Abstract

Atom and nanoparticle arrays trapped in optical lattices are shown to be capable of sustaining collective oscillations of frequency proportional to the strength of the external light field. The spectrum of these oscillations determines the mechanical stability of the arrays. This phenomenon is studied for dimers, strings, and two-dimensional planar arrays. Laterally confined particles free to move along an optical channel are also considered as an example of collective motion in partially-confined systems. The fundamental concepts of dynamical response in optical matter introduced here constitute the basis for potential applications to quantum information technology and signal processing. Experimental realizations of these systems are proposed.

© 2007 Optical Society of America

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  1. M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms," Nature 415, 39-44 (2002).
    [CrossRef]
  2. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
    [CrossRef]
  3. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical matter: Crystallization and binding in intense optical fields," Science 249, 749-754 (1990).
    [CrossRef]
  4. P. Münstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, "Observation of cavity-mediated longrange light forces between strongly coupled atoms," Phys. Rev. Lett. 84, 4068-4071 (2000).
    [CrossRef]
  5. B. Nagorny, T. Elsässer, and A. Hemmerich, "Collective atomic motion in an optical lattice formed inside a high finesse cavity," Phys. Rev. Lett. 91, 153003 (2003).
    [CrossRef]
  6. D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, "Fast quantum gates for neutral atoms," Phys. Rev. Lett. 85, 2208-2211 (2000).
    [CrossRef]
  7. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  8. C. A. Ashley and S. Doniach, "Theory of extended x-ray absorption edge fine structure (EXAFS) in crystalline solids," Phys. Rev. B 11, 1279-1288 (1975).
    [CrossRef]
  9. A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
    [CrossRef]
  10. A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
    [CrossRef]
  11. P.M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
    [CrossRef]
  12. M. Pelton, M. Liu, H. Y. Kim, G. Smith, P. Guyot-Sionnest, and N. F. Scherer, "Optical trapping and alignment of single gold nanorods by using plasmon resonances," Opt. Lett. 31, 2075-2077 (2006).
    [CrossRef]
  13. D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
    [CrossRef]
  14. D. G. Grier and Y. Roichman, "Holographic optical trapping," Appl. Opt. 45, 880-887 (2006).
    [CrossRef]
  15. M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nat. Phys. 3, 477-480 (2007).
    [CrossRef]
  16. F. J. García de Abajo, T. Brixner, and W. Pfeiffer, "Nanoscale force manipulation in the vicinity of a metal nanostructure," J. Phys. B 40, S249-S258 (2007).
    [CrossRef]
  17. N. K. Metzger, K. Dholakia, and E. M. Wright, "Observation of bistability and hysteresis in optical binding of two dielectric spheres," Phys. Rev. Lett. 96, 068102 (2006).
    [CrossRef]
  18. S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
    [CrossRef]
  19. M. Hoppenbrouwers and W. van de Water, "Modes of motion of a colloidal crystal," Phys. Rev. Lett. 80, 3871-3874 (1998).
    [CrossRef]
  20. M. Polin, D. G. Grier, and S. R. Quake, "Anomalous vibrational dispersion in holographically trapped colloidal arrays," Phys. Rev. Lett. 96, 088101 (2006).
    [CrossRef]
  21. J. P. Gordon and A. Ashkin, "Motion of atoms in a radiation trap," Phys. Rev. A 21, 1606-1617 (1980).
    [CrossRef]
  22. P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2000).
    [CrossRef]
  23. R. Loudon, The Quantum Theory of Light (Oxford University Press, Oxford, 2000).
  24. P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
    [CrossRef]
  25. M. Guillon, "Field enhancement in a chain of optically bound dipoles," Opt. Express 14, 3045-3055 (2006).
    [CrossRef]
  26. F. J. García de Abajo, "Electromagnetic forces and torques in nanoparticles irradiated by plane waves," J. Quant. Spectrosc. Radiat. Transfer 89, 3-9 (2004).
  27. T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006).
    [CrossRef]
  28. T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field," J. Opt. Soc. Am. A 23, 2324-2330 (2006).
    [CrossRef]
  29. F. Depasse and J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D 27, 914-919 (1994).
  30. M. S. Safronova, C. J. Williams, and C.W. Clark, "Optimizing the fast Rydberg quantum gate," Phys. Rev. A 67, 040303(R) (2003).
  31. It should be noted that Rb has another resonance of width Γ = 2 π×2 MHz at 795 nm (frequency ω1), which combined with the 780 nm resonance (frequency ω0) gives an effective value of Γ = 2 π×6 MHz for light tuned far from this region (|ω. ω0|>> ω0. ω1). However, we are discussing here light tuned very close to the 780 nm resonance (|ω. ω0|<< ω0. ω1), for which the lower-frequency resonance can be overlooked.
  32. F. J. García de Abajo, "Interaction of radiation and fast electrons with clusters of dielectrics: A multiple scattering approach," Phys. Rev. Lett. 82, 2776-2779 (1999).
    [CrossRef]
  33. F. J. García de Abajo, "Momentum transfer to small particles by passing electron beams," Phys. Rev. B 70, 115422 (2004).
    [CrossRef]
  34. A. Ashkin and J. M. Dziedzic, "Optical levitation in high vacuum," Appl. Phys. Lett. 28, 333-335 (1976).
    [CrossRef]
  35. B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
    [CrossRef]
  36. W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
    [CrossRef]

