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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Self-trapping transition in nonlinear cubic lattices.

Uta Naether1, Alejandro J Martínez, Diego Guzmán-Silva

  • 1Departamento de Física, MSI-Nucleus on Advanced Optics, and Center for Optics and Photonics, Facultad de Ciencias, Universidad de Chile, Santiago, Chile. unaether@u.uchile.cl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 16, 2013
PubMed
Summary

Researchers determined the critical nonlinearity for energy localization in discrete nonlinear cubic (Kerr) lattices. This finding helps predict transitions from delocalized to localized states in various dimensions.

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Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Lattice theory

Background:

  • Discrete nonlinear lattices exhibit complex energy propagation behaviors.
  • Understanding energy localization is crucial for designing novel materials and devices.

Purpose of the Study:

  • To determine the critical nonlinearity value for dynamic energy localization in cubic (Kerr) lattices.
  • To develop a general criterion for predicting the transition from delocalized to localized states.

Main Methods:

  • Analysis of effective frequency and participation ratio in 1D, 2D, and 3D lattices.
  • Development of a "dynamical tongue" criterion in parameter space.
  • Computation of dynamically excited frequencies to validate stationary ansatz.

Main Results:

  • A general criterion for the delocalized-to-localized transition was established.
  • An analytical estimate for critical nonlinearity was derived.
  • A parameter was found to be nearly constant for 2D systems and validated on binary lattices.

Conclusions:

  • The study provides a fundamental understanding of energy localization in nonlinear lattices.
  • The developed criterion and analytical estimate offer predictive power for lattice dynamics.
  • Findings are applicable to 2D binary lattices, demonstrating broad utility.