Selective state spectroscopy and multifractality in disordered Bose-Einstein condensates: a numerical study

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.