2007 (2)

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nat. Phys. 3, 477-480 (2007).
[CrossRef]

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, "Nanoscale force manipulation in the vicinity of a metal nanostructure," J. Phys. B 40, S249-S258 (2007).
[CrossRef]

2006 (7)

N. K. Metzger, K. Dholakia, and E. M. Wright, "Observation of bistability and hysteresis in optical binding of two dielectric spheres," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef]

M. Polin, D. G. Grier, and S. R. Quake, "Anomalous vibrational dispersion in holographically trapped colloidal arrays," Phys. Rev. Lett. 96, 088101 (2006).
[CrossRef]

T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006).
[CrossRef]

D. G. Grier and Y. Roichman, "Holographic optical trapping," Appl. Opt. 45, 880-887 (2006).
[CrossRef]

M. Guillon, "Field enhancement in a chain of optically bound dipoles," Opt. Express 14, 3045-3055 (2006).
[CrossRef]

M. Pelton, M. Liu, H. Y. Kim, G. Smith, P. Guyot-Sionnest, and N. F. Scherer, "Optical trapping and alignment of single gold nanorods by using plasmon resonances," Opt. Lett. 31, 2075-2077 (2006).
[CrossRef]

T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field," J. Opt. Soc. Am. A 23, 2324-2330 (2006).
[CrossRef]

2005 (1)

P.M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
[CrossRef]

2004 (4)

W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
[CrossRef]

F. J. García de Abajo, "Electromagnetic forces and torques in nanoparticles irradiated by plane waves," J. Quant. Spectrosc. Radiat. Transfer 89, 3-9 (2004).

P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
[CrossRef]

F. J. García de Abajo, "Momentum transfer to small particles by passing electron beams," Phys. Rev. B 70, 115422 (2004).
[CrossRef]

2003 (3)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef]

M. S. Safronova, C. J. Williams, and C.W. Clark, "Optimizing the fast Rydberg quantum gate," Phys. Rev. A 67, 040303(R) (2003).

B. Nagorny, T. Elsässer, and A. Hemmerich, "Collective atomic motion in an optical lattice formed inside a high finesse cavity," Phys. Rev. Lett. 91, 153003 (2003).
[CrossRef]

2002 (2)

M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms," Nature 415, 39-44 (2002).
[CrossRef]

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

2000 (3)

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

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, "Fast quantum gates for neutral atoms," Phys. Rev. Lett. 85, 2208-2211 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2000).
[CrossRef]

1999 (1)

F. J. García de Abajo, "Interaction of radiation and fast electrons with clusters of dielectrics: A multiple scattering approach," Phys. Rev. Lett. 82, 2776-2779 (1999).
[CrossRef]

1998 (1)

M. Hoppenbrouwers and W. van de Water, "Modes of motion of a colloidal crystal," Phys. Rev. Lett. 80, 3871-3874 (1998).
[CrossRef]

1994 (1)

F. Depasse and J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D 27, 914-919 (1994).

1990 (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical matter: Crystallization and binding in intense optical fields," Science 249, 749-754 (1990).
[CrossRef]

1989 (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef]

1988 (1)

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

1987 (1)

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef]

1980 (2)

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

A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
[CrossRef]

1976 (1)

A. Ashkin and J. M. Dziedzic, "Optical levitation in high vacuum," Appl. Phys. Lett. 28, 333-335 (1976).
[CrossRef]

1975 (1)

