Abstract

We review the modifications and implications of the effect of light forces on atoms when the field is enclosed in an optical resonator of high finesse. The systems considered range from a single atom strongly coupled to a single mode of a high-Q microcavity to a large ensemble of atoms in a highly degenerate quasi-confocal resonator. We set up general models that allow us to obtain analytic expressions for the optical potential, friction, and diffusion. In the bad-cavity limit the modified cooling properties can be attributed to the spectral modifications of light absorption and spontaneous emission in a form of generalized and enhanced Doppler cooling. For the strong coupling regime in a good cavity, we identify the dynamical coupling between the light field intensity and the atomic motion as the central mechanism underlying the cavity-induced cooling. The dynamical cavity cooling, which does not rely on spontaneous emission, can be enhanced by multimode cavity geometries because of the effect of coherent photon redistribution between different modes. The model is then generalized to include several distinct frequencies to account for more general trap geometries. Finally we show that the field-induced buildup of correlations between the motion of different particles plays a central role in the scaling behavior of the system. Depending on the geometry and parameters, its effect ranges from strong destructive interference, slowing down the cooling process, to self-organized crystallization, implying atomic self-trapping and faster cooling to lower temperatures by cooperative coherent scattering.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Chu, “Nobel lecture: the manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
    [CrossRef]
  2. C. Cohen-Tannoudji, “Nobel lecture: manipulating atoms with photons,” Rev. Mod. Phys. 70, 707–719 (1998).
    [CrossRef]
  3. W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).
    [CrossRef]
  4. S. Haroche, “Cavity quantum electrodynamics,” in Fundamental Systems in Quantum Optics, Les Houches Summer School, Proceedings, Vol. 53, J. Dalibard, J.-M. Raimond, and J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), pp. 767–940.
  5. P. Berman, ed., Cavity Quantum Electrodynamics (Academic, San Diego, Calif., 1994.).
  6. R. J. Thompson, G. Rempe, and H. J. Kimble, “Observation of normal-mode splitting for an atom in an optical cavity,” Phys. Rev. Lett. 68, 1132–1135 (1992).
    [CrossRef] [PubMed]
  7. H. Mabuchi, M. S. Chapman, T. Q. A. Turchette, and H. J. Kimble, “Real-time detection of individual atoms falling through a high-finesse optical cavity,” Opt. Lett. 21, 1393–1395 (1996).
    [CrossRef] [PubMed]
  8. C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
    [CrossRef]
  9. P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Dynamics of single-atom motion observed in a high-finesse cavity,” Phys. Rev. Lett. 82, 3791–3794 (1999).
    [CrossRef]
  10. J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
    [CrossRef]
  11. P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997).
    [CrossRef]
  12. C. Cohen-Tannoudji, “Atomic motion in laser light,” in Fundamental Systems in Quantum Optics, Les Houches Summer School Proceedings, Vol. 53, J. Dalibard, J.-M. Raimond, and J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), pp. 1–164.
  13. H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, New York, 1999).
  14. J. Dalibard and C. Cohen-Tannoudji, “Laser cooling below the Doppler limit by polarization gradients: simple theoretical models,” J. Opt. Soc. Am. B 6, 2023–2045 (1989).
    [CrossRef]
  15. A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
    [CrossRef] [PubMed]
  16. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  17. D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981).
    [CrossRef]
  18. D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. A 59, 2623–2626 (1987).
  19. T. W. Mossberg, M. Lewenstein, and D. J. Gauthier, “Trapping and cooling of atoms in a vacuum perturbed in a frequency-dependent manner,” Phys. Rev. Lett. 67, 1723–1726 (1991).
    [CrossRef] [PubMed]
  20. M. Lewenstein and L. Roso, “Cooling of atoms in colored vacua,” Phys. Rev. A 47, 3385–3389 (1993).
    [CrossRef] [PubMed]
  21. J. I. Cirac, M. Lewenstein, and P. Zoller, “Laser cooling a trapped atom in a cavity: bad-cavity limit,” Phys. Rev. A 51, 1650–1654 (1995).
    [CrossRef] [PubMed]
  22. V. Vuletić and S. Chu, “Laser cooling of atoms, ions, or molecules by coherent scattering,” Phys. Rev. Lett. 84, 3787–3790 (2000).
    [CrossRef] [PubMed]
  23. V. Vuletić, H. W. Chan, and A. T. Black, “Three-dimensional cavity Doppler cooling and cavity sideband cooling by coherent scattering,” Phys. Rev. A 64, 033405 (2001).
    [CrossRef]
  24. G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
    [CrossRef]
  25. P. Münstermann, T. Fischer, P. W. H. Pinkse, and G. Rempe, “Single slow atoms from an atomic fountain observed in a high-finesse optical cavity,” Opt. Commun. 159, 63–67 (1999).
    [CrossRef]
  26. P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365–368 (2000).
    [CrossRef] [PubMed]
  27. C. J. Hood, T. W. Lynn, A. C. Doherty, and A. S. P. H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
    [CrossRef] [PubMed]
  28. P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Observation of cavity-mediated long-range light forces between strongly coupled atoms,” Phys. Rev. Lett. 84, 4068–4071 (2000).
    [CrossRef] [PubMed]
  29. J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
    [CrossRef]
  30. J. Dalibard and C. Cohen-Tannoudji, “Atomic motion in laser light: connection between semiclassical and quantum descriptions,” J. Phys. B 18, 1661–1683 (1985).
    [CrossRef]
  31. A. C. Doherty, T. W. Lynn, C. J. Hood, and H. J. Kimble, “Trapping of single atoms with single photons in cavity QED,” Phys. Rev. A 63, 013401 (2000).
    [CrossRef]
  32. I. Protsenko, P. Domokos, V. Lefèvre, J. Hare, J. M. Raimond, and L. Davidovich, “Quantum theory of a thresholdless laser,” Phys. Rev. A 59, 1667–1681 (1999).
    [CrossRef]
  33. J. Dalibard and C. Cohen-Tannoudji, “Dressed-atom approach to atomic motion in laser light: the dipole force revisited,” J. Opt. Soc. Am. B 2, 1707–1720 (1985).
    [CrossRef]
  34. T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, “Collective light forces on atoms in a high-finesse cavity,” New J. Phys. 3, 11.1–11.20 (2001).
  35. P. Domokos, T. Salzburger, and H. Ritsch, “Dissipative motion of an atom with transverse coherent driving in a cavity with many degenerate modes,” Phys. Rev. A 66, 043406 (2002).
    [CrossRef]
  36. S. Pirandola, D. Vitali, and P. Tombesi, “Trapping and cooling single atoms with far-off-resonance intracavity doughnut modes,” Phys. Rev. A 67, 023404 (2003).
    [CrossRef]
  37. P. Domokos, M. Gangl, and H. Ritsch, “Single-atom detection in high-Q multimode cavities,” Opt. Commun. 185, 115–123 (2000).
    [CrossRef]
  38. A. Hemmerich, “Quantum entanglement in dilute optical lattices,” Phys. Rev. A 60, 943–946 (1999).
    [CrossRef]
  39. M. Gangl and H. Ritsch, “Cold atoms in a high-Q ring cavity,” Phys. Rev. A 61, 043405 (2000).
    [CrossRef]
  40. P. Horak and H. Ritsch, “Scaling properties of cavity-enhanced atom cooling,” Phys. Rev. A 64, 033422 (2001).
    [CrossRef]
  41. S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
    [CrossRef]
  42. Y. B. Ovchinnikov, S. V. Shul’ga, and V. I. Balykin, “An atomic trap based on evanescent light waves,” J. Phys. B 24, 3173–3178 (1991).
    [CrossRef]
  43. Y. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
    [CrossRef]
  44. H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D gas of laser cooled atoms in a planar matter waveguide,” Phys. Rev. Lett. 81, 5298–5301 (1998).
    [CrossRef]
  45. F. Treussart, J. Hare, L. Collot, V. Lefèvre, D. S. Weiss, V. S. Sandoghdar, J. M. Raimond, and S. Haroche, “Quantized atom-field force at the surface of a microsphere,” Opt. Lett. 19, 1651–1653 (1994).
    [CrossRef] [PubMed]
  46. H. Mabuchi and H. J. Kimble, “Atom galleries for whispering atoms: binding atoms in stable orbits around an optical resonator,” Opt. Lett. 19, 749–752 (1994).
    [CrossRef] [PubMed]
  47. A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
    [CrossRef] [PubMed]
  48. K. Ellinger, J. Cooper, and P. Zoller, “Light-pressure force in N-atom systems,” Phys. Rev. A 49, 3909–3933 (1994).
    [CrossRef] [PubMed]
  49. M. Gangl and H. Ritsch, “Collective dynamical cooling of neutral particles in a high-Q optical cavity,” Phys. Rev. A 61, 011402 (2000).
    [CrossRef]
  50. P. Domokos and H. Ritsch, “Collective cooling and self-organization of atoms in a cavity,” Phys. Rev. Lett. 89, 253003 (2002).
    [CrossRef] [PubMed]
  51. B. Deb and G. Kurizki, “Formation of giant quasibound cold diatoms by strong atom-cavity coupling,” Phys. Rev. Lett. 83, 714–717 (1999).
    [CrossRef]
  52. J. I. Kim, R. B. B. Santos, and P. Nussenzveig, “Manipulation of cold atomic collisions by cavity QED effects,” Phys. Rev. Lett. 86, 1474–1477 (2001).
    [CrossRef] [PubMed]
  53. M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
    [CrossRef]
  54. H. W. Chan, A. T. Black, and V. Vuletić, “Observation of collective-emission-induced cooling of atoms in an optical cavity,” Phys. Rev. Lett. 90, 063003 (2003).
    [CrossRef] [PubMed]
  55. B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).
  56. M. Gangl and H. Ritsch, “Cavity-mediated dark-state cool-ing without spontaneous emission,” Phys. Rev. A 64, 063414 (2001).
    [CrossRef]
  57. M. A. Olshanii and V. G. Minogin, “Three-dimensional velocity-selective coherent population trapping of a (3+3)-level atom,” Opt. Commun. 89, 393–398 (1992).
    [CrossRef]
  58. M. Gangl and H. Ritsch, “Cavity assisted polarization gradient cooling,” J. Phys. B 35, 4565–4582 (2002).
    [CrossRef]
  59. T. Fischer, P. Maunz, P. W. H. Pinkse, T. Puppe, and G. Rempe, “Feedback on the motion of a single atom in an optical cavity,” Phys. Rev. Lett. 88, 163002 (2002).
    [CrossRef] [PubMed]
  60. A. Mosk, S. Jochim, H. Moritz, T. Elsässer, M. Weidemüller, and R. Grimm, “Resonator-enhanced optical dipole trap for fermionic lithium atoms,” Opt. Lett. 26, 1837–1839 (2001).
    [CrossRef]
  61. J. F. Roch, K. Vigneron, A. Sinatra, and P. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
    [CrossRef]
  62. J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” arXiv.org e-Print archive, http://lanl.arxiv.org/abs/quant-ph/0211013 (2002).
  63. P. Horak and H. Ritsch, “Manipulating a Bose-condensate with a single photon,” Eur. Phys. J. D 13, 279–287 (2001).
    [CrossRef]
  64. P. Horak and H. Ritsch, “Dissipative dynamics of Bose condensates in optical cavities,” Phys. Rev. A 63, 023603 (2001).
    [CrossRef]
  65. P. Domokos and H. Ritsch, “Efficient loading and cooling in a dynamic optical evanescent-wave microtrap,” Europhys. Lett. 54, 306–312 (2001).
    [CrossRef]
  66. P. Horak and H. Ritsch, “Cavity assisted quasiparticle damping in a Bose–Einstein condensate,” Phys. Rev. A 63, 051603 (2001).
    [CrossRef]
  67. D. Jaksch, S. Gardiner, K. Schulze, J. Cirac, and P. Zoller, “Uniting Bose-Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4773–4776 (2001).
    [CrossRef]
  68. R. Bonifacio, G. Robb, and B. M. Neil, “Propagation, cavity, and Doppler-broadening effects in the collective atomic recoil laser,” Phys. Rev. A 56, 912–924 (1997).
    [CrossRef]
  69. R. Bonifacio, L. D. Salvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716–1724 (1994).
    [CrossRef] [PubMed]
  70. P. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A 59, 585–596 (2001).
    [CrossRef]
  71. R. Bonifacio, B. M. Neil, and G. Robb, “Self-cooling in a system of driven two-level atoms,” Opt. Commun. 161, 1–5 (1999).
    [CrossRef]
  72. V. Vuletić, “Cavity cooling with a hot cavity,” in Laser Physics at the Limits, H. Figger, D. Meschede, and C. Zimmermann, eds. (Springer, New York, 2001), pp. 67–74.

