  21. T. Takekoshi, B. M. Patterson, and R. J. Knize, "Observation of optically trapped cold cesium molecules," Phys. Rev. Lett. 81, 5105-5108 (1998).
    [CrossRef]
  22. Laser-induced SSO due to Doppler effect was proposed in A. E. Kaplan, "On Doppler instability of resonantly absorbing (or amplifying) systems in a strong field," Abstr. the 6th Natl. Conf. on Nonlinear Optics (Minsk), publ. by Moscow St. Univ., Moscow, 1972, p. 26.
  23. J. P. Dowling and J. Gea-Banacloche, "Evanescent light-wave atom mirrors, resonators waveguides, and traps," Adv. Atomic Mol. Opt. Phys. 37, 1-94 (1996).
  24. S.A. Schaaf and P. L. Chambre, Flow of Rarefied Gases, Princeton University Press, 1961.
  25. We also neglect the spatial modulation of FL with the period λ /2 mimicking a standing wave pattern; since ka » 1 as opposite to the Lamb-Dicke limit, this modulation will average out. Besides, it is present only for the standing wave and vanishes for a traveling wave pumping, J. Javanainen, M. Kaivola, U. Nielsen, O. Poulsen, and E. Riis, "Laser cooling of a fast ion-beam," J. Opt. Soc. Am. B 2, 1768-1775 (1985).
    [CrossRef]
  26. A. E. Kaplan, "Hysteresis in cyclotron resonance based on weak-relativistic mass-effect of the electron," Phys. Rev. Lett. 48, 138-141 (1982).
    [CrossRef]
  27. A. E. Kaplan, "Relativistic nonlinear optics of a single cyclotron electron," Phys. Rev. Lett. 56, 456-459 (1986).
    [CrossRef] [PubMed]
  28. A. E. Kaplan and Y. J. Ding, "Hysteretic and multiphoton optical resonances of a single cyclotron electron," IEEE JQE  24, 1470-1482 (1988).
    [CrossRef]
  29. R. Blömel, C. Kappler, W. Quint, and H. Walther, "Chaos and order of laser-cooled ions in a Paul trap," Phys. Rev. A 40, 808-823 (1989).
  30. E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, "Sideband cooling of ions in radio-frequency traps," Phys. Rev. A 60, 439-449 (1999).
  31. Th. Sauter, H. Gilhaus, I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, "On the photo-dynamics of single ions in a trap," Z. Phys. D 10, 153-163 (1988).
    [CrossRef]
  32. J. Javanainen, "Light pressure cooling of a trapped 3-level ions," in Fundamentals of Laser Interaction. Lecture Notes in Physics, 229, 249-258, Ed. F. Ehlotzky, NY, Springer (1985).
  33. K. T. Gahagan and G. A. Swartzlander, Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996)
    [CrossRef] [PubMed]
  34. K. T. Gahagan and G. A. Swartzlander, Jr., "Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap," JOSA B 16, 533-537 (1999).
    [CrossRef]
  35. S. T. Thornton and J. B. Marion, Classical dynamics of particles and systems, 5-th ed., Thomson Brooks/Cole, Belmont, CA, 2004.
  36. H. C. van de Hulst, Light scattering by small particles, Dover, New York, 1981.
  37. P. K. Ghosh, Ion traps, Clarendon Press, Oxford, 1995.

1999 (2)

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, "Sideband cooling of ions in radio-frequency traps," Phys. Rev. A 60, 439-449 (1999).

K. T. Gahagan and G. A. Swartzlander, Jr., "Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap," JOSA B 16, 533-537 (1999).
[CrossRef]

1998 (5)

T. Takekoshi, B. M. Patterson, and R. J. Knize, "Observation of optically trapped cold cesium molecules," Phys. Rev. Lett. 81, 5105-5108 (1998).
[CrossRef]

S. Chu, "The manipulation of neutral particles," Rev. Mod. Phys. 70, 685-706 (1998).
[CrossRef]

C. N. Cohen-Tannoudji, "Manipulating atoms with photons," Rev. Mod. Phys. 70, 707-719 (1998).
[CrossRef]

W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

For review on coherent quantum-state manipulation of trapped ions see e. g. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, "Experimental issues in coherent quantum-state manipulation of trapped atomic ions," J. of Research of the NIST,  103, 259-328 (1998).

