Abstract

We study the dynamics of a fast gaseous beam in a high Q ring cavity counter propagating a strong pump laser with large detuning from any particle optical resonance. As spontaneous emission is strongly suppressed the particles can be treated as polarizable point masses forming a dynamic moving mirror. Above a threshold intensity the particles exhibit spatial periodic ordering enhancing collective coherent backscattering which decelerates the beam. Based on a linear stability analysis in their accelerated rest frame we derive analytic bounds for the intensity threshold of this selforganization as a function of particle number, average velocity, kinetic temperature, pump detuning and resonator linewidth. The analytical results agree well with time dependent simulations of the N-particle motion including field damping and spontaneous emission noise. Our results give conditions which may be easily evaluated for stopping and cooling a fast molecular beam.

© 2007 Optical Society of America

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  1. S. Chu, "Nobel Lecture: The manipulation of neutral particles," C. Cohen-Tannoudji, "Nobel Lecture: Manipulating atoms with photons," and W. D. Phillips, "Nobel Lecture: Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70,685-741 (1998).
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    [CrossRef]
  3. P. Domokos and H. Ritsch, "Mechanical effects of light in optical resonators, " J. Opt. Soc. Am. B 20,1098-1130 (2003).
    [CrossRef]
  4. A. Beige, P. L. Knight, and G. Vitiello, "Cooling many particles at once," New J. Phys. 7,96 (2005)
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  5. V. Vuleti’c and S. Chu, "Laser cooling of atoms, ions, or molecules by coherent scattering," Phys. Rev. Lett. 84,3787-3790 (2000).
    [CrossRef] [PubMed]
  6. H. W. Chan, A. T. Black, and V. Vuletic, "Observation of collective-emission-induced cooling of atoms in an optical cavity," Phys. Rev. Lett. 90,063003 (2003).
    [CrossRef]
  7. P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse,and G. Rempe, "Cavity cooling of a single atom," Nature London 428,50-52 (2004).
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    [CrossRef] [PubMed]
  10. J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96,023002 (2006).
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    [CrossRef]
  13. H.L. Bethlem, G. Berden, F.M.H. Crompvoets, R.T. Jongma, A.J.A. van Roij, and G. Meijer, "Electrostatic trapping of ammonia molecules," Nature London 406491-494 (2000).
    [CrossRef] [PubMed]
  14. N. Vanhaecke, W.D. Melo, B.L. Tolra, D. Comparat, and P. Pillet, "Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap," Phys. Rev. Lett. 89,063001 (2002).
    [CrossRef] [PubMed]
  15. R. Fulton, A.I. Bishop, M.N. Shneider, and P.F. Barker, "Controlling the motion of cold molecules with deep periodic optical potentials," Nature Physics 2465-468 (2006).
    [CrossRef]
  16. R. Fulton, A.I. Bishop, and P.F. Barker, "Optical Stark Decelerator for molecules," Phys. Rev. Lett. 93,243004 (2004).
    [CrossRef]
  17. R. Bonifacio, C. Pellegrini, and L.M. Narducci, "Collective instabilities and high-gain regime in a free electron laser," Opt. Comm. 50,373-378 (1984).
    [CrossRef]
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    [CrossRef] [PubMed]
  19. D. Kruse, C. von Cube, C. Zimmermann, and Ph.W. Courteille, ‘Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91,183601 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  21. C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
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  23. M. Gangl and H. Ritsch, "Cold atoms in a high-Q ring cavity," Phys. Rev. A 61,043405 (2000).
    [CrossRef]
  24. J. K. Asb’oth, P. Domokos, H. Ritsch and A. Vukics, "Self-organization of atoms in a cavity field: Threshold, bistability, and scaling laws," Phys. Rev A 72 (5) 053417 (2005).
    [CrossRef]
  25. D. Nagy, J. K. Asb’oth, P. Domokos, and H. Ritsch, "Self-organization of a laser-driven cold gas in a ring cavity," EuroPhys Lett. 74(2),254 (2006).
    [CrossRef]
  26. G.R.M. Robb, N. Piovella, A. Ferraro, R. Bonifacio, Ph. W. Courteille, and C. Zimmermann, "Collective atomic recoil lasing including friction and diffusion effects," Phys. Rev. A 69, 041403 (R) (2004).
    [CrossRef]