2003 (2)

S. Pirandola, D. Vitali, and P. Tombesi, “Trapping and cooling single atoms with far-off-resonance intracavity doughnut modes,” Phys. Rev. A 67, 023404 (2003).
[CrossRef]

H. W. Chan, A. T. Black, and V. Vuletić, “Observation of collective-emission-induced cooling of atoms in an optical cavity,” Phys. Rev. Lett. 90, 063003 (2003).
[CrossRef] [PubMed]

2002 (4)

M. Gangl and H. Ritsch, “Cavity assisted polarization gradient cooling,” J. Phys. B 35, 4565–4582 (2002).
[CrossRef]

T. Fischer, P. Maunz, P. W. H. Pinkse, T. Puppe, and G. Rempe, “Feedback on the motion of a single atom in an optical cavity,” Phys. Rev. Lett. 88, 163002 (2002).
[CrossRef] [PubMed]

P. Domokos and H. Ritsch, “Collective cooling and self-organization of atoms in a cavity,” Phys. Rev. Lett. 89, 253003 (2002).
[CrossRef] [PubMed]

P. Domokos, T. Salzburger, and H. Ritsch, “Dissipative motion of an atom with transverse coherent driving in a cavity with many degenerate modes,” Phys. Rev. A 66, 043406 (2002).
[CrossRef]

2001 (13)

T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, “Collective light forces on atoms in a high-finesse cavity,” New J. Phys. 3, 11.1–11.20 (2001).

P. Horak and H. Ritsch, “Scaling properties of cavity-enhanced atom cooling,” Phys. Rev. A 64, 033422 (2001).
[CrossRef]

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

V. Vuletić, H. W. Chan, and A. T. Black, “Three-dimensional cavity Doppler cooling and cavity sideband cooling by coherent scattering,” Phys. Rev. A 64, 033405 (2001).
[CrossRef]

A. Mosk, S. Jochim, H. Moritz, T. Elsässer, M. Weidemüller, and R. Grimm, “Resonator-enhanced optical dipole trap for fermionic lithium atoms,” Opt. Lett. 26, 1837–1839 (2001).
[CrossRef]

J. I. Kim, R. B. B. Santos, and P. Nussenzveig, “Manipulation of cold atomic collisions by cavity QED effects,” Phys. Rev. Lett. 86, 1474–1477 (2001).
[CrossRef] [PubMed]

P. Horak and H. Ritsch, “Manipulating a Bose-condensate with a single photon,” Eur. Phys. J. D 13, 279–287 (2001).
[CrossRef]

P. Horak and H. Ritsch, “Dissipative dynamics of Bose condensates in optical cavities,” Phys. Rev. A 63, 023603 (2001).
[CrossRef]

P. Domokos and H. Ritsch, “Efficient loading and cooling in a dynamic optical evanescent-wave microtrap,” Europhys. Lett. 54, 306–312 (2001).
[CrossRef]

P. Horak and H. Ritsch, “Cavity assisted quasiparticle damping in a Bose–Einstein condensate,” Phys. Rev. A 63, 051603 (2001).
[CrossRef]

D. Jaksch, S. Gardiner, K. Schulze, J. Cirac, and P. Zoller, “Uniting Bose-Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4773–4776 (2001).
[CrossRef]

M. Gangl and H. Ritsch, “Cavity-mediated dark-state cool-ing without spontaneous emission,” Phys. Rev. A 64, 063414 (2001).
[CrossRef]

P. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A 59, 585–596 (2001).
[CrossRef]

2000 (8)

M. Gangl and H. Ritsch, “Collective dynamical cooling of neutral particles in a high-Q optical cavity,” Phys. Rev. A 61, 011402 (2000).
[CrossRef]

M. Gangl and H. Ritsch, “Cold atoms in a high-Q ring cavity,” Phys. Rev. A 61, 043405 (2000).
[CrossRef]

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365–368 (2000).
[CrossRef] [PubMed]

C. J. Hood, T. W. Lynn, A. C. Doherty, and A. S. P. H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Observation of cavity-mediated long-range light forces between strongly coupled atoms,” Phys. Rev. Lett. 84, 4068–4071 (2000).
[CrossRef] [PubMed]

P. Domokos, M. Gangl, and H. Ritsch, “Single-atom detection in high-Q multimode cavities,” Opt. Commun. 185, 115–123 (2000).
[CrossRef]

A. C. Doherty, T. W. Lynn, C. J. Hood, and H. J. Kimble, “Trapping of single atoms with single photons in cavity QED,” Phys. Rev. A 63, 013401 (2000).
[CrossRef]

V. Vuletić and S. Chu, “Laser cooling of atoms, ions, or molecules by coherent scattering,” Phys. Rev. Lett. 84, 3787–3790 (2000).
[CrossRef] [PubMed]

1999 (7)

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Dynamics of single-atom motion observed in a high-finesse cavity,” Phys. Rev. Lett. 82, 3791–3794 (1999).
[CrossRef]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

I. Protsenko, P. Domokos, V. Lefèvre, J. Hare, J. M. Raimond, and L. Davidovich, “Quantum theory of a thresholdless laser,” Phys. Rev. A 59, 1667–1681 (1999).
[CrossRef]

A. Hemmerich, “Quantum entanglement in dilute optical lattices,” Phys. Rev. A 60, 943–946 (1999).
[CrossRef]

P. Münstermann, T. Fischer, P. W. H. Pinkse, and G. Rempe, “Single slow atoms from an atomic fountain observed in a high-finesse optical cavity,” Opt. Commun. 159, 63–67 (1999).
[CrossRef]

B. Deb and G. Kurizki, “Formation of giant quasibound cold diatoms by strong atom-cavity coupling,” Phys. Rev. Lett. 83, 714–717 (1999).
[CrossRef]

R. Bonifacio, B. M. Neil, and G. Robb, “Self-cooling in a system of driven two-level atoms,” Opt. Commun. 161, 1–5 (1999).
[CrossRef]

1998 (7)

H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D gas of laser cooled atoms in a planar matter waveguide,” Phys. Rev. Lett. 81, 5298–5301 (1998).
[CrossRef]

M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
[CrossRef]

G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
[CrossRef]

S. Chu, “Nobel lecture: the manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
[CrossRef]

C. Cohen-Tannoudji, “Nobel lecture: manipulating atoms with photons,” Rev. Mod. Phys. 70, 707–719 (1998).
[CrossRef]

W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).
[CrossRef]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

1997 (5)

P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997).
[CrossRef]

B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).

J. F. Roch, K. Vigneron, A. Sinatra, and P. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Y. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

R. Bonifacio, G. Robb, and B. M. Neil, “Propagation, cavity, and Doppler-broadening effects in the collective atomic recoil laser,” Phys. Rev. A 56, 912–924 (1997).
[CrossRef]

1996 (2)

A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

H. Mabuchi, M. S. Chapman, T. Q. A. Turchette, and H. J. Kimble, “Real-time detection of individual atoms falling through a high-finesse optical cavity,” Opt. Lett. 21, 1393–1395 (1996).
[CrossRef] [PubMed]

1995 (1)

J. I. Cirac, M. Lewenstein, and P. Zoller, “Laser cooling a trapped atom in a cavity: bad-cavity limit,” Phys. Rev. A 51, 1650–1654 (1995).
[CrossRef] [PubMed]

1994 (4)

1993 (1)

M. Lewenstein and L. Roso, “Cooling of atoms in colored vacua,” Phys. Rev. A 47, 3385–3389 (1993).
[CrossRef] [PubMed]

1992 (2)

R. J. Thompson, G. Rempe, and H. J. Kimble, “Observation of normal-mode splitting for an atom in an optical cavity,” Phys. Rev. Lett. 68, 1132–1135 (1992).
[CrossRef] [PubMed]

M. A. Olshanii and V. G. Minogin, “Three-dimensional velocity-selective coherent population trapping of a (3+3)-level atom,” Opt. Commun. 89, 393–398 (1992).
[CrossRef]

1991 (2)

T. W. Mossberg, M. Lewenstein, and D. J. Gauthier, “Trapping and cooling of atoms in a vacuum perturbed in a frequency-dependent manner,” Phys. Rev. Lett. 67, 1723–1726 (1991).
[CrossRef] [PubMed]

Y. B. Ovchinnikov, S. V. Shul’ga, and V. I. Balykin, “An atomic trap based on evanescent light waves,” J. Phys. B 24, 3173–3178 (1991).
[CrossRef]

1989 (1)

1988 (1)

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

1987 (1)

D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. A 59, 2623–2626 (1987).