1997 (1)

A. Ashkin, "Optical trapping and manipulation of neutral particles using lasers," Proc. Natl. Acad. Sci. USA,  94, 4853-4860 (1997).
[CrossRef] [PubMed]

1996 (2)

J. P. Dowling and J. Gea-Banacloche, "Evanescent light-wave atom mirrors, resonators waveguides, and traps," Adv. Atomic Mol. Opt. Phys. 37, 1-94 (1996).

K. T. Gahagan and G. A. Swartzlander, Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996)
[CrossRef] [PubMed]

1994 (2)

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser - a laser with one-atom in an optical-resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

H. Metcalf and P. van der Straten, "Cooling and trapping of neutral atoms," Phys. Rep. 244, 203-286 (1994).
[CrossRef]

1989 (1)

R. Blömel, C. Kappler, W. Quint, and H. Walther, "Chaos and order of laser-cooled ions in a Paul trap," Phys. Rev. A 40, 808-823 (1989).

1988 (2)

Th. Sauter, H. Gilhaus, I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, "On the photo-dynamics of single ions in a trap," Z. Phys. D 10, 153-163 (1988).
[CrossRef]

A. E. Kaplan and Y. J. Ding, "Hysteretic and multiphoton optical resonances of a single cyclotron electron," IEEE JQE  24, 1470-1482 (1988).
[CrossRef]

1986 (3)

A. E. Kaplan, "Relativistic nonlinear optics of a single cyclotron electron," Phys. Rev. Lett. 56, 456-459 (1986).
[CrossRef] [PubMed]

P. Filipowicz, J. Javanainen, and P. Meystre, "Theory of a microscopic maser," Phys. Rev. A 34, 3077-3087 (1986).
[CrossRef] [PubMed]

S. Chu, J. B. Bjorkholm, A. Ashkin, and A. Cable, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

1985 (4)

A. Ashkin and J. M. Dziedzic, "Observation of radiation-pressure trapping of particles by alternating lightbeams," Phys. Rev. Lett. 54, 1245-1248 (1985).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. B. Bjorkholm, A. Cable, and A. Ashkin, "3-dimensional viscosous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48-51 (1985).
[CrossRef] [PubMed]

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

We also neglect the spatial modulation of FL with the period λ /2 mimicking a standing wave pattern; since ka » 1 as opposite to the Lamb-Dicke limit, this modulation will average out. Besides, it is present only for the standing wave and vanishes for a traveling wave pumping, J. Javanainen, M. Kaivola, U. Nielsen, O. Poulsen, and E. Riis, "Laser cooling of a fast ion-beam," J. Opt. Soc. Am. B 2, 1768-1775 (1985).
[CrossRef]

1982 (1)

A. E. Kaplan, "Hysteresis in cyclotron resonance based on weak-relativistic mass-effect of the electron," Phys. Rev. Lett. 48, 138-141 (1982).
[CrossRef]

1980 (1)

For reviews on particle trapping by gradient forces, see A. Ashkin, "Applications of laser-radiation pressure," Science  210, 1081-1088 (1980) and Refs. [12-15] below.
[PubMed]

1979 (1)

D. J. Wineland and W. M. Itano, "Laser cooling of atoms," Phys. Rev. A 20, 1521-1540 (1979).

1978 (2)

W. Neuhauser,M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, "Optical-sideband cooling of visible atom cloud confined in parabolic well," Phys. Rev. Lett. 41, 233-236 (1978).
[CrossRef]

J. B. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, "Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure," Phys. Rev. Lett. 41, 1361-1364 (1978).
[CrossRef]

1976 (1)

V. S. Letokhov, V. G. Minogin, and B. D. Pavlik, "Cooling and trapping of atoms and molecules by a resonant laser field," Opt. Comm. 19, 72-75 (1976).
[CrossRef]

1975 (1)

T. W. Hänsch and A. L. Schawlow, "Cooling of gasses by laser radiation," Opt. Comm. 13, 68-69 (1975).
[CrossRef]

Abbel, J.

