Abstract

Photons carry momentum, and thus their scattering not only modifies light propagation but at the same time induces forces on particles. Confining mobile scatterers and light in a closed volume thus generates a complex coupled nonlinear dynamics. As a striking example, one finds a phase transition from random order to a crystalline structure if particles within a resonator are illuminated by a sufficiently strong laser. This phase transition can be simply understood as a minimization of the optical potential energy of the particles in concurrence with a maximization of light scattering into the resonator. Here, we generalize the self-ordering dynamics to several illumination colors and cavity modes. In this enlarged model, particles adapt dynamically to current illumination conditions to ensure maximal simultaneous scattering of all frequencies into the resonator as a sort of self-optimizing light collection system with built-in memory. Such adaptive self-ordering dynamics in optical resonators could be implemented in a wide range of systems from cold atoms and molecules to mobile nanoparticles in solution. In the quantum regime, it enables exploration of uncharted regions of multiparticle phases, allowing simulation of Hopfield networks, associative memories, or generalized Hamiltonian mean field models.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Mechanical effects of light in optical resonators

Peter Domokos and Helmut Ritsch
J. Opt. Soc. Am. B 20(5) 1098-1130 (2003)

Stability analysis of two photorefractive ring resonator circuits: the flip-flop and the feature extractor

A. A. Zozulya, M. Saffman, and D. Z. Anderson
J. Opt. Soc. Am. B 12(6) 1036-1047 (1995)

References

  • View by:
  • |
  • |
  • |

  1. P. Domokos, H. Ritsch, “Collective cooling and self-organization of atoms in a cavity,” Phys. Rev. Lett. 89, 253003 (2002).
    [Crossref]
  2. A. T. Black, H. W. Chan, V. Vuletić, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
    [Crossref]
  3. K. Arnold, M. Baden, M. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
    [Crossref]
  4. T. Grießer, H. Ritsch, M. Hemmerling, G. Robb, “A Vlasov approach to bunching and self-ordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010).
    [Crossref]
  5. H. Ritsch, P. Domokos, F. Brennecke, T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
    [Crossref]
  6. P. Domokos, T. Salzburger, 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]
  7. S. Gopalakrishnan, B. L. Lev, P. M. Goldbart, “Emergent crystallinity and frustration with Bose-Einstein condensates in multimode cavities,” Nat. Phys. 5, 845–850 (2009).
    [Crossref]
  8. M. Burns, J. Fournier, J. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Sci. Mag. 249(4970), 749–754 (1990).
  9. W. Singer, M. Frick, S. Bernet, M. Ritsch-Marte, “Self-organized array of regularly spaced microbeads in a fiber-optical trap,” J. Opt. Soc. Am. B 20, 1568–1574 (2003).
    [Crossref]
  10. K. Dholakia, P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
    [Crossref]
  11. P. Chaumet, M. Nieto-Vesperinas, “Optical binding of particles with or without the presence of a flat dielectric surface,” Phys. Rev. B 64, 035422 (2001).
    [Crossref]
  12. R. W. Bowman, M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
    [Crossref]
  13. B. Schmittberger, J. Greenberg, D. Gauthier, “Free-space, multimode spatial self-organization of cold, thermal atoms,” in 43rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics (American Physical Society, 2012), abstract ID BAPS.2012.DAMOP.H2.10.
  14. D. E. Chang, J. I. Cirac, H. J. Kimble, “Self-organization of atoms along a nanophotonic waveguide,” Phys. Rev. Lett. 110, 113606 (2013).
    [Crossref]
  15. G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
    [Crossref]
  16. S. Ostermann, M. Sonnleitner, H. Ritsch, “Scattering approach to two-colour light forces and self-ordering of polarizable particles,” New J. Phys. 16, 043017 (2014).
    [Crossref]
  17. S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch, M. Arndt, “Master equation for the motion of a polarizable particle in a multimode cavity,” New J. Phys. 12, 083003 (2010).
    [Crossref]
  18. K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
    [Crossref]
  19. S. Krämer, H. Ritsch, “Self-ordering dynamics of ultracold atoms in multicolored cavity fields,” arXiv:1404.5348 (2014).
  20. W. Niedenzu, T. Grießer, H. Ritsch, “Kinetic theory of cavity cooling and self-organisation of a cold gas,” Eur. Phys. Lett. 96, 43001 (2011).
  21. I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, W. D. Phillips, “Photonic band gaps in optical lattices,” Phys. Rev. A 52, 1394 (1995).
    [Crossref]
  22. K. M. Douglass, S. Sukhov, A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
    [Crossref]