1985 (2)

J. Dalibard and C. Cohen-Tannoudji, “Dressed-atom approach to atomic motion in laser light: the dipole force revisited,” J. Opt. Soc. Am. B 2, 1707–1720 (1985).
[CrossRef]

J. Dalibard and C. Cohen-Tannoudji, “Atomic motion in laser light: connection between semiclassical and quantum descriptions,” J. Phys. B 18, 1661–1683 (1985).
[CrossRef]

1981 (1)

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981).
[CrossRef]

1980 (1)

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Arimondo, E.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Ashkin, A.

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Aspect, A.

A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Balykin, V. I.

Y. B. Ovchinnikov, S. V. Shul’ga, and V. I. Balykin, “An atomic trap based on evanescent light waves,” J. Phys. B 24, 3173–3178 (1991).
[CrossRef]

Berman, P.

P. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A 59, 585–596 (2001).
[CrossRef]

Black, A. T.

H. W. Chan, A. T. Black, and V. Vuletić, “Observation of collective-emission-induced cooling of atoms in an optical cavity,” Phys. Rev. Lett. 90, 063003 (2003).
[CrossRef] [PubMed]

V. Vuletić, H. W. Chan, and A. T. Black, “Three-dimensional cavity Doppler cooling and cavity sideband cooling by coherent scattering,” Phys. Rev. A 64, 033405 (2001).
[CrossRef]

Bonifacio, R.

R. Bonifacio, B. M. Neil, and G. Robb, “Self-cooling in a system of driven two-level atoms,” Opt. Commun. 161, 1–5 (1999).
[CrossRef]

R. Bonifacio, G. Robb, and B. M. Neil, “Propagation, cavity, and Doppler-broadening effects in the collective atomic recoil laser,” Phys. Rev. A 56, 912–924 (1997).
[CrossRef]

R. Bonifacio, L. D. Salvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716–1724 (1994).
[CrossRef] [PubMed]

Chan, H. W.

H. W. Chan, A. T. Black, and V. Vuletić, “Observation of collective-emission-induced cooling of atoms in an optical cavity,” Phys. Rev. Lett. 90, 063003 (2003).
[CrossRef] [PubMed]

V. Vuletić, H. W. Chan, and A. T. Black, “Three-dimensional cavity Doppler cooling and cavity sideband cooling by coherent scattering,” Phys. Rev. A 64, 033405 (2001).
[CrossRef]

Chapman, M. S.

Chu, S.

V. Vuletić and S. Chu, “Laser cooling of atoms, ions, or molecules by coherent scattering,” Phys. Rev. Lett. 84, 3787–3790 (2000).
[CrossRef] [PubMed]

S. Chu, “Nobel lecture: the manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
[CrossRef]

Cirac, J.

D. Jaksch, S. Gardiner, K. Schulze, J. Cirac, and P. Zoller, “Uniting Bose-Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4773–4776 (2001).
[CrossRef]

Cirac, J. I.

J. I. Cirac, M. Lewenstein, and P. Zoller, “Laser cooling a trapped atom in a cavity: bad-cavity limit,” Phys. Rev. A 51, 1650–1654 (1995).
[CrossRef] [PubMed]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, “Nobel lecture: manipulating atoms with photons,” Rev. Mod. Phys. 70, 707–719 (1998).
[CrossRef]

B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).

J. Dalibard and C. Cohen-Tannoudji, “Laser cooling below the Doppler limit by polarization gradients: simple theoretical models,” J. Opt. Soc. Am. B 6, 2023–2045 (1989).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

J. Dalibard and C. Cohen-Tannoudji, “Atomic motion in laser light: connection between semiclassical and quantum descriptions,” J. Phys. B 18, 1661–1683 (1985).
[CrossRef]

J. Dalibard and C. Cohen-Tannoudji, “Dressed-atom approach to atomic motion in laser light: the dipole force revisited,” J. Opt. Soc. Am. B 2, 1707–1720 (1985).
[CrossRef]

Collot, L.

Cooper, J.

K. Ellinger, J. Cooper, and P. Zoller, “Light-pressure force in N-atom systems,” Phys. Rev. A 49, 3909–3933 (1994).
[CrossRef] [PubMed]

Courtois, J.-Y.

A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

D’Angelo, E. J.

R. Bonifacio, L. D. Salvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716–1724 (1994).
[CrossRef] [PubMed]

Dalibard, J.

Davidovich, L.

I. Protsenko, P. Domokos, V. Lefèvre, J. Hare, J. M. Raimond, and L. Davidovich, “Quantum theory of a thresholdless laser,” Phys. Rev. A 59, 1667–1681 (1999).
[CrossRef]

Deb, B.

B. Deb and G. Kurizki, “Formation of giant quasibound cold diatoms by strong atom-cavity coupling,” Phys. Rev. Lett. 83, 714–717 (1999).
[CrossRef]

Doherty, A. C.

A. C. Doherty, T. W. Lynn, C. J. Hood, and H. J. Kimble, “Trapping of single atoms with single photons in cavity QED,” Phys. Rev. A 63, 013401 (2000).
[CrossRef]

C. J. Hood, T. W. Lynn, A. C. Doherty, and A. S. P. H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

Domokos, P.

P. Domokos, T. Salzburger, and H. Ritsch, “Dissipative motion of an atom with transverse coherent driving in a cavity with many degenerate modes,” Phys. Rev. A 66, 043406 (2002).
[CrossRef]

P. Domokos and H. Ritsch, “Collective cooling and self-organization of atoms in a cavity,” Phys. Rev. Lett. 89, 253003 (2002).
[CrossRef] [PubMed]

P. Domokos and H. Ritsch, “Efficient loading and cooling in a dynamic optical evanescent-wave microtrap,” Europhys. Lett. 54, 306–312 (2001).
[CrossRef]

P. Domokos, M. Gangl, and H. Ritsch, “Single-atom detection in high-Q multimode cavities,” Opt. Commun. 185, 115–123 (2000).
[CrossRef]

I. Protsenko, P. Domokos, V. Lefèvre, J. Hare, J. M. Raimond, and L. Davidovich, “Quantum theory of a thresholdless laser,” Phys. Rev. A 59, 1667–1681 (1999).
[CrossRef]

Ellinger, K.

K. Ellinger, J. Cooper, and P. Zoller, “Light-pressure force in N-atom systems,” Phys. Rev. A 49, 3909–3933 (1994).
[CrossRef] [PubMed]

Elsässer, T.

Feld, M. S.

D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. A 59, 2623–2626 (1987).

Fischer, T.

T. Fischer, P. Maunz, P. W. H. Pinkse, T. Puppe, and G. Rempe, “Feedback on the motion of a single atom in an optical cavity,” Phys. Rev. Lett. 88, 163002 (2002).
[CrossRef] [PubMed]

T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, “Collective light forces on atoms in a high-finesse cavity,” New J. Phys. 3, 11.1–11.20 (2001).

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Observation of cavity-mediated long-range light forces between strongly coupled atoms,” Phys. Rev. Lett. 84, 4068–4071 (2000).
[CrossRef] [PubMed]

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365–368 (2000).
[CrossRef] [PubMed]

P. Münstermann, T. Fischer, P. W. H. Pinkse, and G. Rempe, “Single slow atoms from an atomic fountain observed in a high-finesse optical cavity,” Opt. Commun. 159, 63–67 (1999).
[CrossRef]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Dynamics of single-atom motion observed in a high-finesse cavity,” Phys. Rev. Lett. 82, 3791–3794 (1999).
[CrossRef]

Gangl, M.

M. Gangl and H. Ritsch, “Cavity assisted polarization gradient cooling,” J. Phys. B 35, 4565–4582 (2002).
[CrossRef]

M. Gangl and H. Ritsch, “Cavity-mediated dark-state cool-ing without spontaneous emission,” Phys. Rev. A 64, 063414 (2001).
[CrossRef]

M. Gangl and H. Ritsch, “Collective dynamical cooling of neutral particles in a high-Q optical cavity,” Phys. Rev. A 61, 011402 (2000).
[CrossRef]

P. Domokos, M. Gangl, and H. Ritsch, “Single-atom detection in high-Q multimode cavities,” Opt. Commun. 185, 115–123 (2000).
[CrossRef]

M. Gangl and H. Ritsch, “Cold atoms in a high-Q ring cavity,” Phys. Rev. A 61, 043405 (2000).
[CrossRef]

G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
[CrossRef]

Gardiner, S.

D. Jaksch, S. Gardiner, K. Schulze, J. Cirac, and P. Zoller, “Uniting Bose-Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4773–4776 (2001).
[CrossRef]

Gauck, H.

H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D gas of laser cooled atoms in a planar matter waveguide,” Phys. Rev. Lett. 81, 5298–5301 (1998).
[CrossRef]

Gauthier, D. J.

T. W. Mossberg, M. Lewenstein, and D. J. Gauthier, “Trapping and cooling of atoms in a vacuum perturbed in a frequency-dependent manner,” Phys. Rev. Lett. 67, 1723–1726 (1991).
[CrossRef] [PubMed]

Gheri, K. M.

P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997).
[CrossRef]

Gordon, J. P.

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Grangier, P.

J. F. Roch, K. Vigneron, A. Sinatra, and P. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Grimm, R.

A. Mosk, S. Jochim, H. Moritz, T. Elsässer, M. Weidemüller, and R. Grimm, “Resonator-enhanced optical dipole trap for fermionic lithium atoms,” Opt. Lett. 26, 1837–1839 (2001).
[CrossRef]

Y. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

Hare, J.

