Slow relaxation and sensitivity to disorder in trapped lattice fermions after a quench

TL;DR

This paper investigates how non-interacting fermions in a disordered optical lattice with a harmonic trap relax after a quench, revealing slow dynamics and heightened sensitivity to disorder due to Bragg-localization.

Contribution

It provides analytical and numerical analysis of post-quench dynamics in a non-interacting fermionic system with disorder, highlighting the slow relaxation caused by Bragg-localization effects.

Findings

Relaxation to the non-thermal state is extremely slow due to Bragg-localization.

The system's sensitivity to disorder exceeds that predicted by Anderson localization.

Post-quench occupation functions and density profiles exhibit non-trivial, slow evolution.

Abstract

We consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of (a) a strong optical lattice, (b) a harmonic trap, and (c) uncorrelated on-site disorder. After a quench, in which the center of the harmonic trap is displaced, we study the occupation function of the fermions and the time-evolution of experimental observables. Specifically, we present numerical and analytical results for the post-quench occupation function of the fermions, and analyse the time-evolution of the real-space density profile. Unsurprisingly for a non-interacting (and therefore integrable) system, the infinite-time limit of the density profile is non-thermal. However, due to Bragg-localization of the higher-energy single-particle states, the approach to even this non-thermal state is extremely slow. We quantify this statement, and show that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localization.