2014 (2)

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

S. Ostermann, M. Sonnleitner, H. Ritsch, “Scattering approach to two-colour light forces and self-ordering of polarizable particles,” New J. Phys. 16, 043017 (2014).
[Crossref]

2013 (3)

R. W. Bowman, M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
[Crossref]

D. E. Chang, J. I. Cirac, H. J. Kimble, “Self-organization of atoms along a nanophotonic waveguide,” Phys. Rev. Lett. 110, 113606 (2013).
[Crossref]

H. Ritsch, P. Domokos, F. Brennecke, T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

2012 (2)

K. Arnold, M. Baden, M. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

K. M. Douglass, S. Sukhov, A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

2011 (1)

W. Niedenzu, T. Grießer, H. Ritsch, “Kinetic theory of cavity cooling and self-organisation of a cold gas,” Eur. Phys. Lett. 96, 43001 (2011).

2010 (4)

T. Grießer, H. Ritsch, M. Hemmerling, G. Robb, “A Vlasov approach to bunching and self-ordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010).
[Crossref]

K. Dholakia, P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[Crossref]

S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch, M. Arndt, “Master equation for the motion of a polarizable particle in a multimode cavity,” New J. Phys. 12, 083003 (2010).
[Crossref]

K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

2009 (1)

S. Gopalakrishnan, B. L. Lev, P. M. Goldbart, “Emergent crystallinity and frustration with Bose-Einstein condensates in multimode cavities,” Nat. Phys. 5, 845–850 (2009).
[Crossref]

2003 (2)

A. T. Black, H. W. Chan, V. Vuletić, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

W. Singer, M. Frick, S. Bernet, M. Ritsch-Marte, “Self-organized array of regularly spaced microbeads in a fiber-optical trap,” J. Opt. Soc. Am. B 20, 1568–1574 (2003).
[Crossref]

2002 (2)

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

P. Domokos, T. Salzburger, 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 (1)

P. Chaumet, M. Nieto-Vesperinas, “Optical binding of particles with or without the presence of a flat dielectric surface,” Phys. Rev. B 64, 035422 (2001).
[Crossref]

1995 (1)

I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, W. D. Phillips, “Photonic band gaps in optical lattices,” Phys. Rev. A 52, 1394 (1995).
[Crossref]

1990 (1)

M. Burns, J. Fournier, J. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Sci. Mag. 249(4970), 749–754 (1990).

Ackemann, T.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

Arndt, M.

S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch, M. Arndt, “Master equation for the motion of a polarizable particle in a multimode cavity,” New J. Phys. 12, 083003 (2010).
[Crossref]

Arnold, A. S.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

Arnold, K.

K. Arnold, M. Baden, M. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

Asenbaum, P.

S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch, M. Arndt, “Master equation for the motion of a polarizable particle in a multimode cavity,” New J. Phys. 12, 083003 (2010).
[Crossref]

Baden, M.

K. Arnold, M. Baden, M. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

Barrett, M.

K. Arnold, M. Baden, M. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

Baumann, K.

K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

Bernet, S.

Black, A. T.

A. T. Black, H. W. Chan, V. Vuletić, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

Bowman, R. W.

R. W. Bowman, M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
[Crossref]

Brennecke, F.

H. Ritsch, P. Domokos, F. Brennecke, T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

Burns, M.

M. Burns, J. Fournier, J. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Sci. Mag. 249(4970), 749–754 (1990).

Chan, H. W.

A. T. Black, H. W. Chan, V. Vuletić, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

Chang, D. E.

D. E. Chang, J. I. Cirac, H. J. Kimble, “Self-organization of atoms along a nanophotonic waveguide,” Phys. Rev. Lett. 110, 113606 (2013).
[Crossref]

Chaumet, P.

P. Chaumet, M. Nieto-Vesperinas, “Optical binding of particles with or without the presence of a flat dielectric surface,” Phys. Rev. B 64, 035422 (2001).
[Crossref]

Cirac, J. I.

D. E. Chang, J. I. Cirac, H. J. Kimble, “Self-organization of atoms along a nanophotonic waveguide,” Phys. Rev. Lett. 110, 113606 (2013).
[Crossref]

Deutsch, I. H.

I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, W. D. Phillips, “Photonic band gaps in optical lattices,” Phys. Rev. A 52, 1394 (1995).
[Crossref]

Dholakia, K.

K. Dholakia, P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[Crossref]

Dogariu, A.

K. M. Douglass, S. Sukhov, A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

Domokos, P.

