Fermi polaron in a one-dimensional quasi-periodic optical lattice: the simplest many-body localization challenge

TL;DR

This paper explores how a Fermi polaron behaves in a one-dimensional quasi-periodic optical lattice, revealing how disorder influences localization and providing a phase diagram relevant for cold-atom experiments.

Contribution

It introduces a variational method to study many-body localization of Fermi polarons in quasi-periodic lattices, enabling analysis of large systems and phase diagram prediction.

Findings

Polaron energy and wave-function are strongly affected by quasi-random potential.

Identified critical disorder strengths for localization transitions.

Predicted phase diagram can be tested in current cold-atom experiments.

Abstract

We theoretically investigate the behavior of a moving impurity immersed in a sea of fermionic atoms that are confined in a quasi-periodic (bichromatic) optical lattice, within a standard variational approach. We consider both repulsive and attractive contact interactions for such a simplest many-body localization problem of Fermi polarons. The variational approach enables us to access relatively large systems and therefore may be used to understand many-body localization in the thermodynamic limit. The energy and wave-function of the polaron states are found to be strongly affected by the quasi-random lattice potential and their experimental measurements (i.e., via radio-frequency spectroscopy or quantum gas microscope) therefore provide a sensitive way to underpin the localization transition. We determine a phase diagram by calculating two critical quasi-random disorder strengths, which correspond to the onset of the localization of the ground-state polaron state and the many-body localization of all polaron states, respectively. Our predicted phase diagram could be straightforwardly examined in current cold-atom experiments.