2006 (3)

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96,023002 (2006).
[CrossRef] [PubMed]

R. Fulton, A.I. Bishop, M.N. Shneider, and P.F. Barker, "Controlling the motion of cold molecules with deep periodic optical potentials," Nature Physics 2465-468 (2006).
[CrossRef]

D. Nagy, J. K. Asb’oth, P. Domokos, and H. Ritsch, "Self-organization of a laser-driven cold gas in a ring cavity," EuroPhys Lett. 74(2),254 (2006).
[CrossRef]

2005 (3)

S. Slama, C. von Cube, B. Deh, A. Ludewig, C. Zimmermann and Ph. W. Courteille, "Phase-sensitive detection of bragg scattering at 1D optical lattices," Phys. Rev. Lett. 94,193901 (2005).
[CrossRef] [PubMed]

A. Beige, P. L. Knight, and G. Vitiello, "Cooling many particles at once," New J. Phys. 7,96 (2005)
[CrossRef]

J. K. Asb’oth, P. Domokos, H. Ritsch and A. Vukics, "Self-organization of atoms in a cavity field: Threshold, bistability, and scaling laws," Phys. Rev A 72 (5) 053417 (2005).
[CrossRef]

2004 (4)

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse,and G. Rempe, "Cavity cooling of a single atom," Nature London 428,50-52 (2004).
[CrossRef] [PubMed]

Th . Elsässer, B . Nagorny and A. Hemmerich, "Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity," Phys. Rev. A 69,033403 (2004).
[CrossRef]

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

R. Fulton, A.I. Bishop, and P.F. Barker, "Optical Stark Decelerator for molecules," Phys. Rev. Lett. 93,243004 (2004).
[CrossRef]

2003 (4)

D. Kruse, C. von Cube, C. Zimmermann, and Ph.W. Courteille, ‘Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91,183601 (2003).
[CrossRef] [PubMed]

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

A. T. Black, H.W. Chan, and V. Vuletic, "Observation of collective friction forces due to spatial self-organization of atoms: from rayleigh to bragg scattering," Phys. Rev. Lett. 91,203001 (2003).
[CrossRef] [PubMed]

P. Domokos and H. Ritsch, "Mechanical effects of light in optical resonators, " J. Opt. Soc. Am. B 20,1098-1130 (2003).
[CrossRef]

2002 (2)

E.A. Cornell and C. E. Wieman, "Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, " Rev. Mod. Phys. 74,875-893 (2002).
[CrossRef]

N. Vanhaecke, W.D. Melo, B.L. Tolra, D. Comparat, and P. Pillet, "Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap," Phys. Rev. Lett. 89,063001 (2002).
[CrossRef] [PubMed]

2000 (3)

H.L. Bethlem, G. Berden, F.M.H. Crompvoets, R.T. Jongma, A.J.A. van Roij, and G. Meijer, "Electrostatic trapping of ammonia molecules," Nature London 406491-494 (2000).
[CrossRef] [PubMed]

V. Vuleti’c and S. Chu, "Laser cooling of atoms, ions, or molecules by coherent scattering," Phys. Rev. Lett. 84,3787-3790 (2000).
[CrossRef] [PubMed]

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

1998 (1)

S. Chu, "Nobel Lecture: The manipulation of neutral particles," C. Cohen-Tannoudji, "Nobel Lecture: Manipulating atoms with photons," and W. D. Phillips, "Nobel Lecture: Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70,685-741 (1998).
[CrossRef]

1994 (1)

R. Bonifacio, l. De 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]

1984 (1)

R. Bonifacio, C. Pellegrini, and L.M. Narducci, "Collective instabilities and high-gain regime in a free electron laser," Opt. Comm. 50,373-378 (1984).
[CrossRef]

Asb’oth, J. K.

