Skip to main content
Log in

Experimental and numerical exploration of intrinsic localized modes in an atomic lattice

  • Review
  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

This review focuses attention on the experimental studies of intrinsic localized modes (ILMs) produced in driven atomic lattices. Production methods involve the application of modulational instability under carefully controlled conditions. One experimental approach is to drive the atomic lattice far from equilibrium to produce ILMs, the second is to apply a driver of only modest strength but nearby in frequency to a plane wave mode so that a slow transformation from large amplitude standing waves to ILMs takes place. Since, in either case, the number of ILMs produced is small, the experimental observation tool appropriate for this task is four-wave mixing. This nonlinear detection technique makes use of the nonlinearity associated with an ILM to enhance its signal over that produced by the more numerous, but linear, spin waves. The final topic deals with numerical simulations of a nonlinear nanoscale atomic lattice where the new feature is running ILMs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Henry, B.R.: Local modes and their application to the analysis of polyatomic overtone spectra. J. Phys. Chem. 80, 2160–2164 (1976)

    Article  Google Scholar 

  2. Henry, B.R.: The use of local modes in the description of highly vibrationally excited molecules. Acc. Chem. Res. 10, 207–213 (1977)

    Article  Google Scholar 

  3. Henry, B.R.: The local mode model. In: Durig, J.R. (ed.) Vibrational Spectra and Structure, vol. 10, pp. 269–319. Elsevier, New York (1981)

    Google Scholar 

  4. Sage, M.L., Jortner, J.: Bond modes. Adv. Chem. Phys. 47, 293–323 (1981)

    Article  Google Scholar 

  5. Child, M.S., Halonen, L.: Overtone frequencies and intensities in the local mode picture. Adv. Chem. Phys. 57, 1–57 (1984)

    Article  Google Scholar 

  6. Henry, B.R.: The local mode model and overtone spectra: a probe of molecular structure and conformation. Acc. Chem. Res. 20, 429–435 (1987)

    Article  Google Scholar 

  7. Henry, B.R., Kjaergaard, H.G.: Local modes. Can. J. Chem. 80, 1635–1642 (2002)

    Article  Google Scholar 

  8. Lifshitz, I.M.: Some problems of the dynamic theory of non-ideal crystal lattices. Nuovo Cim. Suppl. 3, 716–734 (1956)

    Article  MathSciNet  Google Scholar 

  9. Maradudin, A.A., Montroll, E.W., Weiss, G.H.: Theory of lattice dynamics in the harmonic approximation. In: Seitz, F., Turnbull, D. (eds.) Solid State Physics Supplement 3. Academic Press, New York (1963)

    Google Scholar 

  10. Lifshitz, I.M., Kosevich, A.M.: The dynamics of a crystal lattice with defects. Rep. Prog. Phys. 29, 217–254 (1966)

    Article  ADS  Google Scholar 

  11. Maradudin, A.A., Montroll, E.W., Weiss, G.H., Ipatova, I.P.: Theory of Lattice Dynamics in the Harmonic Approximation, vol. 3. Academic Press, New York (1971)

    Google Scholar 

  12. Bilz, H., Strauch, D., Wehner, R.K.: Vibrational infrared and raman spectra of non-metals. In: Genzel, L. (ed.) Handbuch der Physik, vol. XXV, Pt. 2d, Springer, Berlin (1984)

    Google Scholar 

  13. Sievers, A.J.: Localized and resonance states in ionic crystals. In: Wallis, R.F. (ed.) Localized Excitations in Solids, pp. 27–45. Plenum, New York (1968)

    Google Scholar 

  14. Newman, R.C.: Infra-red absorption due to localized modes of vibration of impurity complexes in ionic and semiconducting crystals. Adv. Phys. 18, 545–663 (1969)

    Article  ADS  Google Scholar 

  15. Barker, A.S., Sievers, A.J.: Optical studies of the vibrational properties of disordered solids. Rev. Mod. Phys. 47, S1–S179 (1975)