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, "Sideband cooling of ions in radio-frequency traps," Phys. Rev. A 60, 439-449 (1999).

An, K.

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser - a laser with one-atom in an optical-resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, "Optical trapping and manipulation of neutral particles using lasers," Proc. Natl. Acad. Sci. USA,  94, 4853-4860 (1997).
[CrossRef] [PubMed]

S. Chu, J. B. Bjorkholm, A. Ashkin, and A. Cable, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, "Observation of radiation-pressure trapping of particles by alternating lightbeams," Phys. Rev. Lett. 54, 1245-1248 (1985).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. B. Bjorkholm, A. Cable, and A. Ashkin, "3-dimensional viscosous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48-51 (1985).
[CrossRef] [PubMed]

For reviews on particle trapping by gradient forces, see A. Ashkin, "Applications of laser-radiation pressure," Science  210, 1081-1088 (1980) and Refs. [12-15] below.
[PubMed]

J. B. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, "Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure," Phys. Rev. Lett. 41, 1361-1364 (1978).
[CrossRef]

Becker, Th.

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, "Sideband cooling of ions in radio-frequency traps," Phys. Rev. A 60, 439-449 (1999).

Bjorkholm, J. B.

S. Chu, J. B. Bjorkholm, A. Ashkin, and A. Cable, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. B. Bjorkholm, A. Cable, and A. Ashkin, "3-dimensional viscosous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48-51 (1985).
[CrossRef] [PubMed]

J. B. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, "Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure," Phys. Rev. Lett. 41, 1361-1364 (1978).
[CrossRef]

Blatt, R.

Th. Sauter, H. Gilhaus, I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, "On the photo-dynamics of single ions in a trap," Z. Phys. D 10, 153-163 (1988).
[CrossRef]

Blömel, R.

R. Blömel, C. Kappler, W. Quint, and H. Walther, "Chaos and order of laser-cooled ions in a Paul trap," Phys. Rev. A 40, 808-823 (1989).

Cable, A.

S. Chu, J. B. Bjorkholm, A. Ashkin, and A. Cable, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. B. Bjorkholm, A. Cable, and A. Ashkin, "3-dimensional viscosous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48-51 (1985).
[CrossRef] [PubMed]

Childs, J. J.

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser - a laser with one-atom in an optical-resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

Chu, S.

S. Chu, "The manipulation of neutral particles," Rev. Mod. Phys. 70, 685-706 (1998).
[CrossRef]

S. Chu, J. B. Bjorkholm, A. Ashkin, and A. Cable, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. B. Bjorkholm, A. Cable, and A. Ashkin, "3-dimensional viscosous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48-51 (1985).
[CrossRef] [PubMed]

Cohen-Tannoudji, C. N.

C. N. Cohen-Tannoudji, "Manipulating atoms with photons," Rev. Mod. Phys. 70, 707-719 (1998).
[CrossRef]

Dasari, R. R.

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser - a laser with one-atom in an optical-resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

Dehmelt, H. G.

W. Neuhauser,M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, "Optical-sideband cooling of visible atom cloud confined in parabolic well," Phys. Rev. Lett. 41, 233-236 (1978).
[CrossRef]

Ding, Y. J.

A. E. Kaplan and Y. J. Ding, "Hysteretic and multiphoton optical resonances of a single cyclotron electron," IEEE JQE  24, 1470-1482 (1988).
[CrossRef]

Dowling, J. P.

J. P. Dowling and J. Gea-Banacloche, "Evanescent light-wave atom mirrors, resonators waveguides, and traps," Adv. Atomic Mol. Opt. Phys. 37, 1-94 (1996).

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, "Observation of radiation-pressure trapping of particles by alternating lightbeams," Phys. Rev. Lett. 54, 1245-1248 (1985).
[CrossRef] [PubMed]

Feld, M. S.

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser - a laser with one-atom in an optical-resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

Filipowicz, P.