D. Nagy, J. K. Asb’oth, P. Domokos, and H. Ritsch, "Self-organization of a laser-driven cold gas in a ring cavity," EuroPhys Lett. 74(2),254 (2006).
[CrossRef]

J. K. Asb’oth, P. Domokos, H. Ritsch and A. Vukics, "Self-organization of atoms in a cavity field: Threshold, bistability, and scaling laws," Phys. Rev A 72 (5) 053417 (2005).
[CrossRef]

Barker, P.F.

R. Fulton, A.I. Bishop, M.N. Shneider, and P.F. Barker, "Controlling the motion of cold molecules with deep periodic optical potentials," Nature Physics 2465-468 (2006).
[CrossRef]

R. Fulton, A.I. Bishop, and P.F. Barker, "Optical Stark Decelerator for molecules," Phys. Rev. Lett. 93,243004 (2004).
[CrossRef]

Beige, A.

A. Beige, P. L. Knight, and G. Vitiello, "Cooling many particles at once," New J. Phys. 7,96 (2005)
[CrossRef]

Berden, G.

H.L. Bethlem, G. Berden, F.M.H. Crompvoets, R.T. Jongma, A.J.A. van Roij, and G. Meijer, "Electrostatic trapping of ammonia molecules," Nature London 406491-494 (2000).
[CrossRef] [PubMed]

Bethlem, H.L.

H.L. Bethlem, G. Berden, F.M.H. Crompvoets, R.T. Jongma, A.J.A. van Roij, and G. Meijer, "Electrostatic trapping of ammonia molecules," Nature London 406491-494 (2000).
[CrossRef] [PubMed]

Bishop, A.I.

R. Fulton, A.I. Bishop, M.N. Shneider, and P.F. Barker, "Controlling the motion of cold molecules with deep periodic optical potentials," Nature Physics 2465-468 (2006).
[CrossRef]

R. Fulton, A.I. Bishop, and P.F. Barker, "Optical Stark Decelerator for molecules," Phys. Rev. Lett. 93,243004 (2004).
[CrossRef]

Black, A. T.

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

A. T. Black, H.W. Chan, and V. Vuletic, "Observation of collective friction forces due to spatial self-organization of atoms: from rayleigh to bragg scattering," Phys. Rev. Lett. 91,203001 (2003).
[CrossRef] [PubMed]

Bonifacio, R.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

R. Bonifacio, l. De 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]

R. Bonifacio, C. Pellegrini, and L.M. Narducci, "Collective instabilities and high-gain regime in a free electron laser," Opt. Comm. 50,373-378 (1984).
[CrossRef]

Chan, H. W.

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

Chan, H.W.

A. T. Black, H.W. Chan, and V. Vuletic, "Observation of collective friction forces due to spatial self-organization of atoms: from rayleigh to bragg scattering," Phys. Rev. Lett. 91,203001 (2003).
[CrossRef] [PubMed]

Chu, S.

S. Chu, "Nobel Lecture: The manipulation of neutral particles," C. Cohen-Tannoudji, "Nobel Lecture: Manipulating atoms with photons," and W. D. Phillips, "Nobel Lecture: Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70,685-741 (1998).
[CrossRef]

Comparat, D.

N. Vanhaecke, W.D. Melo, B.L. Tolra, D. Comparat, and P. Pillet, "Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap," Phys. Rev. Lett. 89,063001 (2002).
[CrossRef] [PubMed]

Cornell, E.A.

E.A. Cornell and C. E. Wieman, "Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, " Rev. Mod. Phys. 74,875-893 (2002).
[CrossRef]

Courteille, Ph. W.

S. Slama, C. von Cube, B. Deh, A. Ludewig, C. Zimmermann and Ph. W. Courteille, "Phase-sensitive detection of bragg scattering at 1D optical lattices," Phys. Rev. Lett. 94,193901 (2005).
[CrossRef] [PubMed]

Courteille, Ph.W.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

D. Kruse, C. von Cube, C. Zimmermann, and Ph.W. Courteille, ‘Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91,183601 (2003).
[CrossRef] [PubMed]

Crompvoets, F.M.H.

