Localization in momentum space of ultracold atoms in incommensurate lattices

TL;DR

This paper investigates how disorder causes localization of ultracold atoms in momentum space within incommensurate lattices, revealing a transition from localized oscillations to diffusion, with implications for experimental detection.

Contribution

It provides a detailed characterization of momentum space localization and identifies observable signatures of the localization transition in ultracold atom systems.

Findings

Localized momentum oscillations at low disorder

Oscillations vanish after transition to diffusion

Predicted oscillation frequency and visibility for experiments

Abstract

We characterize the disorder induced localization in momentum space for ultracold atoms in one-dimensional incommensurate lattices, according to the dual Aubry-Andr\'e model. For low disorder the system is localized in momentum space, and the momentum distribution exhibits time-periodic oscillations of the relative intensity of its components. The behavior of these oscillations is explained by means of a simple three-mode approximation. We predict their frequency and visibility by using typical parameters of feasible experiments. Above the transition the system diffuses in momentum space, and the oscillations vanish when averaged over different realizations, offering a clear signature of the transition.