I. Protsenko, P. Domokos, V. Lefèvre, J. Hare, J. M. Raimond, and L. Davidovich, “Quantum theory of a thresholdless laser,” Phys. Rev. A 59, 1667–1681 (1999).
[CrossRef]

F. Treussart, J. Hare, L. Collot, V. Lefèvre, D. S. Weiss, V. S. Sandoghdar, J. M. Raimond, and S. Haroche, “Quantized atom-field force at the surface of a microsphere,” Opt. Lett. 19, 1651–1653 (1994).
[CrossRef] [PubMed]

Haroche, S.

Hartl, M.

H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D gas of laser cooled atoms in a planar matter waveguide,” Phys. Rev. Lett. 81, 5298–5301 (1998).
[CrossRef]

Hechenblaikner, G.

G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
[CrossRef]

P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997).
[CrossRef]

Heinzen, D. J.

D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. A 59, 2623–2626 (1987).

Hemmerich, A.

A. Hemmerich, “Quantum entanglement in dilute optical lattices,” Phys. Rev. A 60, 943–946 (1999).
[CrossRef]

Hijmans, T. W.

B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).

Hood, C. J.

A. C. Doherty, T. W. Lynn, C. J. Hood, and H. J. Kimble, “Trapping of single atoms with single photons in cavity QED,” Phys. Rev. A 63, 013401 (2000).
[CrossRef]

C. J. Hood, T. W. Lynn, A. C. Doherty, and A. S. P. H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

Horak, P.

P. Horak and H. Ritsch, “Scaling properties of cavity-enhanced atom cooling,” Phys. Rev. A 64, 033422 (2001).
[CrossRef]

P. Horak and H. Ritsch, “Manipulating a Bose-condensate with a single photon,” Eur. Phys. J. D 13, 279–287 (2001).
[CrossRef]

P. Horak and H. Ritsch, “Dissipative dynamics of Bose condensates in optical cavities,” Phys. Rev. A 63, 023603 (2001).
[CrossRef]

P. Horak and H. Ritsch, “Cavity assisted quasiparticle damping in a Bose–Einstein condensate,” Phys. Rev. A 63, 051603 (2001).
[CrossRef]

G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
[CrossRef]

P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997).
[CrossRef]

Jaksch, D.

D. Jaksch, S. Gardiner, K. Schulze, J. Cirac, and P. Zoller, “Uniting Bose-Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4773–4776 (2001).
[CrossRef]

Jochim, S.

Kaiser, R.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Kim, J. I.

J. I. Kim, R. B. B. Santos, and P. Nussenzveig, “Manipulation of cold atomic collisions by cavity QED effects,” Phys. Rev. Lett. 86, 1474–1477 (2001).
[CrossRef] [PubMed]

Kimble, A. S. P. H. J.

C. J. Hood, T. W. Lynn, A. C. Doherty, and A. S. P. H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

Kimble, H. J.

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

A. C. Doherty, T. W. Lynn, C. J. Hood, and H. J. Kimble, “Trapping of single atoms with single photons in cavity QED,” Phys. Rev. A 63, 013401 (2000).
[CrossRef]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

H. Mabuchi, M. S. Chapman, T. Q. A. Turchette, and H. J. Kimble, “Real-time detection of individual atoms falling through a high-finesse optical cavity,” Opt. Lett. 21, 1393–1395 (1996).
[CrossRef] [PubMed]

H. Mabuchi and H. J. Kimble, “Atom galleries for whispering atoms: binding atoms in stable orbits around an optical resonator,” Opt. Lett. 19, 749–752 (1994).
[CrossRef] [PubMed]

R. J. Thompson, G. Rempe, and H. J. Kimble, “Observation of normal-mode splitting for an atom in an optical cavity,” Phys. Rev. Lett. 68, 1132–1135 (1992).
[CrossRef] [PubMed]

Kishimoto, Y.

M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
[CrossRef]

Kleppner, D.

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981).
[CrossRef]

Koga, J.

M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
[CrossRef]

Kulin, S.

B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).

Kurizki, G.

B. Deb and G. Kurizki, “Formation of giant quasibound cold diatoms by strong atom-cavity coupling,” Phys. Rev. Lett. 83, 714–717 (1999).
[CrossRef]

Labeyrie, G.

A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

Landragin, A.

A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

Leduc, M.

B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).

Lefèvre, V.

I. Protsenko, P. Domokos, V. Lefèvre, J. Hare, J. M. Raimond, and L. Davidovich, “Quantum theory of a thresholdless laser,” Phys. Rev. A 59, 1667–1681 (1999).
[CrossRef]

F. Treussart, J. Hare, L. Collot, V. Lefèvre, D. S. Weiss, V. S. Sandoghdar, J. M. Raimond, and S. Haroche, “Quantized atom-field force at the surface of a microsphere,” Opt. Lett. 19, 1651–1653 (1994).
[CrossRef] [PubMed]

Lewenstein, M.

J. I. Cirac, M. Lewenstein, and P. Zoller, “Laser cooling a trapped atom in a cavity: bad-cavity limit,” Phys. Rev. A 51, 1650–1654 (1995).
[CrossRef] [PubMed]

M. Lewenstein and L. Roso, “Cooling of atoms in colored vacua,” Phys. Rev. A 47, 3385–3389 (1993).
[CrossRef] [PubMed]

T. W. Mossberg, M. Lewenstein, and D. J. Gauthier, “Trapping and cooling of atoms in a vacuum perturbed in a frequency-dependent manner,” Phys. Rev. Lett. 67, 1723–1726 (1991).
[CrossRef] [PubMed]

Lynn, T. W.

C. J. Hood, T. W. Lynn, A. C. Doherty, and A. S. P. H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

A. C. Doherty, T. W. Lynn, C. J. Hood, and H. J. Kimble, “Trapping of single atoms with single photons in cavity QED,” Phys. Rev. A 63, 013401 (2000).
[CrossRef]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

Mabuchi, H.

Manek, I.

Y. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

Maunz, P.

T. Fischer, P. Maunz, P. W. H. Pinkse, T. Puppe, and G. Rempe, “Feedback on the motion of a single atom in an optical cavity,” Phys. Rev. Lett. 88, 163002 (2002).
[CrossRef] [PubMed]

T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, “Collective light forces on atoms in a high-finesse cavity,” New J. Phys. 3, 11.1–11.20 (2001).

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Observation of cavity-mediated long-range light forces between strongly coupled atoms,” Phys. Rev. Lett. 84, 4068–4071 (2000).
[CrossRef] [PubMed]

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365–368 (2000).
[CrossRef] [PubMed]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Dynamics of single-atom motion observed in a high-finesse cavity,” Phys. Rev. Lett. 82, 3791–3794 (1999).
[CrossRef]

McKeever, J.

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

Minogin, V. G.

M. A. Olshanii and V. G. Minogin, “Three-dimensional velocity-selective coherent population trapping of a (3+3)-level atom,” Opt. Commun. 89, 393–398 (1992).
[CrossRef]

Mlynek, J.

H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D gas of laser cooled atoms in a planar matter waveguide,” Phys. Rev. Lett. 81, 5298–5301 (1998).
[CrossRef]

Moritz, H.

Mosk, A.

Mossberg, T. W.

T. W. Mossberg, M. Lewenstein, and D. J. Gauthier, “Trapping and cooling of atoms in a vacuum perturbed in a frequency-dependent manner,” Phys. Rev. Lett. 67, 1723–1726 (1991).
[CrossRef] [PubMed]

Münstermann, P.

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Observation of cavity-mediated long-range light forces between strongly coupled atoms,” Phys. Rev. Lett. 84, 4068–4071 (2000).
[CrossRef] [PubMed]

P. Münstermann, T. Fischer, P. W. H. Pinkse, and G. Rempe, “Single slow atoms from an atomic fountain observed in a high-finesse optical cavity,” Opt. Commun. 159, 63–67 (1999).
[CrossRef]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Dynamics of single-atom motion observed in a high-finesse cavity,” Phys. Rev. Lett. 82, 3791–3794 (1999).
[CrossRef]

Narducci, L. M.

R. Bonifacio, L. D. Salvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716–1724 (1994).
[CrossRef] [PubMed]

Neil, B. M.

R. Bonifacio, B. M. Neil, and G. Robb, “Self-cooling in a system of driven two-level atoms,” Opt. Commun. 161, 1–5 (1999).
[CrossRef]

R. Bonifacio, G. Robb, and B. M. Neil, “Propagation, cavity, and Doppler-broadening effects in the collective atomic recoil laser,” Phys. Rev. A 56, 912–924 (1997).
[CrossRef]

Nussenzveig, P.

J. I. Kim, R. B. B. Santos, and P. Nussenzveig, “Manipulation of cold atomic collisions by cavity QED effects,” Phys. Rev. Lett. 86, 1474–1477 (2001).
[CrossRef] [PubMed]

Olshanii, M. A.

M. A. Olshanii and V. G. Minogin, “Three-dimensional velocity-selective coherent population trapping of a (3+3)-level atom,” Opt. Commun. 89, 393–398 (1992).
[CrossRef]

Ovchinnikov, Y. B.

Y. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

Y. B. Ovchinnikov, S. V. Shul’ga, and V. I. Balykin, “An atomic trap based on evanescent light waves,” J. Phys. B 24, 3173–3178 (1991).
[CrossRef]

Peik, E.

B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).

Pfau, T.

H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D gas of laser cooled atoms in a planar matter waveguide,” Phys. Rev. Lett. 81, 5298–5301 (1998).
[CrossRef]

Phillips, W. D.

W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).
[CrossRef]

Pinkse, P. W. H.

T. Fischer, P. Maunz, P. W. H. Pinkse, T. Puppe, and G. Rempe, “Feedback on the motion of a single atom in an optical cavity,” Phys. Rev. Lett. 88, 163002 (2002).
[CrossRef] [PubMed]

T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, “Collective light forces on atoms in a high-finesse cavity,” New J. Phys. 3, 11.1–11.20 (2001).

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365–368 (2000).
[CrossRef] [PubMed]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Observation of cavity-mediated long-range light forces between strongly coupled atoms,” Phys. Rev. Lett. 84, 4068–4071 (2000).
[CrossRef] [PubMed]

P. Münstermann, T. Fischer, P. W. H. Pinkse, and G. Rempe, “Single slow atoms from an atomic fountain observed in a high-finesse optical cavity,” Opt. Commun. 159, 63–67 (1999).
[CrossRef]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Dynamics of single-atom motion observed in a high-finesse cavity,” Phys. Rev. Lett. 82, 3791–3794 (1999).
[CrossRef]

Pirandola, S.