H.L. Bethlem, G. Berden, F.M.H. Crompvoets, R.T. Jongma, A.J.A. van Roij, and G. Meijer, "Electrostatic trapping of ammonia molecules," Nature London 406491-494 (2000).
[CrossRef] [PubMed]

Deh, B.

S. Slama, C. von Cube, B. Deh, A. Ludewig, C. Zimmermann and Ph. W. Courteille, "Phase-sensitive detection of bragg scattering at 1D optical lattices," Phys. Rev. Lett. 94,193901 (2005).
[CrossRef] [PubMed]

Domokos, P.

D. Nagy, J. K. Asb’oth, P. Domokos, and H. Ritsch, "Self-organization of a laser-driven cold gas in a ring cavity," EuroPhys Lett. 74(2),254 (2006).
[CrossRef]

J. K. Asb’oth, P. Domokos, H. Ritsch and A. Vukics, "Self-organization of atoms in a cavity field: Threshold, bistability, and scaling laws," Phys. Rev A 72 (5) 053417 (2005).
[CrossRef]

P. Domokos and H. Ritsch, "Mechanical effects of light in optical resonators, " J. Opt. Soc. Am. B 20,1098-1130 (2003).
[CrossRef]

Elsässer, Th

Th . Elsässer, B . Nagorny and A. Hemmerich, "Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity," Phys. Rev. A 69,033403 (2004).
[CrossRef]

Fulton, R.

R. Fulton, A.I. Bishop, M.N. Shneider, and P.F. Barker, "Controlling the motion of cold molecules with deep periodic optical potentials," Nature Physics 2465-468 (2006).
[CrossRef]

R. Fulton, A.I. Bishop, and P.F. Barker, "Optical Stark Decelerator for molecules," Phys. Rev. Lett. 93,243004 (2004).
[CrossRef]

Gangl, M.

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

Hemmerich, A.

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96,023002 (2006).
[CrossRef] [PubMed]

Th . Elsässer, B . Nagorny and A. Hemmerich, "Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity," Phys. Rev. A 69,033403 (2004).
[CrossRef]

Jongma, R.T.

H.L. Bethlem, G. Berden, F.M.H. Crompvoets, R.T. Jongma, A.J.A. van Roij, and G. Meijer, "Electrostatic trapping of ammonia molecules," Nature London 406491-494 (2000).
[CrossRef] [PubMed]

Klinner, J.

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96,023002 (2006).
[CrossRef] [PubMed]

Knight, P. L.

A. Beige, P. L. Knight, and G. Vitiello, "Cooling many particles at once," New J. Phys. 7,96 (2005)
[CrossRef]

Kruse, D.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

D. Kruse, C. von Cube, C. Zimmermann, and Ph.W. Courteille, ‘Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91,183601 (2003).
[CrossRef] [PubMed]

Lindholdt, M.

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96,023002 (2006).
[CrossRef] [PubMed]

Ludewig, A.

S. Slama, C. von Cube, B. Deh, A. Ludewig, C. Zimmermann and Ph. W. Courteille, "Phase-sensitive detection of bragg scattering at 1D optical lattices," Phys. Rev. Lett. 94,193901 (2005).
[CrossRef] [PubMed]

Maunz, P.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse,and G. Rempe, "Cavity cooling of a single atom," Nature London 428,50-52 (2004).
[CrossRef] [PubMed]

Meijer, G.

H.L. Bethlem, G. Berden, F.M.H. Crompvoets, R.T. Jongma, A.J.A. van Roij, and G. Meijer, "Electrostatic trapping of ammonia molecules," Nature London 406491-494 (2000).
[CrossRef] [PubMed]

Melo, W.D.

N. Vanhaecke, W.D. Melo, B.L. Tolra, D. Comparat, and P. Pillet, "Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap," Phys. Rev. Lett. 89,063001 (2002).
[CrossRef] [PubMed]

Nagorny, B

Th . Elsässer, B . Nagorny and A. Hemmerich, "Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity," Phys. Rev. A 69,033403 (2004).
[CrossRef]

Nagorny, B.

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96,023002 (2006).
[CrossRef] [PubMed]

Nagy, D.