H. Ritsch, P. Domokos, F. Brennecke, T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

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

Douglass, K. M.

K. M. Douglass, S. Sukhov, A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

Esslinger, T.

H. Ritsch, P. Domokos, F. Brennecke, T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

Firth, W. J.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

Fournier, J.

M. Burns, J. Fournier, J. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Sci. Mag. 249(4970), 749–754 (1990).

Frick, M.

Gauthier, D.

B. Schmittberger, J. Greenberg, D. Gauthier, “Free-space, multimode spatial self-organization of cold, thermal atoms,” in 43rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics (American Physical Society, 2012), abstract ID BAPS.2012.DAMOP.H2.10.

Goldbart, P. M.

S. Gopalakrishnan, B. L. Lev, P. M. Goldbart, “Emergent crystallinity and frustration with Bose-Einstein condensates in multimode cavities,” Nat. Phys. 5, 845–850 (2009).
[Crossref]

Golovchenko, J.

M. Burns, J. Fournier, J. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Sci. Mag. 249(4970), 749–754 (1990).

Gomes, P. M.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

Gopalakrishnan, S.

S. Gopalakrishnan, B. L. Lev, P. M. Goldbart, “Emergent crystallinity and frustration with Bose-Einstein condensates in multimode cavities,” Nat. Phys. 5, 845–850 (2009).
[Crossref]

Greenberg, J.

B. Schmittberger, J. Greenberg, D. Gauthier, “Free-space, multimode spatial self-organization of cold, thermal atoms,” in 43rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics (American Physical Society, 2012), abstract ID BAPS.2012.DAMOP.H2.10.

Grießer, T.

W. Niedenzu, T. Grießer, H. Ritsch, “Kinetic theory of cavity cooling and self-organisation of a cold gas,” Eur. Phys. Lett. 96, 43001 (2011).

T. Grießer, H. Ritsch, M. Hemmerling, G. Robb, “A Vlasov approach to bunching and self-ordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010).
[Crossref]

Guerlin, C.

K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

Hammerer, K.

S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch, M. Arndt, “Master equation for the motion of a polarizable particle in a multimode cavity,” New J. Phys. 12, 083003 (2010).
[Crossref]

Hemmerling, M.

T. Grießer, H. Ritsch, M. Hemmerling, G. Robb, “A Vlasov approach to bunching and self-ordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010).
[Crossref]

Kaiser, R.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

Kimble, H. J.

D. E. Chang, J. I. Cirac, H. J. Kimble, “Self-organization of atoms along a nanophotonic waveguide,” Phys. Rev. Lett. 110, 113606 (2013).
[Crossref]

Krämer, S.

S. Krämer, H. Ritsch, “Self-ordering dynamics of ultracold atoms in multicolored cavity fields,” arXiv:1404.5348 (2014).

Labeyrie, G.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

Lev, B. L.

S. Gopalakrishnan, B. L. Lev, P. M. Goldbart, “Emergent crystallinity and frustration with Bose-Einstein condensates in multimode cavities,” Nat. Phys. 5, 845–850 (2009).
[Crossref]

Niedenzu, W.

W. Niedenzu, T. Grießer, H. Ritsch, “Kinetic theory of cavity cooling and self-organisation of a cold gas,” Eur. Phys. Lett. 96, 43001 (2011).

Nieto-Vesperinas, M.

P. Chaumet, M. Nieto-Vesperinas, “Optical binding of particles with or without the presence of a flat dielectric surface,” Phys. Rev. B 64, 035422 (2001).
[Crossref]

Nimmrichter, S.

S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch, M. Arndt, “Master equation for the motion of a polarizable particle in a multimode cavity,” New J. Phys. 12, 083003 (2010).
[Crossref]

Oppo, G.-L.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

Ostermann, S.

S. Ostermann, M. Sonnleitner, H. Ritsch, “Scattering approach to two-colour light forces and self-ordering of polarizable particles,” New J. Phys. 16, 043017 (2014).
[Crossref]

Padgett, M. J.

R. W. Bowman, M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
[Crossref]

Phillips, W. D.

I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, W. D. Phillips, “Photonic band gaps in optical lattices,” Phys. Rev. A 52, 1394 (1995).
[Crossref]

Ritsch, H.

S. Ostermann, M. Sonnleitner, H. Ritsch, “Scattering approach to two-colour light forces and self-ordering of polarizable particles,” New J. Phys. 16, 043017 (2014).
[Crossref]

H. Ritsch, P. Domokos, F. Brennecke, T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

W. Niedenzu, T. Grießer, H. Ritsch, “Kinetic theory of cavity cooling and self-organisation of a cold gas,” Eur. Phys. Lett. 96, 43001 (2011).