S. Pirandola, D. Vitali, and P. Tombesi, “Trapping and cooling single atoms with far-off-resonance intracavity doughnut modes,” Phys. Rev. A 67, 023404 (2003).
[CrossRef]

Protsenko, I.

I. Protsenko, P. Domokos, V. Lefèvre, J. Hare, J. M. Raimond, and L. Davidovich, “Quantum theory of a thresholdless laser,” Phys. Rev. A 59, 1667–1681 (1999).
[CrossRef]

Puppe, T.

T. Fischer, P. Maunz, P. W. H. Pinkse, T. Puppe, and G. Rempe, “Feedback on the motion of a single atom in an optical cavity,” Phys. Rev. Lett. 88, 163002 (2002).
[CrossRef] [PubMed]

T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, “Collective light forces on atoms in a high-finesse cavity,” New J. Phys. 3, 11.1–11.20 (2001).

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Raimond, J. M.

I. Protsenko, P. Domokos, V. Lefèvre, J. Hare, J. M. Raimond, and L. Davidovich, “Quantum theory of a thresholdless laser,” Phys. Rev. A 59, 1667–1681 (1999).
[CrossRef]

F. Treussart, J. Hare, L. Collot, V. Lefèvre, D. S. Weiss, V. S. Sandoghdar, J. M. Raimond, and S. Haroche, “Quantized atom-field force at the surface of a microsphere,” Opt. Lett. 19, 1651–1653 (1994).
[CrossRef] [PubMed]

Raizen, M. G.

M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
[CrossRef]

Rasel, E.

B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).

Rempe, G.

T. Fischer, P. Maunz, P. W. H. Pinkse, T. Puppe, and G. Rempe, “Feedback on the motion of a single atom in an optical cavity,” Phys. Rev. Lett. 88, 163002 (2002).
[CrossRef] [PubMed]

T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, “Collective light forces on atoms in a high-finesse cavity,” New J. Phys. 3, 11.1–11.20 (2001).

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365–368 (2000).
[CrossRef] [PubMed]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Observation of cavity-mediated long-range light forces between strongly coupled atoms,” Phys. Rev. Lett. 84, 4068–4071 (2000).
[CrossRef] [PubMed]

P. Münstermann, T. Fischer, P. W. H. Pinkse, and G. Rempe, “Single slow atoms from an atomic fountain observed in a high-finesse optical cavity,” Opt. Commun. 159, 63–67 (1999).
[CrossRef]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Dynamics of single-atom motion observed in a high-finesse cavity,” Phys. Rev. Lett. 82, 3791–3794 (1999).
[CrossRef]

R. J. Thompson, G. Rempe, and H. J. Kimble, “Observation of normal-mode splitting for an atom in an optical cavity,” Phys. Rev. Lett. 68, 1132–1135 (1992).
[CrossRef] [PubMed]

Ritsch, H.

P. Domokos, T. Salzburger, and H. Ritsch, “Dissipative motion of an atom with transverse coherent driving in a cavity with many degenerate modes,” Phys. Rev. A 66, 043406 (2002).
[CrossRef]

P. Domokos and H. Ritsch, “Collective cooling and self-organization of atoms in a cavity,” Phys. Rev. Lett. 89, 253003 (2002).
[CrossRef] [PubMed]

M. Gangl and H. Ritsch, “Cavity assisted polarization gradient cooling,” J. Phys. B 35, 4565–4582 (2002).
[CrossRef]

P. Horak and H. Ritsch, “Manipulating a Bose-condensate with a single photon,” Eur. Phys. J. D 13, 279–287 (2001).
[CrossRef]

P. Horak and H. Ritsch, “Dissipative dynamics of Bose condensates in optical cavities,” Phys. Rev. A 63, 023603 (2001).
[CrossRef]

P. Domokos and H. Ritsch, “Efficient loading and cooling in a dynamic optical evanescent-wave microtrap,” Europhys. Lett. 54, 306–312 (2001).
[CrossRef]

P. Horak and H. Ritsch, “Cavity assisted quasiparticle damping in a Bose–Einstein condensate,” Phys. Rev. A 63, 051603 (2001).
[CrossRef]

M. Gangl and H. Ritsch, “Cavity-mediated dark-state cool-ing without spontaneous emission,” Phys. Rev. A 64, 063414 (2001).
[CrossRef]

P. Horak and H. Ritsch, “Scaling properties of cavity-enhanced atom cooling,” Phys. Rev. A 64, 033422 (2001).
[CrossRef]

M. Gangl and H. Ritsch, “Cold atoms in a high-Q ring cavity,” Phys. Rev. A 61, 043405 (2000).
[CrossRef]

P. Domokos, M. Gangl, and H. Ritsch, “Single-atom detection in high-Q multimode cavities,” Opt. Commun. 185, 115–123 (2000).
[CrossRef]

M. Gangl and H. Ritsch, “Collective dynamical cooling of neutral particles in a high-Q optical cavity,” Phys. Rev. A 61, 011402 (2000).
[CrossRef]

G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
[CrossRef]

P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997).
[CrossRef]

Robb, G.

R. Bonifacio, B. M. Neil, and G. Robb, “Self-cooling in a system of driven two-level atoms,” Opt. Commun. 161, 1–5 (1999).
[CrossRef]

R. Bonifacio, G. Robb, and B. M. Neil, “Propagation, cavity, and Doppler-broadening effects in the collective atomic recoil laser,” Phys. Rev. A 56, 912–924 (1997).
[CrossRef]

Roch, J. F.

J. F. Roch, K. Vigneron, A. Sinatra, and P. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Roso, L.

M. Lewenstein and L. Roso, “Cooling of atoms in colored vacua,” Phys. Rev. A 47, 3385–3389 (1993).
[CrossRef] [PubMed]

Salvo, L. D.

R. Bonifacio, L. D. Salvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716–1724 (1994).
[CrossRef] [PubMed]

Salzburger, T.

P. Domokos, T. Salzburger, and H. Ritsch, “Dissipative motion of an atom with transverse coherent driving in a cavity with many degenerate modes,” Phys. Rev. A 66, 043406 (2002).
[CrossRef]

Sandoghdar, V. S.

Santos, R. B. B.

J. I. Kim, R. B. B. Santos, and P. Nussenzveig, “Manipulation of cold atomic collisions by cavity QED effects,” Phys. Rev. Lett. 86, 1474–1477 (2001).
[CrossRef] [PubMed]

Saubaméa, B.

B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).

Schneble, D.

H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D gas of laser cooled atoms in a planar matter waveguide,” Phys. Rev. Lett. 81, 5298–5301 (1998).
[CrossRef]

Schnitzler, H.

H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D gas of laser cooled atoms in a planar matter waveguide,” Phys. Rev. Lett. 81, 5298–5301 (1998).
[CrossRef]

Schulze, K.

D. Jaksch, S. Gardiner, K. Schulze, J. Cirac, and P. Zoller, “Uniting Bose-Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4773–4776 (2001).
[CrossRef]

Shul’ga, S. V.

Y. B. Ovchinnikov, S. V. Shul’ga, and V. I. Balykin, “An atomic trap based on evanescent light waves,” J. Phys. B 24, 3173–3178 (1991).
[CrossRef]

Sinatra, A.

J. F. Roch, K. Vigneron, A. Sinatra, and P. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Stecher, H.

P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997).
[CrossRef]

Sundaram, B.

M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
[CrossRef]

Tajima, T.

M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
[CrossRef]

Takuma, H.

M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
[CrossRef]

Thompson, R. J.

R. J. Thompson, G. Rempe, and H. J. Kimble, “Observation of normal-mode splitting for an atom in an optical cavity,” Phys. Rev. Lett. 68, 1132–1135 (1992).
[CrossRef] [PubMed]

Tombesi, P.

S. Pirandola, D. Vitali, and P. Tombesi, “Trapping and cooling single atoms with far-off-resonance intracavity doughnut modes,” Phys. Rev. A 67, 023404 (2003).
[CrossRef]

Treussart, F.

Turchette, T. Q. A.

van Enk, S. J.

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

Vansteenkiste, N.

A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Vernooy, D. W.

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

Vigneron, K.

J. F. Roch, K. Vigneron, A. Sinatra, and P. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

Vitali, D.

S. Pirandola, D. Vitali, and P. Tombesi, “Trapping and cooling single atoms with far-off-resonance intracavity doughnut modes,” Phys. Rev. A 67, 023404 (2003).
[CrossRef]

Vuletic, V.

H. W. Chan, A. T. Black, and V. Vuletić, “Observation of collective-emission-induced cooling of atoms in an optical cavity,” Phys. Rev. Lett. 90, 063003 (2003).
[CrossRef] [PubMed]

V. Vuletić, H. W. Chan, and A. T. Black, “Three-dimensional cavity Doppler cooling and cavity sideband cooling by coherent scattering,” Phys. Rev. A 64, 033405 (2001).
[CrossRef]

V. Vuletić and S. Chu, “Laser cooling of atoms, ions, or molecules by coherent scattering,” Phys. Rev. Lett. 84, 3787–3790 (2000).
[CrossRef] [PubMed]

Weidemüller, M.

Weiss, D. S.

Westbrook, C. I.

A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

Ye, J.

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

Zoller, P.

