Fractal universality in near-threshold magnetic lanthanide dimers

Area of Science:

• Quantum physics
• Atomic and molecular physics
• Condensed matter physics

Background:

• Ergodic quantum systems exhibit similarities, while nonergodic, fractal systems possess unique characteristics.
• Ultracold magnetic dysprosium atoms colliding exhibit soft chaotic behavior with minimal disorder.
• Weakly bound dysprosium lanthanide molecules in external magnetic fields represent a system with fractal properties.

Purpose of the Study:

• To investigate the fractal properties of weakly bound dysprosium lanthanide molecules in an external magnetic field.
• To broaden the classification of chaotic behavior in quantum systems by analyzing molecular wave functions.
• To identify and characterize a dynamic phase transition within these molecular systems.

Main Methods:

• Utilized exact close-coupling simulations to model the behavior of molecular wave functions.
• Calculated the generalized inverse participation ratio and fractal dimensions for extensive sets of molecular wave functions.
• Applied external magnetic fields, increasing strength up to approximately 100 Gauss (10 mT).

Main Results:

• Observed a dynamic phase transition from partially localized to totally delocalized states as magnetic field strength increased.
• Demonstrated universality in the distribution of these states.
• Proved the existence of a nonergodic delocalized phase within the system.
• Identified strong coupling between near-threshold molecular states and the continuum as the cause for ergodicity violation.

Conclusions:

• The study reveals a controllable dynamic phase transition in fractal quantum systems using magnetic fields.
• A nonergodic delocalized phase exists in these molecular systems, challenging traditional ergodic assumptions.
• The findings contribute to understanding complex quantum behaviors and phase transitions in disordered systems.