P. Filipowicz, J. Javanainen, and P. Meystre, "Theory of a microscopic maser," Phys. Rev. A 34, 3077-3087 (1986).
[CrossRef] [PubMed]

Freeman, R. R.

J. B. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, "Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure," Phys. Rev. Lett. 41, 1361-1364 (1978).
[CrossRef]

Gahagan, K. T.

K. T. Gahagan and G. A. Swartzlander, Jr., "Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap," JOSA B 16, 533-537 (1999).
[CrossRef]

K. T. Gahagan and G. A. Swartzlander, Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996)
[CrossRef] [PubMed]

Gea-Banacloche, J.

J. P. Dowling and J. Gea-Banacloche, "Evanescent light-wave atom mirrors, resonators waveguides, and traps," Adv. Atomic Mol. Opt. Phys. 37, 1-94 (1996).

Gilhaus, H.

Th. Sauter, H. Gilhaus, I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, "On the photo-dynamics of single ions in a trap," Z. Phys. D 10, 153-163 (1988).
[CrossRef]

Hänsch, T. W.

T. W. Hänsch and A. L. Schawlow, "Cooling of gasses by laser radiation," Opt. Comm. 13, 68-69 (1975).
[CrossRef]

Hohenstatt, M.

W. Neuhauser,M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, "Optical-sideband cooling of visible atom cloud confined in parabolic well," Phys. Rev. Lett. 41, 233-236 (1978).
[CrossRef]

Hollberg, L.

S. Chu, L. Hollberg, J. B. Bjorkholm, A. Cable, and A. Ashkin, "3-dimensional viscosous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48-51 (1985).
[CrossRef] [PubMed]

Itano, W. M.

For review on coherent quantum-state manipulation of trapped ions see e. g. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, "Experimental issues in coherent quantum-state manipulation of trapped atomic ions," J. of Research of the NIST,  103, 259-328 (1998).

D. J. Wineland and W. M. Itano, "Laser cooling of atoms," Phys. Rev. A 20, 1521-1540 (1979).

Javanainen, J.

Kaivola, M.

Kaplan, A. E.

A. E. Kaplan and Y. J. Ding, "Hysteretic and multiphoton optical resonances of a single cyclotron electron," IEEE JQE  24, 1470-1482 (1988).
[CrossRef]

A. E. Kaplan, "Relativistic nonlinear optics of a single cyclotron electron," Phys. Rev. Lett. 56, 456-459 (1986).
[CrossRef] [PubMed]

A. E. Kaplan, "Hysteresis in cyclotron resonance based on weak-relativistic mass-effect of the electron," Phys. Rev. Lett. 48, 138-141 (1982).
[CrossRef]

Kappler, C.

R. Blömel, C. Kappler, W. Quint, and H. Walther, "Chaos and order of laser-cooled ions in a Paul trap," Phys. Rev. A 40, 808-823 (1989).

King, B. E.

For review on coherent quantum-state manipulation of trapped ions see e. g. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, "Experimental issues in coherent quantum-state manipulation of trapped atomic ions," J. of Research of the NIST,  103, 259-328 (1998).

Knize, R. J.

T. Takekoshi, B. M. Patterson, and R. J. Knize, "Observation of optically trapped cold cesium molecules," Phys. Rev. Lett. 81, 5105-5108 (1998).
[CrossRef]

Leibfried, D.

For review on coherent quantum-state manipulation of trapped ions see e. g. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, "Experimental issues in coherent quantum-state manipulation of trapped atomic ions," J. of Research of the NIST,  103, 259-328 (1998).

Letokhov, V. S.

V. S. Letokhov, V. G. Minogin, and B. D. Pavlik, "Cooling and trapping of atoms and molecules by a resonant laser field," Opt. Comm. 19, 72-75 (1976).
[CrossRef]

Meekhof, D. M.

For review on coherent quantum-state manipulation of trapped ions see e. g. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, "Experimental issues in coherent quantum-state manipulation of trapped atomic ions," J. of Research of the NIST,  103, 259-328 (1998).