D. Jaksch, S. Gardiner, K. Schulze, J. Cirac, and P. Zoller, “Uniting Bose-Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4773–4776 (2001).
[CrossRef]

J. I. Cirac, M. Lewenstein, and P. Zoller, “Laser cooling a trapped atom in a cavity: bad-cavity limit,” Phys. Rev. A 51, 1650–1654 (1995).
[CrossRef] [PubMed]

K. Ellinger, J. Cooper, and P. Zoller, “Light-pressure force in N-atom systems,” Phys. Rev. A 49, 3909–3933 (1994).
[CrossRef] [PubMed]

Eur. Phys. J. D (1)

P. Horak and H. Ritsch, “Manipulating a Bose-condensate with a single photon,” Eur. Phys. J. D 13, 279–287 (2001).
[CrossRef]

Europhys. Lett. (1)

P. Domokos and H. Ritsch, “Efficient loading and cooling in a dynamic optical evanescent-wave microtrap,” Europhys. Lett. 54, 306–312 (2001).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (3)

J. Dalibard and C. Cohen-Tannoudji, “Atomic motion in laser light: connection between semiclassical and quantum descriptions,” J. Phys. B 18, 1661–1683 (1985).
[CrossRef]

Y. B. Ovchinnikov, S. V. Shul’ga, and V. I. Balykin, “An atomic trap based on evanescent light waves,” J. Phys. B 24, 3173–3178 (1991).
[CrossRef]

M. Gangl and H. Ritsch, “Cavity assisted polarization gradient cooling,” J. Phys. B 35, 4565–4582 (2002).
[CrossRef]

Nature (1)

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, “Trapping an atom with single photons,” Nature 404, 365–368 (2000).
[CrossRef] [PubMed]

New J. Phys. (1)

T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, “Collective light forces on atoms in a high-finesse cavity,” New J. Phys. 3, 11.1–11.20 (2001).

Opt. Commun. (4)

P. Domokos, M. Gangl, and H. Ritsch, “Single-atom detection in high-Q multimode cavities,” Opt. Commun. 185, 115–123 (2000).
[CrossRef]

P. Münstermann, T. Fischer, P. W. H. Pinkse, and G. Rempe, “Single slow atoms from an atomic fountain observed in a high-finesse optical cavity,” Opt. Commun. 159, 63–67 (1999).
[CrossRef]

M. A. Olshanii and V. G. Minogin, “Three-dimensional velocity-selective coherent population trapping of a (3+3)-level atom,” Opt. Commun. 89, 393–398 (1992).
[CrossRef]

R. Bonifacio, B. M. Neil, and G. Robb, “Self-cooling in a system of driven two-level atoms,” Opt. Commun. 161, 1–5 (1999).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Phys. Rev. A (23)

D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. A 59, 2623–2626 (1987).

M. Lewenstein and L. Roso, “Cooling of atoms in colored vacua,” Phys. Rev. A 47, 3385–3389 (1993).
[CrossRef] [PubMed]

J. I. Cirac, M. Lewenstein, and P. Zoller, “Laser cooling a trapped atom in a cavity: bad-cavity limit,” Phys. Rev. A 51, 1650–1654 (1995).
[CrossRef] [PubMed]

V. Vuletić, H. W. Chan, and A. T. Black, “Three-dimensional cavity Doppler cooling and cavity sideband cooling by coherent scattering,” Phys. Rev. A 64, 033405 (2001).
[CrossRef]

G. Hechenblaikner, M. Gangl, P. Horak, and H. Ritsch, “Cooling an atom in a weakly driven high-Q cavity,” Phys. Rev. A 58, 3030–3042 (1998).
[CrossRef]

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

A. Hemmerich, “Quantum entanglement in dilute optical lattices,” Phys. Rev. A 60, 943–946 (1999).
[CrossRef]

M. Gangl and H. Ritsch, “Cold atoms in a high-Q ring cavity,” Phys. Rev. A 61, 043405 (2000).
[CrossRef]

P. Horak and H. Ritsch, “Scaling properties of cavity-enhanced atom cooling,” Phys. Rev. A 64, 033422 (2001).
[CrossRef]

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, “Cooling of a single atom in an optical trap inside a resonator,” Phys. Rev. A 64, 013407 (2001).
[CrossRef]

P. Domokos, T. Salzburger, and H. Ritsch, “Dissipative motion of an atom with transverse coherent driving in a cavity with many degenerate modes,” Phys. Rev. A 66, 043406 (2002).
[CrossRef]

S. Pirandola, D. Vitali, and P. Tombesi, “Trapping and cooling single atoms with far-off-resonance intracavity doughnut modes,” Phys. Rev. A 67, 023404 (2003).
[CrossRef]

M. G. Raizen, J. Koga, B. Sundaram, Y. Kishimoto, H. Takuma, and T. Tajima, “Stochastic cooling of atoms using lasers,” Phys. Rev. A 58, 4757–4760 (1998).
[CrossRef]

M. Gangl and H. Ritsch, “Cavity-mediated dark-state cool-ing without spontaneous emission,” Phys. Rev. A 64, 063414 (2001).
[CrossRef]

A. C. Doherty, T. W. Lynn, C. J. Hood, and H. J. Kimble, “Trapping of single atoms with single photons in cavity QED,” Phys. Rev. A 63, 013401 (2000).
[CrossRef]

I. Protsenko, P. Domokos, V. Lefèvre, J. Hare, J. M. Raimond, and L. Davidovich, “Quantum theory of a thresholdless laser,” Phys. Rev. A 59, 1667–1681 (1999).
[CrossRef]

K. Ellinger, J. Cooper, and P. Zoller, “Light-pressure force in N-atom systems,” Phys. Rev. A 49, 3909–3933 (1994).
[CrossRef] [PubMed]

M. Gangl and H. Ritsch, “Collective dynamical cooling of neutral particles in a high-Q optical cavity,” Phys. Rev. A 61, 011402 (2000).
[CrossRef]

P. Horak and H. Ritsch, “Dissipative dynamics of Bose condensates in optical cavities,” Phys. Rev. A 63, 023603 (2001).
[CrossRef]

P. Horak and H. Ritsch, “Cavity assisted quasiparticle damping in a Bose–Einstein condensate,” Phys. Rev. A 63, 051603 (2001).
[CrossRef]

R. Bonifacio, G. Robb, and B. M. Neil, “Propagation, cavity, and Doppler-broadening effects in the collective atomic recoil laser,” Phys. Rev. A 56, 912–924 (1997).
[CrossRef]

R. Bonifacio, L. D. Salvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716–1724 (1994).
[CrossRef] [PubMed]

P. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A 59, 585–596 (2001).
[CrossRef]

Phys. Rev. Lett. (21)

D. Jaksch, S. Gardiner, K. Schulze, J. Cirac, and P. Zoller, “Uniting Bose-Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4773–4776 (2001).
[CrossRef]

J. F. Roch, K. Vigneron, A. Sinatra, and P. Grangier, “Quantum nondemolition measurements using cold trapped atoms,” Phys. Rev. Lett. 78, 634–637 (1997).
[CrossRef]

P. Domokos and H. Ritsch, “Collective cooling and self-organization of atoms in a cavity,” Phys. Rev. Lett. 89, 253003 (2002).
[CrossRef] [PubMed]

B. Deb and G. Kurizki, “Formation of giant quasibound cold diatoms by strong atom-cavity coupling,” Phys. Rev. Lett. 83, 714–717 (1999).
[CrossRef]

J. I. Kim, R. B. B. Santos, and P. Nussenzveig, “Manipulation of cold atomic collisions by cavity QED effects,” Phys. Rev. Lett. 86, 1474–1477 (2001).
[CrossRef] [PubMed]

Y. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D gas of laser cooled atoms in a planar matter waveguide,” Phys. Rev. Lett. 81, 5298–5301 (1998).
[CrossRef]

T. Fischer, P. Maunz, P. W. H. Pinkse, T. Puppe, and G. Rempe, “Feedback on the motion of a single atom in an optical cavity,” Phys. Rev. Lett. 88, 163002 (2002).
[CrossRef] [PubMed]

H. W. Chan, A. T. Black, and V. Vuletić, “Observation of collective-emission-induced cooling of atoms in an optical cavity,” Phys. Rev. Lett. 90, 063003 (2003).
[CrossRef] [PubMed]

B. Saubaméa, T. W. Hijmans, S. Kulin, E. Rasel, E. Peik, M. Leduc, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 79, 3146–3149 (1997).

A. Landragin, J.-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Observation of cavity-mediated long-range light forces between strongly coupled atoms,” Phys. Rev. Lett. 84, 4068–4071 (2000).
[CrossRef] [PubMed]

R. J. Thompson, G. Rempe, and H. J. Kimble, “Observation of normal-mode splitting for an atom in an optical cavity,” Phys. Rev. Lett. 68, 1132–1135 (1992).
[CrossRef] [PubMed]

V. Vuletić and S. Chu, “Laser cooling of atoms, ions, or molecules by coherent scattering,” Phys. Rev. Lett. 84, 3787–3790 (2000).
[CrossRef] [PubMed]

T. W. Mossberg, M. Lewenstein, and D. J. Gauthier, “Trapping and cooling of atoms in a vacuum perturbed in a frequency-dependent manner,” Phys. Rev. Lett. 67, 1723–1726 (1991).
[CrossRef] [PubMed]

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

C. J. Hood, M. S. Chapman, T. W. Lynn, and H. J. Kimble, “Real-time cavity QED with single atoms,” Phys. Rev. Lett. 80, 4157–4160 (1998).
[CrossRef]

P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, “Dynamics of single-atom motion observed in a high-finesse cavity,” Phys. Rev. Lett. 82, 3791–3794 (1999).
[CrossRef]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[CrossRef]

P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997).
[CrossRef]

Rev. Mod. Phys. (3)

S. Chu, “Nobel lecture: the manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998).
[CrossRef]

C. Cohen-Tannoudji, “Nobel lecture: manipulating atoms with photons,” Rev. Mod. Phys. 70, 707–719 (1998).
[CrossRef]

W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).
[CrossRef]

Science (1)

C. J. Hood, T. W. Lynn, A. C. Doherty, and A. S. P. H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[CrossRef] [PubMed]

Other (6)

S. Haroche, “Cavity quantum electrodynamics,” in Fundamental Systems in Quantum Optics, Les Houches Summer School, Proceedings, Vol. 53, J. Dalibard, J.-M. Raimond, and J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), pp. 767–940.

P. Berman, ed., Cavity Quantum Electrodynamics (Academic, San Diego, Calif., 1994.).

C. Cohen-Tannoudji, “Atomic motion in laser light,” in Fundamental Systems in Quantum Optics, Les Houches Summer School Proceedings, Vol. 53, J. Dalibard, J.-M. Raimond, and J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), pp. 1–164.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, New York, 1999).

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Naegerl, D. M. Stamper-Kurn, and H. J. Kimble, “State-insensitive cooling and trapping of single atoms in an optical cavity,” arXiv.org e-Print archive, http://lanl.arxiv.org/abs/quant-ph/0211013 (2002).

