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 light-beams,” 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. A20, 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., and 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. A40, 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.,  A60, 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, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996)
    [Crossref] [PubMed]
  34. K. T. Gahagan and G. A. Swartzlander, “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.,  A60, 439–449 (1999).

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

1998 (4)

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]

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., and Opt. Phys. 37, 1–94 (1996).

K. T. Gahagan and G. A. Swartzlander, “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. A40, 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 light-beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[Crossref] [PubMed]

D. Meschede, H. Walther, and G. Müller, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (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]

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]

1979 (1)

D. J. Wineland and W. M. Itano, “Laser cooling of atoms,” Phys. Rev. A20, 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.,  A60, 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 light-beams,” 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]

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.,  A60, 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. A40, 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]

Chambre, P. L.

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

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., and Opt. Phys. 37, 1–94 (1996).

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by alternating light-beams,” 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, “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, “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., and Opt. Phys. 37, 1–94 (1996).

Ghosh, P. K.

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

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.

D. J. Wineland and W. M. Itano, “Laser cooling of atoms,” Phys. Rev. A20, 1521–1540 (1979).

Javanainen, J.

P. Filipowicz, J. Javanainen, and P. Meystre, “Theory of a microscopic maser,” Phys. Rev. A 34, 3077–3087 (1986).
[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]

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).

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]

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.

Kappler, C.

R. Blömel, C. Kappler, W. Quint, and H. Walther, “Chaos and order of laser-cooled ions in a Paul trap,” Phys. Rev. A40, 808–823 (1989).

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]

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]

Marion, J. B.

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

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]

Minorsky, N.

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

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.,  A60, 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. A40, 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]

Schaaf, S.A.

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

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, “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, “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]

Thornton, S. T.

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

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 de Hulst, H. C.

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

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H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203–286 (1994).
[Crossref]

Walther, H.

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, “Sideband cooling of ions in radio-frequency traps,” Phys. Rev.,  A60, 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. A40, 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.

D. J. Wineland and W. M. Itano, “Laser cooling of atoms,” Phys. Rev. A20, 1521–1540 (1979).

Zanthier, von

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, “Sideband cooling of ions in radio-frequency traps,” Phys. Rev.,  A60, 439–449 (1999).

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

J. P. Dowling and J. Gea-Banacloche, “Evanescent light-wave atom mirrors, resonators waveguides, and traps,” Adv. Atomic, Mol., and 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. Opt. Soc. Am. B (1)

JOSA B (1)

K. T. Gahagan and G. A. Swartzlander, “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. (3)

D. J. Wineland and W. M. Itano, “Laser cooling of atoms,” Phys. Rev. A20, 1521–1540 (1979).

R. Blömel, C. Kappler, W. Quint, and H. Walther, “Chaos and order of laser-cooled ions in a Paul trap,” Phys. Rev. A40, 808–823 (1989).

E. Peik, J. Abbel, Th. Becker, von Zanthier, and H. Walther, “Sideband cooling of ions in radio-frequency traps,” Phys. Rev.,  A60, 439–449 (1999).

Phys. Rev. A (1)

P. Filipowicz, J. Javanainen, and P. Meystre, “Theory of a microscopic maser,” Phys. Rev. A 34, 3077–3087 (1986).
[Crossref] [PubMed]

Phys. Rev. Lett. (10)

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]

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]

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 light-beams,” 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]

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]

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]

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]

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 (10)

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

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.

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).

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]

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.

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

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.

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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)

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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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