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Area of Science:

  • Quantum physics
  • Condensed matter physics

Background:

  • Anderson localization describes the transition of electron wave functions from extended to localized states in disordered systems.
  • The mobility edge signifies the boundary between metallic and localized phases.
  • Multifractality characterizes complex, scale-invariant properties observed in critical phenomena.

Purpose of the Study:

  • To investigate the critical state at the mobility edge of the Anderson localization transition.
  • To observe the multifractal structure of critical wave functions in disordered bosons.
  • To analyze the impact of interactions on spectral resolution and multifractality.

Main Methods:

  • Application of a modified excitation scheme using focused radio frequency pulses.
  • Utilizing two-photon laser scanning microscopy to probe individual localized states.
  • Solving Gross-Pitaevskii equations to account for particle interactions.

Main Results:

  • Demonstration of critical scaling and multifractality near the mobility edge.
  • Observation of universal density correlations in projected cloud images.
  • Analysis of the destructive effects of interactions on spectral resolution and multifractal spectra.

Conclusions:

  • The proposed methods allow for the study of multifractal properties at the Anderson localization transition.
  • Time-of-flight imaging can reveal interference fringes in the localized phase and map energy surfaces in the metallic phase.