D. Nagy, J. K. Asb’oth, P. Domokos, and H. Ritsch, "Self-organization of a laser-driven cold gas in a ring cavity," EuroPhys Lett. 74(2),254 (2006).
[CrossRef]

Narducci, L.M.

R. Bonifacio, C. Pellegrini, and L.M. Narducci, "Collective instabilities and high-gain regime in a free electron laser," Opt. Comm. 50,373-378 (1984).
[CrossRef]

Pellegrini, C.

R. Bonifacio, C. Pellegrini, and L.M. Narducci, "Collective instabilities and high-gain regime in a free electron laser," Opt. Comm. 50,373-378 (1984).
[CrossRef]

Pillet, P.

N. Vanhaecke, W.D. Melo, B.L. Tolra, D. Comparat, and P. Pillet, "Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap," Phys. Rev. Lett. 89,063001 (2002).
[CrossRef] [PubMed]

Pinkse, P. W. H.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse,and G. Rempe, "Cavity cooling of a single atom," Nature London 428,50-52 (2004).
[CrossRef] [PubMed]

Piovella, N.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

Puppe, T.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse,and G. Rempe, "Cavity cooling of a single atom," Nature London 428,50-52 (2004).
[CrossRef] [PubMed]

Rempe, G.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse,and G. Rempe, "Cavity cooling of a single atom," Nature London 428,50-52 (2004).
[CrossRef] [PubMed]

Ritsch, H.

D. Nagy, J. K. Asb’oth, P. Domokos, and H. Ritsch, "Self-organization of a laser-driven cold gas in a ring cavity," EuroPhys Lett. 74(2),254 (2006).
[CrossRef]

J. K. Asb’oth, P. Domokos, H. Ritsch and A. Vukics, "Self-organization of atoms in a cavity field: Threshold, bistability, and scaling laws," Phys. Rev A 72 (5) 053417 (2005).
[CrossRef]

P. Domokos and H. Ritsch, "Mechanical effects of light in optical resonators, " J. Opt. Soc. Am. B 20,1098-1130 (2003).
[CrossRef]

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

Robb, G. R.M.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

Schuster, I.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse,and G. Rempe, "Cavity cooling of a single atom," Nature London 428,50-52 (2004).
[CrossRef] [PubMed]

Shneider, M.N.

R. Fulton, A.I. Bishop, M.N. Shneider, and P.F. Barker, "Controlling the motion of cold molecules with deep periodic optical potentials," Nature Physics 2465-468 (2006).
[CrossRef]

Slama, S.

S. Slama, C. von Cube, B. Deh, A. Ludewig, C. Zimmermann and Ph. W. Courteille, "Phase-sensitive detection of bragg scattering at 1D optical lattices," Phys. Rev. Lett. 94,193901 (2005).
[CrossRef] [PubMed]

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

Syassen, N.

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse,and G. Rempe, "Cavity cooling of a single atom," Nature London 428,50-52 (2004).
[CrossRef] [PubMed]

Tolra, B.L.

N. Vanhaecke, W.D. Melo, B.L. Tolra, D. Comparat, and P. Pillet, "Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap," Phys. Rev. Lett. 89,063001 (2002).
[CrossRef] [PubMed]

van Roij, A.J.A.

H.L. Bethlem, G. Berden, F.M.H. Crompvoets, R.T. Jongma, A.J.A. van Roij, and G. Meijer, "Electrostatic trapping of ammonia molecules," Nature London 406491-494 (2000).
[CrossRef] [PubMed]

Vanhaecke, N.

N. Vanhaecke, W.D. Melo, B.L. Tolra, D. Comparat, and P. Pillet, "Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap," Phys. Rev. Lett. 89,063001 (2002).
[CrossRef] [PubMed]

Vitiello, G.

A. Beige, P. L. Knight, and G. Vitiello, "Cooling many particles at once," New J. Phys. 7,96 (2005)
[CrossRef]

von Cube, C.