V. Vuletić, “Cavity cooling with a hot cavity,” in Laser Physics at the Limits, H. Figger, D. Meschede, and C. Zimmermann, eds. (Springer, New York, 2001), pp. 67–74.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (41)

Fig. 1
Fig. 1

Schematic representation of the system composed of many atoms coupled to a multimode cavity.

Fig. 2
Fig. 2

Time evolution of the field intensity (dotted curve), particle position (solid curve) and particle momentum (dashed curve) for a single atom in a cosine mode. The parameters are U0=-3κ, γ=0.1κ, ΔC=-4κ, and η=1.5κ. The thin horizontal lines mark the position of the field antinodes.

Fig. 3
Fig. 3

Contour plot of the friction coefficient in the bad-cavity regime (κ=10γ) for the coupling constants (a) g=γ/2, (b) g=3γ. Solid contour curves indicate cooling (β<0), dashed curves heating (β>0) regions.

Fig. 4
Fig. 4

Same as Fig. 3 but when the atom is pumped externally. In this case the increasing coupling constant g links the closely independent atom and cavity field system to the dressed atom system, even in the bad-cavity regime.

Fig. 5
Fig. 5

Contour plot of the friction coefficient in the strong-coupling regime (g=3γ, κ=γ); (a) pumping the cavity mode, (b) pumping the atom from the side.

Fig. 6
Fig. 6

Schematic representation of the Sisyphus cooling mechanism for ΔA0, ΔC>0.

Fig. 7
Fig. 7

Schematic representation of the Sisyphus cooling mechanism for ΔA, ΔC<0, ΔAΔCg2.

Fig. 8
Fig. 8

Going beyond the Doppler limit for γκ; g=2γ, ΔA=-3.2γ, ΔC=-1.3γ. The crosses mark the results obtained from quantum Monte Carlo simulations.

Fig. 9
Fig. 9

Steady-state temperature versus cavity decay rate for (a) ΔA=20γ, ΔC=0 and (b) ΔA=-20γ, ΔC=U0=0.312γ. Solid curves show the numerical results obtained from our semiclassical model. The other curves correspond to the analytical results in the weak-driving limit without (dashed) and with (dashed–dotted) adiabatic elimination of the atomic excited state. The other parameters are η=3κ, g=2.5γ, and γ=2π×3 MHz (rubidium atoms).

Fig. 10
Fig. 10

Effects of localization for different pump strengths. (a) Steady-state temperature T versus η (solid curve), temperature obtained from the analytic solution in the weak-driving limit (dashed), and ratio of T and the mean optical potential U0n (dotted–dashed). (b) Atomic position distributions within a potential well for η=2κ and η=4κ (solid curves) as compared with thermal distributions (dashed) of the same temperature and the same mean potential. For these plots κ=γ/2, and the other parameters are as in Fig. 9(a).

Fig. 11
Fig. 11

Trapping time Ttrap versus κ. The parameters for this plot are those of Fig. 9(a).

Fig. 12
Fig. 12

Trapping time Ttrap versus pump strength η with κ=γ/2. The parameters are the same as in Fig. 10.

Fig. 13
Fig. 13

Two-level atom moving in a weakly driven ring cavity with losses from spontaneous emission γ and cavity decay κ.

Fig. 14
Fig. 14

The atom is decelerated while moving along the cavity axis until its kinetic energy becomes so low that it is trapped in a potential well, where its motion damps out to p=0. γ=3κ, g=5κ, ΔA=10κ, ΔC=0, η+=η-=κ=1. Diffusion is omitted.

Fig. 15
Fig. 15

Contour plot of the dipole friction force. η-=η+=κ=1,g=5κ, γ=3κ.

Fig. 16
Fig. 16

Contour plot of the radiation pressure friction force. η-=η+=κ=1,g=5κ, γ=3κ.

Fig. 17
Fig. 17

Contour plot of the total diffusion averaged over one wavelength for η=κ,g=5κ, γ=3κ.

Fig. 18
Fig. 18

Steady-state field intensity for a fixed laser-driven atom where U0=ΔC/2=-10 (μs)-1. The other parameters are (κ, γ, g)=(10, 20, 60) (μs)-1 and the pumping strength η is chosen such that the saturation parameter σσ=0.1. The arrow indicates the position of the atom.

Fig. 19
Fig. 19

Steady-state field intensity for a fixed atom in a driven cavity, where (a) U0=ΔC/2=-10 μs-1 and (b) U0=0, ΔC=-20 μs-1. Only η00 is different from zero and is chosen such that s=0.1. The other parameters are the same as in Fig. 18. The arrows indicate the position of the atom.

Fig. 20
Fig. 20

Trajectory of a rubidium atom with initial velocity v=12 cm/s for the ground mode (first row) and the first six modes (second row) taken into account. Left column, asymmetric oscillations after the initial capture for 0t2 ms; right column, long-term motion after t=5 ms. The field reaches a mean photon number of (left) 2.19 and (right) 1.43. The other parameters are the same as in Fig. 19(a).

Fig. 21
Fig. 21

Transverse spatial intensity pattern of the stationary cavity field for (a) the empty cavity and (b), (c) two atomic positions indicated by the thick vertical lines.

Fig. 22
Fig. 22

Simulated atomic trajectory (solid curve), reconstructed atomic positions (crosses), and fitted atomic path (dotted curve). The atom enters with a velocity of 12 cm/s, and the total trajectory takes 5300κ-1=0.56 ms. The dashed circle indicates the dark ring of the pumped cavity mode u10. The waist of the TEM00 mode is w0=29 μm.

Fig. 23
Fig. 23

(a) Steady-state temperature and (b) the number of spontaneously scattered photons in a cooling time versus the effective coupling constant geff. Dashed curve, κ=γ; solid curve, κ=γ/10. The crosses on the curves indicate the coupling constant corresponding to maximum transverse indices of 2N=0, 2, 4, 8,, starting with a single-mode coupling constant of g=3γ for κ=γ and with g=3γ/10 for κ=γ/10. For the latter the single-mode coupling (maximum index 0) is missing from the plotted range of temperatures.  

Fig. 24
Fig. 24

Top left, geometrical arrangement of the beams. The penetration depth of the blue is just the half of that of the red field. Right, excited transitions and detunings (not to scale) involved in the scheme. Bottom, adiabatic potential for the atomic motion, including the strong Van der Waals attraction of the surface.

Fig. 25
Fig. 25

Top, variation of the photon numbers in the blue- and red-detuned modes. Bottom, oscillations in the trap with decreasing amplitude. Bold curve, mechanical energy of the atom including the kinetic energy and the adiabatic potential energy. The scale for this curve assumes units of the trap depth, which is ∼8.9ℏγ.

Fig. 26
Fig. 26

Probability of trapping the atom as a function of time.

Fig. 27
Fig. 27

Mechanical energy associated with the atomic CM motion. The result for the noisy dynamics involves an averaging over 10,000 trajectories; however, only those that correspond to a trapped atom are counted (48.5% of the trajectories, finally). Dashed line, potential minimum value.

Fig. 28
Fig. 28

Time evolution of the field intensity (solid curve) and particle momenta (dashed curves) for two atoms in a cosine mode. The parameters are U0=-2κ, N2γ=0.1κ, ΔC=-5κ, η=2.5κ, m=100.

Fig. 29
Fig. 29

(a) Variances Vx (solid curve), Vp (short-dashed curve) and intracavity intensity I (dashed curve) as a function of time for an interaction potential of U0=0.03κ and resonant cavity pumping ΔC=0. (b) Variance Vx for different values of the cavity detuning, ΔC=0 (solid curve), ΔC=κ (dotted curve) and ΔC=-κ/2 (dashed curve).

Fig. 30
Fig. 30

Time evolution of the mean kinetic energy per atom obtained from numerical simulations of Eqs. (2.22) averaged over 100 realizations (solid curves). The dashed curves are exponential fits. Lower curves, N=1; upper curves, N=10. The parameters are NU0=-0.6κ, N2Γ0=0.03κ, ΔC=-0.6κ, η=3Nκ, κ=415ωR.

Fig. 31
Fig. 31

(a) Steady-state kinetic energies per atom and (b) cooling times τc for atom numbers from 1 to 100. Crosses show the numerical results for ΔC=-0.6κ, circles for ΔC=-κ. All other parameters are the same as in Fig. 30.

Fig. 32
Fig. 32

(a) Steady-state kinetic energies per atom and (b) cooling times τc for atom numbers from 1 to 10. Parameters are U0=-0.05κ, Γ0=2.510-4κ, ΔC=-κ, η=10κ, κ=415ωR.

Fig. 33
Fig. 33

Frequency of the vibrational CM mode normalized to ω0 over NU0. ΔC=0, κ=1.

Fig. 34
Fig. 34

NU0=2κ, κ=1. Left, overdamped CM oscillation; right, almost undamped relative oscillation.

Fig. 35
Fig. 35

Steady-state field intensity for two fixed atoms in a driven cavity. The parameters are the same as in Fig. 18. The arrows indicate the positions of the atoms.

Fig. 36
Fig. 36

Influence of an incoming atom on an initial trapped one.

Fig. 37
Fig. 37

Trajectories of 10 atoms exhibiting self-organization for a weakly bound case. The system parameters are (g, κ, γ)=(50, 10, 20) μs-1. The atomic detuning is very large, ΔA=-500γ, and the pumping constant is η=1000 μs-1, resulting in a mean photon number of ∼7. The atomic mass number was chosen to be 85, corresponding to rubidium.

Fig. 38
Fig. 38

Steady-state mean number of cavity photons |α|2 as a function of (a) the number of atoms N and (b) the pumping strength η for fixed number of atoms N=30. In (a) the pumping strength η is 500 μs-1 for the lower curve and 1000 μs-1 for the upper curve. Dots, numerically simulation of Eqs. (2.22). In (a) the curves represent Eq. (6.18) solved with perfect localization x2¯=0 (dashed curves) and with fitted values x2¯=0.14 and 0.06 for η=500 and 1000 (solid curves). The system parameters are the same as in Fig. 37.

Fig. 39
Fig. 39

Cavity setup and level scheme for a Jg=1Je=1 transition.

Fig. 40
Fig. 40

Cooling of a multilevel atom. Left, Momentum; right, population of dark and bright states; Γ0=0, κ=30γ, η=30γ, U0=-6γ, ΔC=0.

