Exploring complex phenomena using ultracold atoms in bichromatic lattices

TL;DR

This paper investigates many-body quantum phenomena in quasiperiodic potentials using ultracold atoms, revealing connections with classical mechanics and identifying signatures of different insulating phases through experimental observables.

Contribution

It introduces a visualization method linking many-body quantum phases with classical KAM phenomena and distinguishes insulator phases via perturbative analysis and observable signatures.

Findings

Identification of three characteristic phases: metallic, Anderson, and band insulator.

Observation of nonlinear phenomena such as Arnold tongues and bifurcations.

Perturbative analysis clarifies distinctions between insulator phases.

Abstract

With an underlying common theme of competing length scales, we study the many-body Schr\"{o}dinger equation in a quasiperiodic potential and discuss its connection with the Kolmogorov-Arnold-Moser (KAM) problem of classical mechanics. We propose a possible visualization of such connection in experimentally accessible many-body observables. Those observables are useful probes for the three characteristic phases of the problem: the metallic, Anderson and band insulator phases. In addition, they exhibit fingerprints of non-linear phenomena such as Arnold tongues, bifurcations and devil's staircases. Our numerical treatment is complemented with a perturbative analysis which provides insight on the underlying physics. The perturbation theory approach is particularly useful in illuminating the distinction between the Anderson insulator and the band insulator phases in terms of paired sets of dimerized states.