T. Grießer, H. Ritsch, M. Hemmerling, G. Robb, “A Vlasov approach to bunching and self-ordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010).
[Crossref]

S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch, M. Arndt, “Master equation for the motion of a polarizable particle in a multimode cavity,” New J. Phys. 12, 083003 (2010).
[Crossref]

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

P. Domokos, T. Salzburger, 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. Krämer, H. Ritsch, “Self-ordering dynamics of ultracold atoms in multicolored cavity fields,” arXiv:1404.5348 (2014).

Ritsch-Marte, M.

Robb, G.

T. Grießer, H. Ritsch, M. Hemmerling, G. Robb, “A Vlasov approach to bunching and self-ordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010).
[Crossref]

Robb, G. R.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

Rolston, S. L.

I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, W. D. Phillips, “Photonic band gaps in optical lattices,” Phys. Rev. A 52, 1394 (1995).
[Crossref]

Salzburger, T.

P. Domokos, T. Salzburger, 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]

Schmittberger, B.

B. Schmittberger, J. Greenberg, D. Gauthier, “Free-space, multimode spatial self-organization of cold, thermal atoms,” in 43rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics (American Physical Society, 2012), abstract ID BAPS.2012.DAMOP.H2.10.

Singer, W.

Sonnleitner, M.

S. Ostermann, M. Sonnleitner, H. Ritsch, “Scattering approach to two-colour light forces and self-ordering of polarizable particles,” New J. Phys. 16, 043017 (2014).
[Crossref]

Spreeuw, R. J. C.

I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, W. D. Phillips, “Photonic band gaps in optical lattices,” Phys. Rev. A 52, 1394 (1995).
[Crossref]

Sukhov, S.

K. M. Douglass, S. Sukhov, A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

Tesio, E.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

Vuletic, V.

A. T. Black, H. W. Chan, V. Vuletić, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

Zemánek, P.

K. Dholakia, P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[Crossref]

Eur. Phys. J. D (1)

T. Grießer, H. Ritsch, M. Hemmerling, G. Robb, “A Vlasov approach to bunching and self-ordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010).
[Crossref]

Eur. Phys. Lett. (1)

W. Niedenzu, T. Grießer, H. Ritsch, “Kinetic theory of cavity cooling and self-organisation of a cold gas,” Eur. Phys. Lett. 96, 43001 (2011).

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

Nat. Photonics (2)

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. Robb, A. S. Arnold, R. Kaiser, T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

K. M. Douglass, S. Sukhov, A. Dogariu, “Superdiffusion in optically controlled active media,” Nat. Photonics 6, 834–837 (2012).
[Crossref]

Nat. Phys. (1)

S. Gopalakrishnan, B. L. Lev, P. M. Goldbart, “Emergent crystallinity and frustration with Bose-Einstein condensates in multimode cavities,” Nat. Phys. 5, 845–850 (2009).
[Crossref]

Nature (1)

K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

New J. Phys. (2)

S. Ostermann, M. Sonnleitner, H. Ritsch, “Scattering approach to two-colour light forces and self-ordering of polarizable particles,” New J. Phys. 16, 043017 (2014).
[Crossref]

S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch, M. Arndt, “Master equation for the motion of a polarizable particle in a multimode cavity,” New J. Phys. 12, 083003 (2010).
[Crossref]

Phys. Rev. A (2)

P. Domokos, T. Salzburger, 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]

I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, W. D. Phillips, “Photonic band gaps in optical lattices,” Phys. Rev. A 52, 1394 (1995).
[Crossref]

Phys. Rev. B (1)

P. Chaumet, M. Nieto-Vesperinas, “Optical binding of particles with or without the presence of a flat dielectric surface,” Phys. Rev. B 64, 035422 (2001).
[Crossref]

Phys. Rev. Lett. (4)

D. E. Chang, J. I. Cirac, H. J. Kimble, “Self-organization of atoms along a nanophotonic waveguide,” Phys. Rev. Lett. 110, 113606 (2013).
[Crossref]

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

A. T. Black, H. W. Chan, V. Vuletić, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

K. Arnold, M. Baden, M. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

Rep. Prog. Phys. (1)

R. W. Bowman, M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
[Crossref]

Rev. Mod. Phys. (2)

H. Ritsch, P. Domokos, F. Brennecke, T. Esslinger, “Cold atoms in cavity-generated dynamical optical potentials,” Rev. Mod. Phys. 85, 553–601 (2013).
[Crossref]

K. Dholakia, P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[Crossref]

Sci. Mag. (1)

M. Burns, J. Fournier, J. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Sci. Mag. 249(4970), 749–754 (1990).

Other (2)

B. Schmittberger, J. Greenberg, D. Gauthier, “Free-space, multimode spatial self-organization of cold, thermal atoms,” in 43rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics (American Physical Society, 2012), abstract ID BAPS.2012.DAMOP.H2.10.