Fig. 41
Fig. 41

Left, cooling of a kicked dark atom with κ=30γ, γ0=0.1γ, η=30γ, U0=-6γ, ΔC=0. Right, evolution of the dark state (upper) and bright state (lower) population of the atom.

Equations (105)

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

ρ˙=-i [H, ρ]+Lρ.
H=a=1Np^a22m-ΔAσaz-i(ηt(x^a)σa-ηt*(x^a)σa)+n=1M[-Δcanan-iηn(an-an)]-in=1Ma=1N(gn(x^a)σaan-gn*(x^a)anσa),
Lρ=n=1Mκn(2anρan-ananρ-ρanan)+γa=1N2d2uN(u)σaexp(-ikAux^a)ρ×exp(ikAux^a)σa-σaσaρ-ρσaσa.
x˙a=pa/m,
p˙a=fa+b=1Nβabpb/m+Ξa,
Ξa(t) ° Ξb(t)=Dabδ(t-t),
F^a=-aH=i[ηt(xa)σa-ηt*(xa)σa]+in=1M[gn(xa)σaan-gn*(xa)anσa],
a˙n=(iΔC-κn)an+a=1Ngn*(xa)σa+ηn+ξn,
σ˙a=(iΔA-γ)σa+2σazn=1Mgn(xa)an+2σazηt(xa)+ζa,
σ˙az=-n=1M[gn(xa)σaan+gn*(xa)anσa]-[ηt(xa)σa+ηt*(xa)σa]-2γ(σaz+1/2)+ζaz.
ξn(t1)ξm(t2)=2κnδnmδ(t1-t2),
ζa(t1)ζb(t2)=2γδabδ(t1-t2),
ζaz(t1)ζb(t2)=2γσaδabδ(t1-t2),
ζa(t1)ζbz(t2)=2γσaδabδ(t1-t2),
ζaz(t1)ζbz(t2)=2γ(σaz+1/2)δabδ(t1-t2);
w˙=B(x1,, xN)w+η+ξ,
O(t)=12π-dΩ exp(-iΩt)O(Ω),
w(0)(Ω)=-(iΩ+B)-1[η2πδ(Ω)+ξ(Ω)].
ω(0)=-B-1η.
fa=i[aηt(xa)sa(0)*-aηt*(xa)sa(0)]+in=1M[agn(xa)sa(0)*αn(0)-agn*(xa)αn(0)*sa(0)].
R{F^a(t1)°F^b(t2)-F^a(t1)°F^b(t2)}
=Dabδ(t1-t2).
σa=σn(0)+b=1Nvbσab(1)+O(v2)
an=an(0)+b=1Nvbanb(1)+O(v2),
wb(1)=B-1(bw(0)),
ωb(1)=B-1(bω(0)),
βab=i[aηt(xa)°sab(1)*-aηt*(xa)°sab(1)]+in=1M[(agn(xa)°sab(1)*)αn(0)-αn(0)*(agn*(xa)°sab(1))-(agn*(xa)°αnb(1))sa(0)*+(agn(xa)°αnb(1)*)sa(0)].
σagiΔA-γ Eˆ(x^a).
Heff=a=1Npa22M-n=1MΔCanan-iηn(an-an)+U0a=1NE^(xa)Eˆ(xa),
Leff ρ=n=1Mκ(2anρan-{anan, ρ}+)+Γ0a=1N2d2uN(u)Eˆ(x^a)exp(-ikAux^a)ρ×exp(ikAux^a)E^(x^a)-{E^(x^a)Eˆ(x^a)}.
U0=g2ΔAΔA2+γ2
Γ0=g2γΔA2+γ2.
α˙n=(iΔC-κ)αn-(iU0+Γ0)a=1Nfn*(xa)E(xa)+ηn+ξn,
p˙a=-U0|E(xa)|2-iΓ0[E*(xa)E(xa)-E(xa)E*(xa)]+ξp(a),
ξm*ξn=κδnm+a=1NΓ0fm(xa)fn*(xa),
ξpi(a)ξn=iΓ0iE(xa)fn*(xa),
ξpi(a)ξpj(a)=22kA2Γ0|E(xa)|2ui2¯δij+Γ02[iE*(xa)jE(xa)+iE(xa)jE*(xa)].
ξpi(a)=2Γ0R{iE(xa)}ζ1(a)+2Γ0I{iE(xa)}ζ2(a),
R{ξn}=Γ0/2I{fn(xa)}ζ1(a)-Γ0/2R{fn(xa)}ζ2(a),
I{ξn}=Γ0/2R{fn(xa)}ζ1(a)+Γ0/2I{fn(xa)}ζ2(a),
α˙=[iΔC-κ-(iU0+Γ0)cos2(kx)]α+η,
p˙=U0|α|2sin(2kx),
αα(0)-ηiΔC-κ,
s=s(0)+vs(1)g(x)αiΔA-γ+v g(x)α(iΔA-γ)2,
s=12g α exp(ikx)i(ΔA-kv)-γ+12g α exp(-ikx)i(ΔA+kv)-γ,
F(1)=v2[f(x)]2g2|α|22γΔA(ΔA2+γ2)2,
ss(0)ηiΔA-γ,
α=α(0)+vα(1)g(x)siΔC-κ+v g(x)s(iΔC-κ)2,
α=12gs exp(ikx)i(ΔC-kv)-κ+12gs exp(-ikx)i(ΔC+kv)-κ.
F(1)=v2[f(x)]2g2|s|22κΔC(ΔC2+κ2)2.
|+=cos θ|e, 0+i sin θ|g, 1,
|-=i sin θ|e, 0+cos θ|g, 1,
Δ±=-ΔA+ΔC2±(ΔA-ΔC)24+g2(x).
ω+=ω>+g2(x)/|ωA-ωC|,
ω-=ω<-g2(x)/|ωA-ωC|,
Ddip=22[f(x)]2η2g2|D|2×γ1+4ΔAg2f2(x)γκΔA+γΔC|D|2,
Drec=22kA2u2¯g2η2|D|2 γ,
α=αr|α| αr+αi|α| αi,
α=-αi|α| αr+αr|α| αi,
D=ξξξp°(ξ, ξ, ξp)=d1000d1d30d3d2,
d1=12 [κ+Γ0f2(x)],
d2=2Γ0|α|2([f(x)]2+2kA2u2¯f2(x)),
d3=Γ0|α|f(x)f(x).
kBT=Dtot¯/2β¯.
Ptherm(x)exp-U0ncos2(kx)kBT.
E(+)(x, t)=E [a+(t)exp(ikx)+a-(t)exp(-ikx)],
a˙±=[-κ-Γ0+i(ΔC-U0)]a±-(Γ0+iU0)×aexp(2ikxa)+η±.
a+=[-κ-Γ0+i(ΔC-U0)]η++(Γ0+iU0)η-exp(-2ikxa)[κ+2Γ0+i(2U0-ΔC)](iΔC-κ),
a-=[-κ-Γ0+i(ΔC-U0)]η-+(Γ0+iU0)η+exp(2ikxa)[κ+2Γ0+i(2U0-ΔC)](iΔC-κ).
frp=2kΓ0(a+a+-a-a-),
fdip=2kU0i(a+a-exp(-2ikxa)-a-a+exp(2ikxa)).
Dtot¯=(2k)2(κ+Γ0) U02+Γ02κ2+ΔC2E(-)E(+)¯.
kBT=(κ+Γ0) (U02+Γ02)[(κ+2Γ0)2+4U02]2U0κ(κΓ0+2Γ02+2U02).
fnm(x, y, z)=Hn2xwHm2yw×exp-x2+y2w2cos(kz).
I(x, y)=n,mfn(x, y)fm(x, y)αn*αm.
geff/g=(2N+1)!!(2N)!!,
α˙=(iΔC-κ)α-(iU0+Γ0)αft(x1, x2)+η,
p˙a=-U0|α|2a|f(xa)|2,
p˙a=-U0|η|2|f(xa)|2[ΔC-U0(ft(x1, x2)]2+[κ+Γ0(ft(x1, x2)]2;
f(xi)xi2/2,p˙i=-2|α|2U0xi,
α˙(t)=(iΔc-iU0Vx-κ)α(t)+η,
V˙x=2Vxp/m,
V˙xp=Vp/m-2|α|2U0Vx,
V˙p=-4|α|2U0Vxp.
Vxp=0,Vp=2|α|2U0Vx,
α=η(κ+iΔC-iU0Vx).
F(1)¯=-k2η2U024κ4,D¯=k2κ η2U028κ4.
kBT=-D¯F(1)¯=κ2.
E(t)=E(0)-kBT2exp-tτc+kBT2,
τc=m2|F1¯|=κ4η2U02 ωR-1.
a˙±=(-κ-NΓ0+i(Δc-NU0))a±-(Γ0+iU0)×an=1Nexp(2ikxn)η±.
a˙±=[-κ-2Γ0+i(Δc-2U0)]a±-2(Γ0+iU0)aexp(2ikxCM)cos(kxrel)+η±.
E(-)E(+)=4η2κ2+Δc2cos2(kx-μCM),
μ=2U0N(2U0N-Δc)κ2+(2U0N-Δc).
fdipn=-U0ddx E(-)E(+)x=xn=4kU0η2κ2+Δc2sin 2(kxn-μCM),
¨n+ω02n=ω02μCM,
ω02=8k2U0η2m(κ2+Δc2),
n(t)=[n(0)-CM(0)]cos ω0t+CM(0)cos ωCMt.
|α|2¯=N2|ηeff |2κ2(1-k2x2¯)1+[1+(U0N/κ)k2x2¯]2,
α˙+=η+(-κ+iΔC)α+-(Γ0+iU0)/2×{[α++α-exp(-2ikza)](Π-+Π0)-[β++β-exp(-2ikza)]ρg1,g-1}.
|ψDS=1|A|2+|B|2 (B|g-1+A|g1),
α+=β-=η(κ-iΔC),α-=β+=0;
|ψBS=1|A|2+|B|2 (A*|g-1-B*|g1),
α+=β-=κ-iΔC+(Γ0+iU0)/2(κ-iΔC)[κ+Γ0+i(U0-ΔC)] η,
α-=β+exp(4ikza)=-(Γ0+iU0)exp(2ikza)2(κ-iΔC)[κ+Γ0+i(U0-ΔC)] η.

Metrics