Dynamics of Localization Phenomena for Hardcore Bosons in Optical Lattices

TL;DR

This paper studies how ultracold hardcore bosons in optical lattices experience localization due to disorder, demonstrating Anderson localization through real-time dynamics and steady-state analysis.

Contribution

It reveals that disorder with algebraic correlations induces localization of all single-particle states and characterizes the steady state of mobile bosons after sudden interaction with the disorder.

Findings

All single-particle states become localized due to disorder.

Mobile bosons reach a steady state with exponential decay of correlations.

Initial confinement prevents expansion, confirming Anderson localization.

Abstract

We investigate the behavior of ultracold bosons in optical lattices with a disorder potential generated via a secondary species frozen in random configurations. The statistics of disorder is associated with the physical state in which the secondary species is prepared. The resulting random potential, albeit displaying algebraic correlations, is found to lead to localization of all single-particle states. We then investigate the real-time dynamics of localization for a hardcore gas of mobile bosons which are brought into sudden interaction with the random potential. Regardless of their initial state and for any disorder strength, the mobile particles are found to reach a steady state characterized by exponentially decaying off-diagonal correlations and by the absence of quasi-condensation; when the mobile particles are initially confined in a tight trap and then released in the disorder potential, their expansion is stopped and the steady state is exponentially localized in real space, clearly revealing Anderson localization.