S. Slama, C. von Cube, B. Deh, A. Ludewig, C. Zimmermann and Ph. W. Courteille, "Phase-sensitive detection of bragg scattering at 1D optical lattices," Phys. Rev. Lett. 94,193901 (2005).
[CrossRef] [PubMed]

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

D. Kruse, C. von Cube, C. Zimmermann, and Ph.W. Courteille, ‘Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91,183601 (2003).
[CrossRef] [PubMed]

Vukics, A.

J. K. Asb’oth, P. Domokos, H. Ritsch and A. Vukics, "Self-organization of atoms in a cavity field: Threshold, bistability, and scaling laws," Phys. Rev A 72 (5) 053417 (2005).
[CrossRef]

Vuletic, V.

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

A. T. Black, H.W. Chan, and V. Vuletic, "Observation of collective friction forces due to spatial self-organization of atoms: from rayleigh to bragg scattering," Phys. Rev. Lett. 91,203001 (2003).
[CrossRef] [PubMed]

Wieman, C. E.

E.A. Cornell and C. E. Wieman, "Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, " Rev. Mod. Phys. 74,875-893 (2002).
[CrossRef]

Zimmermann, C.

S. Slama, C. von Cube, B. Deh, A. Ludewig, C. Zimmermann and Ph. W. Courteille, "Phase-sensitive detection of bragg scattering at 1D optical lattices," Phys. Rev. Lett. 94,193901 (2005).
[CrossRef] [PubMed]

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

D. Kruse, C. von Cube, C. Zimmermann, and Ph.W. Courteille, ‘Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91,183601 (2003).
[CrossRef] [PubMed]

EuroPhys Lett. (1)

D. Nagy, J. K. Asb’oth, P. Domokos, and H. Ritsch, "Self-organization of a laser-driven cold gas in a ring cavity," EuroPhys Lett. 74(2),254 (2006).
[CrossRef]

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

Nature London (2)

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse,and G. Rempe, "Cavity cooling of a single atom," Nature London 428,50-52 (2004).
[CrossRef] [PubMed]

H.L. Bethlem, G. Berden, F.M.H. Crompvoets, R.T. Jongma, A.J.A. van Roij, and G. Meijer, "Electrostatic trapping of ammonia molecules," Nature London 406491-494 (2000).
[CrossRef] [PubMed]

Nature Physics (1)

R. Fulton, A.I. Bishop, M.N. Shneider, and P.F. Barker, "Controlling the motion of cold molecules with deep periodic optical potentials," Nature Physics 2465-468 (2006).
[CrossRef]

New J. Phys. (1)

A. Beige, P. L. Knight, and G. Vitiello, "Cooling many particles at once," New J. Phys. 7,96 (2005)
[CrossRef]

Opt. Comm. (1)

R. Bonifacio, C. Pellegrini, and L.M. Narducci, "Collective instabilities and high-gain regime in a free electron laser," Opt. Comm. 50,373-378 (1984).
[CrossRef]

Phys. Rev A (1)

J. K. Asb’oth, P. Domokos, H. Ritsch and A. Vukics, "Self-organization of atoms in a cavity field: Threshold, bistability, and scaling laws," Phys. Rev A 72 (5) 053417 (2005).
[CrossRef]

Phys. Rev. A (3)

Th . Elsässer, B . Nagorny and A. Hemmerich, "Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity," Phys. Rev. A 69,033403 (2004).
[CrossRef]

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

R. Bonifacio, l. De 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]

Phys. Rev. Lett. (9)

D. Kruse, C. von Cube, C. Zimmermann, and Ph.W. Courteille, ‘Observation of lasing mediated by collective atomic recoil," Phys. Rev. Lett. 91,183601 (2003).
[CrossRef] [PubMed]

S. Slama, C. von Cube, B. Deh, A. Ludewig, C. Zimmermann and Ph. W. Courteille, "Phase-sensitive detection of bragg scattering at 1D optical lattices," Phys. Rev. Lett. 94,193901 (2005).
[CrossRef] [PubMed]

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, and Ph.W. Courteille, G. R.M. Robb, N. Piovella, and R. Bonifacio, "Self-synchronization and dissipation-induced threshold in Collective Atomic Recoil Lasing," Phys. Rev. Lett. 93,083601 (2004)
[CrossRef] [PubMed]