    Article  Google Scholar 

  16. Kosevich, A.M., Kovalev, A.S.: Self-localization of vibrations in a one-dimensional anharmonic chain. Sov. Phys.-JETP 40, 891–896 (1974)

    ADS  Google Scholar 

  17. Dolgov, A.S.: The localization of vibrations in a nonlinear crystal structure. Sov. Phys. Solid State 28, 907–910 (1986)

    Google Scholar 

  18. Sievers, A.J., Takeno, S.: Intrinsic localized modes in anharmonic crystals. Phys. Rev. Lett. 61, 970–973 (1988)

    Article  ADS  Google Scholar 

  19. Kiselev, S.A., Bickham, S.R., Sievers, A.J.: Anharmonic gap modes in a perfect 1-D diatomic lattice for standard two-body nearest-neighbor potentials. Phys. Rev. B 48, 13508–13511 (1993)

    Article  ADS  Google Scholar 

  20. Sievers, A.J., Page, J.B.: Unusual anharmonic local mode systems. In: Norton, G.K. Maradudin, A.A. (eds.), Dynamical Properties of Solids: Phonon Physics The Cutting Edge, vol. VII, pp. 137–255. North Holland, Amsterdam (1995)

    Chapter  Google Scholar 

  21. Christodoulides, D.N., Joseph, R.I.: Discrete self-focusing in nonlinear arrays of coupled waveguides. Opt. Lett. 13, 794–796 (1988)

    Article  ADS  Google Scholar 

  22. Flach, S., Willis, C.R.: Discrete breathers. Phys. Repts. 295, 182–264 (1998)

    Article  MathSciNet  Google Scholar 

  23. Kiselev, S.A., Sievers, A.J.: Generation of intrinsic vibrational gap modes in three-dimensional ionic crystals. Phys. Rev. B 55, 5755–5758 (1997)

    Article  ADS  Google Scholar 

  24. Swanson, B.I., Brozik, J.A., Love, S.P., Strouse, G.F., Shreve, A.P., Bishop, A.R., Wang, W.-Z., Salkola, M.I.: Observation of intrinsically localized modes in a discrete low dimensional material. Phys. Rev. Lett. 82, 3288–3291 (1999)

    Article  ADS  Google Scholar 

  25. Markovich, T., Polturak, E., Bossy, J., Farhi, E.: Observation of a new excitation in bcc He-4 by inelastic neutron scattering. Phys. Rev. Lett. 88, 195301 (2002)

    Article  ADS  Google Scholar 

  26. Manley, M.E., Yethiraj, M., Sinn, H., Volz, H.M., Lashley, J.C., Hults, W.L., Lander, G.H., Smith, J.L.: Formation of a new dynamical mode in alpha-uranium observed by inelastic x-ray and neutron scattering. Phys. Rev. Lett. 96, 125501 (2006)

    Article  ADS  Google Scholar 

  27. Xie, A., van der Meer, L., Hoff, W., Austin, R.H.: Long-lived Amide I vibrational modes in myoglobin. Phys. Rev. Lett. 84, 5435–5438 (2000)

    Article  ADS  Google Scholar 

  28. Austin, R.H., Xie, A.H., van der Meer, L., Shinn, M., Neil, G.: Self-trapped states in proteins. J. Phys. Cond. Matter 15, S1693–S1698 (2003)

    Article  ADS  Google Scholar 

  29. Edler, E., Hamm, P., Scott, A.C.: Femtosecond study of self-trapped vibrational excitons in crystalline acetanilide. Phys, Rev. Lett. 88, 067403 (2002)

    Article  ADS  Google Scholar 

  30. Edler, J., Hamm, P.: Spectral response of crystalline acetanilide and N-methylacetamide: vibrational self-trapping in hydrogen-bonded crystals. Phys. Rev. B 69, 214301 (2004)

    Article  ADS  Google Scholar 

  31. Rossler, T., Page, J.B.: Intrinsic localized modes in driven anharmonic lattices with realistic potentials. Phys. Lett. A 204, 418–426 (1995)