Meschede, D.

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

Metcalf, H.

H. Metcalf and P. van der Straten, "Cooling and trapping of neutral atoms," Phys. Rep. 244, 203-286 (1994).
[CrossRef]

Meystre, P.

P. Filipowicz, J. Javanainen, and P. Meystre, "Theory of a microscopic maser," Phys. Rev. A 34, 3077-3087 (1986).
[CrossRef] [PubMed]

Minogin, V. G.

V. S. Letokhov, V. G. Minogin, and B. D. Pavlik, "Cooling and trapping of atoms and molecules by a resonant laser field," Opt. Comm. 19, 72-75 (1976).
[CrossRef]

Monroe, C.

For review on coherent quantum-state manipulation of trapped ions see e. g. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, "Experimental issues in coherent quantum-state manipulation of trapped atomic ions," J. of Research of the NIST,  103, 259-328 (1998).

Müller, G.

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

Neuhauser, W.

Th. Sauter, H. Gilhaus, I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, "On the photo-dynamics of single ions in a trap," Z. Phys. D 10, 153-163 (1988).
[CrossRef]

W. Neuhauser,M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, "Optical-sideband cooling of visible atom cloud confined in parabolic well," Phys. Rev. Lett. 41, 233-236 (1978).
[CrossRef]

Nielsen, U.

Patterson, B. M.

T. Takekoshi, B. M. Patterson, and R. J. Knize, "Observation of optically trapped cold cesium molecules," Phys. Rev. Lett. 81, 5105-5108 (1998).
[CrossRef]

Pavlik, B. D.

V. S. Letokhov, V. G. Minogin, and B. D. Pavlik, "Cooling and trapping of atoms and molecules by a resonant laser field," Opt. Comm. 19, 72-75 (1976).
[CrossRef]

Pearson, D. B.

J. B. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, "Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure," Phys. Rev. Lett. 41, 1361-1364 (1978).
[CrossRef]

Peik, E.

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, "Sideband cooling of ions in radio-frequency traps," Phys. Rev. A 60, 439-449 (1999).

Phillips, W. D.

W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

Poulsen, O.

Quint, W.

R. Blömel, C. Kappler, W. Quint, and H. Walther, "Chaos and order of laser-cooled ions in a Paul trap," Phys. Rev. A 40, 808-823 (1989).

Riis, E.

Sauter, Th.

Th. Sauter, H. Gilhaus, I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, "On the photo-dynamics of single ions in a trap," Z. Phys. D 10, 153-163 (1988).
[CrossRef]

Schawlow, A. L.

T. W. Hänsch and A. L. Schawlow, "Cooling of gasses by laser radiation," Opt. Comm. 13, 68-69 (1975).
[CrossRef]

Siemers, I.

Th. Sauter, H. Gilhaus, I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, "On the photo-dynamics of single ions in a trap," Z. Phys. D 10, 153-163 (1988).
[CrossRef]

Swartzlander, G. A.

K. T. Gahagan and G. A. Swartzlander, Jr., "Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap," JOSA B 16, 533-537 (1999).
[CrossRef]

K. T. Gahagan and G. A. Swartzlander, Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996)
[CrossRef] [PubMed]

Takekoshi, T.

T. Takekoshi, B. M. Patterson, and R. J. Knize, "Observation of optically trapped cold cesium molecules," Phys. Rev. Lett. 81, 5105-5108 (1998).
[CrossRef]

Toschek, P. E.

Th. Sauter, H. Gilhaus, I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, "On the photo-dynamics of single ions in a trap," Z. Phys. D 10, 153-163 (1988).
[CrossRef]

W. Neuhauser,M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, "Optical-sideband cooling of visible atom cloud confined in parabolic well," Phys. Rev. Lett. 41, 233-236 (1978).
[CrossRef]

van der Straten, P.

H. Metcalf and P. van der Straten, "Cooling and trapping of neutral atoms," Phys. Rep. 244, 203-286 (1994).
[CrossRef]

von Zanthier, Th.

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, "Sideband cooling of ions in radio-frequency traps," Phys. Rev. A 60, 439-449 (1999).