S. Krämer, H. Ritsch, “Self-ordering dynamics of ultracold atoms in multicolored cavity fields,” arXiv:1404.5348 (2014).

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 (8)

Fig. 1.
Fig. 1.

Mobile particles inside a lossy multimode optical resonator with decay rate κ illuminated by various laser beams with pump strengths η1, η2, and η3.

Fig. 2.
Fig. 2.

Scattered light intensity and stable configurations (red dots) for two scatterers as function of position within one wavelength of the fundamental mode. The density plot shows the associated cavity light intensity Ptot and the contours give zero-force lines for each particle illuminated with frequencies near the five lowest-order modes ωn, n{1,2,3,4,5}. On the left, we only pump at the fifth mode, i.e., ηl/η=(0,0,0,0,1), while on the right four modes are pumped, i.e., ηr/η=(1,0,1,1,1). Parameters are η=5κ/8, NU0=κ/10, δc=NU0κ.

Fig. 3.
Fig. 3.

Total scattered light intensity as in Fig. 2 for three pump frequencies ηv/η=(0,1,1,1,0), with the different mode intensities color coded. In white areas, all three modes oscillate.

Fig. 4.
Fig. 4.

Stable equilibrium configurations for three particles represented by spheres, whose size and color encode the amount of scattered light Ptot in this configuration. Illumination is set to ηl/η=(1,0,1,0,1) on the left and ηr/η=(1,0,1,1,1) on the right, with the other parameters fixed as in Fig. 2.

Fig. 5.
Fig. 5.

Configuration space trajectories for three particles with periodically time-varying illumination starting at different initial positions. ηt/η periodically cycles through five different illumination conditions given by (1,0,1,0,0,0,1), (0,1,1,0,1,1,0), (0,0,1,0,1,0,0), (0,1,1,1,1,1,0), (1,1,1,1,0,1,0). The illumination changes after the system has reached a stable (zero force) point (red dots). Parameters are η=κ/5, NU0=κ, and δc=NU0/22κ.

Fig. 6.
Fig. 6.

Typical trajectory of two particles with static illumination ηs/η=(1,0,1,1,1,0,1) and random momentum kicks at time intervals Δt=2/κ and friction μ=2κ, with the yellow dot indicating the initial position. As in Fig. 2, the background density shows the scattered intensity Ptot and red dots indicate equilibrium positions with zero average light force. Other parameters are η=κ/5, U0=κ/2, and δc=NU0/22κ.

Fig. 7.
Fig. 7.

Positions of the two particles’ modulo 2 wavelengths (upper graph) and scattered light intensity Ptot (lower graph) for the trajectory of Fig. 6 with ωR=κπ2/10. The particles spend most time at points of high scattering at x12λ/4 or 3λ/4.

Fig. 8.
Fig. 8.

Time evolution of 100 scatterers under aperiodically time-varying illumination with about 50 high-order modes. The illumination is switched randomly between five illumination patterns consisting of 50 randomly chosen modes after the particles have settled to a stationary state. The two graphs display the total scattered light Ptot (upper figure) and the sum of magnitudes of the order parameters Θtot, as defined in Eq. (5) (lower figure). Other parameters chosen are as in Fig. 5.

Equations (7)

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

H=j=1Npj22m+nI[(δc,nU0,nj=1Nsin2(knxj))anan+ηnj=1Nsin(knxj)(an+an)].
ρ˙=i[H,ρ]+Lρ,withLρ:=nκn(2anρanananρρanan)
x˙j=pjm,
p˙j=nIkn(U0,n|αn|2sin(2knxj)+ηn(αn+αn*)cos(knxj)),
α˙n=i(δc,nU0,nj=1Nsin2(knxj))αnκnαniηnj=1Nsin(knxj)+ξn.
αn(x1,,xN)=ηnjsin(knxj)δcU0jsin2(knxj)+iκ,
Θtot=n|Θn|,Θn=1Njsin(knxj),

Metrics