    Article  ADS  Google Scholar 

  32. Rossler, T., Page, J.B.: Driven intrinsic localized modes and their stability in anharmonic lattices with realistic potentials. Physica B 220, 387–389 (1996)

    Article  ADS  Google Scholar 

  33. Maniadis, P., Flach, S.: Mechanism of discrete breather excitation in driven micro-mechanical cantilever array. Europhys. Lett. 74, 452–458 (2006)

    Article  ADS  Google Scholar 

  34. Sato, M., Hubbard, B.E. Sievers, A.J.: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays. Rev. Mod. Phys. 78, 137–157 (2006)

    Article  ADS  Google Scholar 

  35. Taniuti, T., Washimi, H.: Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma. Phys, Rev. Lett. 21, 209–212 (1968)

    Article  ADS  Google Scholar 

  36. Kivshar, Y.S., Peyrard, M.: Modulational instabilities in discrete lattices. Phys. Rev. A 46, 3198–3205 (1992)

    Article  ADS  Google Scholar 

  37. Suhl, H.: The theory of ferromagnetic resonance at high signal powers. J. Phys. Chem. Solids 1, 209–227 (1957)

    Article  ADS  Google Scholar 

  38. Lai, R., Sievers, A.J.: Modulational instability of nonlinear spin waves in easy axis antiferromagnetic chains. Phys. Rev. B 57, 3433–3443 (1998)

    Article  ADS  Google Scholar 

  39. Lai, R., Sievers, A.J.: Nonlinear nanoscale localization of magnetic excitations in atomic lattices. Phys. Repts. 314, 147–236 (1999)

    Article  ADS  Google Scholar 

  40. English, L.Q., Sato, M., Sievers, A.J.: Modulational instability of nonlinear spin waves in easy axis antiferromagnetic chains. II Influence of sample shape on intrinsic localized modes and dynamic spin defects. Phys. Rev. B 67, 024403 (2003)

    Article  ADS  Google Scholar 

  41. Schwarz, U.T., English, L.Q., Sievers, A.J.: Experimental generation and observation of intrinsic localized spin wave modes in an antiferromagnet. Phys. Rev. Lett. 83, 223–227 (1999)

    Article  ADS  Google Scholar 

  42. English, L.Q., Sato, M., Sievers, A.J.: Nanoscale intrinsic localized modes in an antiferromagnet. J. Appl. Phys. 89, 6707–6709 (2001)

    Article  ADS  Google Scholar 

  43. Sato, M., English, L.Q., Hubbard, B.E., Sievers, A.J.: Influence of sample shape on the production of intrinsic localized modes in an antiferromagnetic lattice. J. Appl. Phys. 91, 8676–8678 (2002)

    Article  ADS  Google Scholar 

  44. Sato, M., Sievers, A.J.: Direct observation of the discrete character of intrinsic localized modes in an antiferromagnet. Nature 432, 486–488 (2004)

    Article  ADS  Google Scholar 

  45. Sato, M., Sievers, A.J.: Counting discrete emission steps from intrinsic localized modes in a quasi-1D antiferromagnetic lattice. Phys. Rev. B 71, 214306 (2005)

    Article  ADS  Google Scholar 

  46. Wrubel, J.P., Sato, M., Sievers, A.J.: Controlled switching of intrinsic localized modes in a one-dimensional lattice. Phys. Rev. Lett. 95, 264101 (2005)

    Article  ADS  Google Scholar 

  47. Lai, R., Kiselev, S.A., Sievers, A.J.: Intrinsic localized spin-wave modes in antiferromagnetic chains with single-ion easy-axis anisotropy. Phys. Rev. B 54, R12665 (1996)

    Article  ADS  Google Scholar 

  48. Lai, R., Sievers, A.J.: (C2H5NH3)2CuCl4: A physical system for the experimental investigation of intrinsic localized modes. Phys. Rev. Lett. 81, 1937 (1998)

    Article  ADS  Google Scholar 

  49. Morgante, A.M., Johansson, M., Aubry, S., Kopidakis, G.: Breather-phonon resonances in finite-size lattices. J. Phys. A-Math. Gen. 35, 4999–5021 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  50. Sato, M., Sievers, A.J.: Driven localized excitations in the acoustic spectrum of small nonlinear macroscopic and microscopic lattices. Phys. Rev. Lett. 98, 214101 (2007)