Walther, H.

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, "Sideband cooling of ions in radio-frequency traps," Phys. Rev. A 60, 439-449 (1999).

R. Blömel, C. Kappler, W. Quint, and H. Walther, "Chaos and order of laser-cooled ions in a Paul trap," Phys. Rev. A 40, 808-823 (1989).

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

Wineland, D. J.

For review on coherent quantum-state manipulation of trapped ions see e. g. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, "Experimental issues in coherent quantum-state manipulation of trapped atomic ions," J. of Research of the NIST,  103, 259-328 (1998).

D. J. Wineland and W. M. Itano, "Laser cooling of atoms," Phys. Rev. A 20, 1521-1540 (1979).

Adv. Atomic Mol. Opt. Phys. (1)

J. P. Dowling and J. Gea-Banacloche, "Evanescent light-wave atom mirrors, resonators waveguides, and traps," Adv. Atomic Mol. Opt. Phys. 37, 1-94 (1996).

IEEE JQE (1)

A. E. Kaplan and Y. J. Ding, "Hysteretic and multiphoton optical resonances of a single cyclotron electron," IEEE JQE  24, 1470-1482 (1988).
[CrossRef]

J. of Research of the NIST (1)

For review on coherent quantum-state manipulation of trapped ions see e. g. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, "Experimental issues in coherent quantum-state manipulation of trapped atomic ions," J. of Research of the NIST,  103, 259-328 (1998).

J. Opt. Soc. Am. B (1)

JOSA B (1)

K. T. Gahagan and G. A. Swartzlander, Jr., "Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap," JOSA B 16, 533-537 (1999).
[CrossRef]

Opt. Comm. (2)

T. W. Hänsch and A. L. Schawlow, "Cooling of gasses by laser radiation," Opt. Comm. 13, 68-69 (1975).
[CrossRef]

V. S. Letokhov, V. G. Minogin, and B. D. Pavlik, "Cooling and trapping of atoms and molecules by a resonant laser field," Opt. Comm. 19, 72-75 (1976).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

H. Metcalf and P. van der Straten, "Cooling and trapping of neutral atoms," Phys. Rep. 244, 203-286 (1994).
[CrossRef]

Phys. Rev. A (3)

P. Filipowicz, J. Javanainen, and P. Meystre, "Theory of a microscopic maser," Phys. Rev. A 34, 3077-3087 (1986).
[CrossRef] [PubMed]

R. Blömel, C. Kappler, W. Quint, and H. Walther, "Chaos and order of laser-cooled ions in a Paul trap," Phys. Rev. A 40, 808-823 (1989).

D. J. Wineland and W. M. Itano, "Laser cooling of atoms," Phys. Rev. A 20, 1521-1540 (1979).

Phys. Rev. Lett. (10)

S. Chu, L. Hollberg, J. B. Bjorkholm, A. Cable, and A. Ashkin, "3-dimensional viscosous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48-51 (1985).
[CrossRef] [PubMed]

T. Takekoshi, B. M. Patterson, and R. J. Knize, "Observation of optically trapped cold cesium molecules," Phys. Rev. Lett. 81, 5105-5108 (1998).
[CrossRef]

A. E. Kaplan, "Hysteresis in cyclotron resonance based on weak-relativistic mass-effect of the electron," Phys. Rev. Lett. 48, 138-141 (1982).
[CrossRef]

A. E. Kaplan, "Relativistic nonlinear optics of a single cyclotron electron," Phys. Rev. Lett. 56, 456-459 (1986).
[CrossRef] [PubMed]

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser - a laser with one-atom in an optical-resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

W. Neuhauser,M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, "Optical-sideband cooling of visible atom cloud confined in parabolic well," Phys. Rev. Lett. 41, 233-236 (1978).
[CrossRef]

S. Chu, J. B. Bjorkholm, A. Ashkin, and A. Cable, "Experimental observation of optically trapped atoms," Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, "Observation of radiation-pressure trapping of particles by alternating lightbeams," Phys. Rev. Lett. 54, 1245-1248 (1985).
[CrossRef] [PubMed]

J. B. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, "Observation of focusing of neutral atoms by dipole forces of resonance-radiation pressure," Phys. Rev. Lett. 41, 1361-1364 (1978).
[CrossRef]

Phys. Rev., A (1)

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, "Sideband cooling of ions in radio-frequency traps," Phys. Rev. A 60, 439-449 (1999).