C. A. Ashley and S. Doniach, "Theory of extended x-ray absorption edge fine structure (EXAFS) in crystalline solids," Phys. Rev. B 11, 1279-1288 (1975).
[CrossRef]

1970 (1)

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

," Phys. Rev. A (1)

M. S. Safronova, C. J. Williams, and C.W. Clark, "Optimizing the fast Rydberg quantum gate," Phys. Rev. A 67, 040303(R) (2003).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Ashkin and J. M. Dziedzic, "Optical levitation in high vacuum," Appl. Phys. Lett. 28, 333-335 (1976).
[CrossRef]

Astrophys. J. (1)

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

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

J. Phys. B (1)

F. J. García de Abajo, T. Brixner, and W. Pfeiffer, "Nanoscale force manipulation in the vicinity of a metal nanostructure," J. Phys. B 40, S249-S258 (2007).
[CrossRef]

J. Phys. D (1)

F. Depasse and J.-M. Vigoureux, "Optical binding force between two Rayleigh particles," J. Phys. D 27, 914-919 (1994).

J. Quant. Spectrosc. Radiat. Transfer (1)

F. J. García de Abajo, "Electromagnetic forces and torques in nanoparticles irradiated by plane waves," J. Quant. Spectrosc. Radiat. Transfer 89, 3-9 (2004).

Nano Lett. (1)

P.M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, "Expanding the optical trapping range of gold nanoparticles," Nano Lett. 5, 1937-1942 (2005).
[CrossRef]

Nat. Phys. (1)

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape," Nat. Phys. 3, 477-480 (2007).
[CrossRef]

Nature (2)

M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms," Nature 415, 39-44 (2002).
[CrossRef]

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef]

Opt. Commun. (1)

P. Zemánek, V. Karásek, and A. Sasso, "Optical forces acting on Rayleigh particle placed into interference field," Opt. Commun. 240, 401-415 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

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

Phys. Rev. B (3)

C. A. Ashley and S. Doniach, "Theory of extended x-ray absorption edge fine structure (EXAFS) in crystalline solids," Phys. Rev. B 11, 1279-1288 (1975).
[CrossRef]

W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004).
[CrossRef]

F. J. García de Abajo, "Momentum transfer to small particles by passing electron beams," Phys. Rev. B 70, 115422 (2004).
[CrossRef]

Phys. Rev. Lett. (11)

F. J. García de Abajo, "Interaction of radiation and fast electrons with clusters of dielectrics: A multiple scattering approach," Phys. Rev. Lett. 82, 2776-2779 (1999).
[CrossRef]

T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006).
[CrossRef]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical binding," Phys. Rev. Lett. 63, 1233-1236 (1989).
[CrossRef]

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

B. Nagorny, T. Elsässer, and A. Hemmerich, "Collective atomic motion in an optical lattice formed inside a high finesse cavity," Phys. Rev. Lett. 91, 153003 (2003).
[CrossRef]

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, "Fast quantum gates for neutral atoms," Phys. Rev. Lett. 85, 2208-2211 (2000).
[CrossRef]

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

N. K. Metzger, K. Dholakia, and E. M. Wright, "Observation of bistability and hysteresis in optical binding of two dielectric spheres," Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef]

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

M. Hoppenbrouwers and W. van de Water, "Modes of motion of a colloidal crystal," Phys. Rev. Lett. 80, 3871-3874 (1998).
[CrossRef]

M. Polin, D. G. Grier, and S. R. Quake, "Anomalous vibrational dispersion in holographically trapped colloidal arrays," Phys. Rev. Lett. 96, 088101 (2006).
[CrossRef]

Science (3)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical matter: Crystallization and binding in intense optical fields," Science 249, 749-754 (1990).
[CrossRef]

A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
[CrossRef]

A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria," Science 235, 1517-1520 (1987).
[CrossRef]

Other (2)

It should be noted that Rb has another resonance of width Γ = 2 π×2 MHz at 795 nm (frequency ω1), which combined with the 780 nm resonance (frequency ω0) gives an effective value of Γ = 2 π×6 MHz for light tuned far from this region (|ω. ω0|>> ω0. ω1). However, we are discussing here light tuned very close to the 780 nm resonance (|ω. ω0|<< ω0. ω1), for which the lower-frequency resonance can be overlooked.

R. Loudon, The Quantum Theory of Light (Oxford University Press, Oxford, 2000).

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