N. Vanhaecke, W.D. Melo, B.L. Tolra, D. Comparat, and P. Pillet, "Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap," Phys. Rev. Lett. 89,063001 (2002).
[CrossRef] [PubMed]

A. T. Black, H.W. Chan, and V. Vuletic, "Observation of collective friction forces due to spatial self-organization of atoms: from rayleigh to bragg scattering," Phys. Rev. Lett. 91,203001 (2003).
[CrossRef] [PubMed]

J. Klinner, M. Lindholdt, B. Nagorny, and A. Hemmerich, "Normal mode splitting and mechanical effects of an optical lattice in a ring cavity," Phys. Rev. Lett. 96,023002 (2006).
[CrossRef] [PubMed]

V. Vuleti’c and S. Chu, "Laser cooling of atoms, ions, or molecules by coherent scattering," Phys. Rev. Lett. 84,3787-3790 (2000).
[CrossRef] [PubMed]

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

R. Fulton, A.I. Bishop, and P.F. Barker, "Optical Stark Decelerator for molecules," Phys. Rev. Lett. 93,243004 (2004).
[CrossRef]

Rev. Mod. Phys. (2)

S. Chu, "Nobel Lecture: The manipulation of neutral particles," C. Cohen-Tannoudji, "Nobel Lecture: Manipulating atoms with photons," and W. D. Phillips, "Nobel Lecture: Laser cooling and trapping of neutral atoms," Rev. Mod. Phys. 70,685-741 (1998).
[CrossRef]

E.A. Cornell and C. E. Wieman, "Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, " Rev. Mod. Phys. 74,875-893 (2002).
[CrossRef]

Other (4)

S. Nussmann, K. Murr, M. Hijlkema, B. Weber, A. Kuhn, and G. Rempe, "Vacuum-stimulated cooling of single atoms in three dimensions," e-print quant-ph/0506067.

B. Nagorny, T. Elsasser, H. Richter, A. Hemmerich, D. Kruse, C. Zimmermann, and P. Courteille, "Optical lattice in a high-finesse ring resonator," Phys. Rev. A 67,031401(R) (2003).
[CrossRef]

A.T. Black, J.K. Thompson, and V. Vuleti´c, "Collective light forces on atoms in resonators," J. Phys. B: At. Mol. Opt. Phys. 38, (2005).
[CrossRef]

G.R.M. Robb, N. Piovella, A. Ferraro, R. Bonifacio, Ph. W. Courteille, and C. Zimmermann, "Collective atomic recoil lasing including friction and diffusion effects," Phys. Rev. A 69, 041403 (R) (2004).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Contour lines of the maximum of the selfconsistent atom density distribution for a cloud at rest as a function of detuning δc and pump amplitude η. The analytic formula for the the selforganization threshold is indicated by the red dashed line. Parameters are N = 200,U 0 = -1/400,κ= 1.

Fig. 2.
Fig. 2.

Same as Fig. 1 for N = 1000,U 0 = -1/375,κ= 1.

Fig. 3.
Fig. 3.

Contour lines of kinetic energy gain of N=200 particles with average initial velocity zero and average kinetic energy h̄κ and U 0 = -0.015κwithin a fixed time interval κt = 60.

Fig. 4.
Fig. 4.

Maximum of particle density distribution after a time κt = 60 for a real space simulation of the dynamics of N=1000 particles. The Line with the crosses gives the analytic threshold condition Eq.23, which agrees quite well with the simulated result.

Fig. 5.
Fig. 5.

Self consistent atomic density distribution below and above threshold for N = 2000 atoms for U0 = -0.001k and Dc = -2k. The analytic threshold result for this set of parameters is hthresh = 31.6.

Fig. 6.
Fig. 6.

Maximum atomic density as a function of pump amplitude for three different iteration numbers of 5 for dotted line, 10 for dashed line, and 100 for solid line.

Fig. 7.
Fig. 7.

Intensity of backscattered field mode as a function of detuning δc and pump amplitude η for N = 1000 atoms U 0 = -0.002κ

Fig. 8.
Fig. 8.

