Localisation of weakly interacting bosons in two dimensions: disorder vs lattice geometry effects

Area of Science:

• Quantum Physics
• Condensed Matter Physics
• Ultracold Atomic Gases

Background:

• Localization phenomena in disordered quantum systems are crucial for understanding material properties.
• Ultracold bosonic gases in optical lattices provide a tunable platform to study quantum phenomena.
• The interplay between disorder and lattice geometry influences the behavior of quantum fluids.

Purpose of the Study:

• To investigate the impact of disorder strength and lattice geometry on localization in a 2D ultracold bosonic gas.
• To quantify localization effects and analyze the transition to localization in different lattice structures.
• To explore the influence of coordination number on the localization transition.

Main Methods:

• Computational experiments were performed at the mean-field level.
• Stationary density profiles of the condensate component were analyzed statistically.
• Disorder strength and lattice geometry (square, triangular, honeycomb) were systematically varied.

Main Results:

• A smooth transition to disorder-induced localization was observed in square and triangular lattices.
• Honeycomb lattices exhibited absence of localization for moderate disorder and partial localization at high disorder.
• Ground state energy spectra showed a continuous distribution emerging due to disorder, unlike sharp peaks in ordered systems.

Conclusions:

• Lattice geometry significantly influences localization phenomena, with honeycomb lattices showing enhanced resistance to disorder.
• Coordination number plays a role in the rate of the localization transition as system size increases.
• Disorder introduces distinct signatures in the energy spectrum, providing a method for its detection.