Proc. Natl. Acad. Sci. USA (1)

A. Ashkin, "Optical trapping and manipulation of neutral particles using lasers," Proc. Natl. Acad. Sci. USA,  94, 4853-4860 (1997).
[CrossRef] [PubMed]

Rev. Mod. Phys. (3)

S. Chu, "The manipulation of neutral particles," Rev. Mod. Phys. 70, 685-706 (1998).
[CrossRef]

C. N. Cohen-Tannoudji, "Manipulating atoms with photons," Rev. Mod. Phys. 70, 707-719 (1998).
[CrossRef]

W. D. Phillips, "Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

Science (1)

For reviews on particle trapping by gradient forces, see A. Ashkin, "Applications of laser-radiation pressure," Science  210, 1081-1088 (1980) and Refs. [12-15] below.
[PubMed]

Z. Phys. D (1)

Th. Sauter, H. Gilhaus, I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, "On the photo-dynamics of single ions in a trap," Z. Phys. D 10, 153-163 (1988).
[CrossRef]

Other (8)

J. Javanainen, "Light pressure cooling of a trapped 3-level ions," in Fundamentals of Laser Interaction. Lecture Notes in Physics, 229, 249-258, Ed. F. Ehlotzky, NY, Springer (1985).

S. T. Thornton and J. B. Marion, Classical dynamics of particles and systems, 5-th ed., Thomson Brooks/Cole, Belmont, CA, 2004.

H. C. van de Hulst, Light scattering by small particles, Dover, New York, 1981.

P. K. Ghosh, Ion traps, Clarendon Press, Oxford, 1995.

S.A. Schaaf and P. L. Chambre, Flow of Rarefied Gases, Princeton University Press, 1961.

Laser-induced SSO due to Doppler effect was proposed in A. E. Kaplan, "On Doppler instability of resonantly absorbing (or amplifying) systems in a strong field," Abstr. the 6th Natl. Conf. on Nonlinear Optics (Minsk), publ. by Moscow St. Univ., Moscow, 1972, p. 26.

See e. g. N. Minorsky, Nonlinear Oscillations, Princeton, NJ, Van Nostrand, 1962.

For reviews on trapping/cooling see e. g. Laser manipulations of atoms and ions, Eds. E. Arimondo, W. D. Phillips, and S. Strumia (N.-Holland, Amst., 1992) and Refs. [6-9] below.

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Figures (1)

Fig. 1.
Fig. 1.

The normalized LASSO amplitude (and peak velocity) u vs the normalized pumping, I=ρ 2/ρ 2 T , for r≫1. Curves: (a), 1: δ=1/√3, 2: δ=1, 3: δ=4, 4: δ=20. Solid lines - stable, broken - unstable modes. Arrows show the directions of hysteresis jumps.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

z̈+Ω2z=[FL(z,z˙,t)+FT(z,z˙)] M ;
F±=(hˉk)(γΩR2)[γ2+(Δωkz˙)2]1
FLF+Fz˙ΔωQ,whereQ=hˉ k2 γ ΩR2 (γ2+Δω2)2 > 0
v˙=v[G(v2)ΓvL˜],G=(2πMv2)1ππFL(z˙)z˙d(Ωt)
δ=Δωγ;ρ=ΩRγ=ΩdEhˉγ;u=vk γ ,
G(ρ,δ,u2)=232(hˉω2Mc2)δρ2D(δ,u2)
ρ2=232(ρT2+ρg2u) D (δ,u2) δ
ρT2=(Mc2hˉω)(Γω),ρg2=ρT2r;
δthr2=ρT2(1+δ2)22δ.
ulowr (ρ2ρthr21) .
whysconstδ32,const=O (1).

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