    Article  ADS  Google Scholar 

  51. Jose, J.V., Saletan, E.J.: Classical Dynamics: A Contemporary Approach. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  52. Campbell, D.K., Flach, S. and Kivshar, Y.S.: Localizing energy through nonlinearity and discreteness. Phys. Today 57, 43–49 (2004)

    Article  ADS  Google Scholar 

  53. Scott, A.C.: Nonlinear Science: Emergence and Dynamics of Coherent Structures. Oxford University Press, New York (1999)

    MATH  Google Scholar 

  54. Scott, A.C.: Active Nonlinear Wave Propagation in Electronics. Wiley-Interscience, New York (1970)

    Google Scholar 

  55. Sato, M., Yasui, S., Hikihara, T., Sievers, A.J.: Management of localized energy in discrete nonlinear transmission lines. Europhys. Lett. 80, 30002 (2007)

    Article  ADS  Google Scholar 

  56. Stearrett, R., English, L.Q.: Experimental generation of intrinsic localized modes in a discrete electrical transmission line. J. Phys. D-Appl. Phys. 40, 5394–5398 (2007)

    Article  ADS  Google Scholar 

  57. Remoissenet, M.: Waves Called Solitons. Springer, Berlin (1999)

    MATH  Google Scholar 

  58. Chen, W., Mills, D.L.: Gap solitons and the nonlinear optical response of superlattices. Phys. Rev. Lett. 58, 160–163 (1987)

    Article  ADS  Google Scholar 

  59. Mills, D.L.: Nonlinear Optics: Basic Concepts. Springer, Berlin (1991)

    Google Scholar 

  60. Chen, W.-Z.: Experimental observation of solitons in a 1-D lattice. Phys. Rev. B 49, 15063 (1994)

    Article  ADS  Google Scholar 

  61. Lou, S., Huang, G.: Experimental study of the solitons in nonlinear diatomic macro-lattices. Mod. Phys. Lett. B 9, 1231–1241 (1995)

    Article  ADS  Google Scholar 

  62. Thakur, R.B., English, L.Q., Sievers, A.J.: Driven intrinsic localized modes in a coupled pendulum array. J. Phys. D-Appl. Phys. 41, 015503 (2008)

    Article  ADS  Google Scholar 

  63. Trias, E., Mazo, J.J., Orlando, T.P.: Discrete breathers in nonlinear lattices: experimental detection in a Josephson array. Phys. Rev. Lett. 84, 741–744 (2000)

    Article  ADS  Google Scholar 

  64. Binder, P., Abraimov, D., Ustinov, A.V., Flach, S., Zolotaryuk, Y.: Observation of breathers in Josephson ladders. Phys. Rev. Lett. 84, 745–748 (2000)

    Article  ADS  Google Scholar 

  65. Mandelik, D., Eisenberg, H.S., Silberberg, Y., Morandotti, R., Aitchison, J.S.: Observation of mutually trapped multiband optical breathers in waveguide arrays. Phys. Rev. Lett. 90, 253902 (2003)

    Article  ADS  Google Scholar 

  66. Fleischer, J.W., Segev, M., Efremidis, N.K., Christodoulides, D.N.: Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422, 147–150 (2003)

    Article  ADS  Google Scholar 

  67. Sato, M., Hubbard, B.E., Sievers, A.J., Ilic, B., Czaplewski, D.A., Craighead, H.G.: Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array. Phys. Rev. Lett. 90, 044102 (2003)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported in part by DOE No. DE-FG02-04ER46154 and by JSPS-Grant-in-Aid for Scientific Research No. (B) 18340086.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Sato.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sato, M., Sievers, A.J. Experimental and numerical exploration of intrinsic localized modes in an atomic lattice. J Biol Phys 35, 57–72 (2009). https://doi.org/10.1007/s10867-009-9135-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-009-9135-2

Keywords

Navigation