Contour lines of maximum of the self consistent atomic density for N = 3000 atoms for U 0 = -0.0017κ and kv = 5κ. For comparison we also show the analytical expression for the selforganization threshold amplitude multiplied by 3 (dotted line).

Fig. 9.
Fig. 9.

(a) Kinetic energy loss per particle within a time interval of κt = 60 as a function of detuning Δ c and pump amplitude η for N = 3000 atoms counterpropagating the cavity axis with initial average momentum of p 0 = 2000h̄κ and temperature kT 0 = h̄κ and (b) average bunching parameter during this time for the same parameters.

Fig. 10.
Fig. 10.

Contour lines of time averaged bunching parameter ∣R∣ found by numerical simulation as function of detuning Δ c and pump amplitude η for parameters above. Again for reference we show the analytical result for the selforganization threshold (x3)

Equations (26)

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E ( x , t ) = E ( + ) ( x , t ) e i ω p t + E ( ) ( x , t ) e i ω p t ,
E ( + ) ( x , t ) = ε [ a + ( t ) e i k x + a ( t ) e i k x ] e z
E ( ) = [ E ( + ) ]
U 0 = Δ a Γ 2 + Δ a 2 g 2 .
d d t a ± ( t ) = [ i Δ ± i n U 0 κ ] a ± ( i ) i n U 0 e 2 i k x a ( t ) + η ± .
ε 2 V ( x ) = U 0 E ( x ) 2 .
E ( x ) 2 = ε 2 [ a + 2 + a 2 + a + a * e 2 i k x + ( a + a * ) e 2 i k x ]
= ε 2 [ a + 2 + a 2 + 2 a + a * cos ( 2 k x + α ) ] ,
f ( x ) = U 0 E ( x ) 2 2 h ¯ k U 0 a + a * sin ( 2 k x + α ) .
a + = i η Δ N U 0 + i κ ( Δ + N U 0 + i κ ) ( Δ N U 0 + i κ ) N 2 U 0 2 R 2 ,
a = i η N U 0 + R ( Δ + N U 0 + i κ ) ( Δ N U 0 + i κ ) N 2 U 0 2 R 2 .
a + a * = η 2 ( Δ N U 0 + i κ ) N U 0 R e i k x 0 ( Δ + N U 0 + i κ ) ( Δ N U 0 + i κ ) N 2 U 0 2 R 2 2 .
Δ N U 0 + i κ = ( Δ N U 0 ) 2 + κ 2 e i ( φ π ) .
cos φ = Δ + N U 0 ( Δ N U 0 ) 2 + κ 2 , sin φ = κ ( Δ N U 0 ) 2 + κ 2 .
V ( x ) = U 0 a + a * cos ( 2 k [ x ( x 0 φ 2 k ) ] ) m g x ,
2 k U 0 a + a * sin φ + mg = 0 .
g = η 2 2 k m N U 0 2 R κ ( Δ + N U 0 + i κ ) ( Δ N U 0 + i κ ) N 2 U 0 2 R 2 2 .
m g = 4 κ a * a k N .
ρ ( x ) = 1 Z exp [ V ( x ) / k B T ] ,
ρ ( 0 ) ( x ) = 1 λ ( 1 + ε r ( x ) ) .
r ( x ) = m = 1 ( A m cos ( mkx ) + B m sin ( mkx ) ) , m = 1 A m 2 + B m 2 = 1 ,
ρ ( 1 ) ( x ) = ( 1 V ( x ) k B T ) / λ =
= 1 λ ( 1 ε A 2 k B T N U 0 2 η 2 ( Δ N U 0 i κ ) ( ( Δ + N U 0 ) 2 + κ 2 ) [ cos ( 2 k ( x x 0 ) ] + O ( ε 2 )
η thresh > k B T ( Δ N U 0 ) 2 + κ 2 ( ( Δ + N U 0 ) 2 + κ 2 ) N U 0 2 .
η thresh > k B T ( ( Δ c N U 0 ) 2 + κ 2 ) 3 2 N U 0 2 .
Δ c F max = NU 0 ± N 2 U 0 2 R 2 κ 2

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