Features of the motion of ultracold atoms in quasiperiodic potentials

TL;DR

This paper investigates the properties of ultracold atoms in quasiperiodic potentials, highlighting how these potentials serve as a bridge between order and chaos, affecting transport and integrability in two-dimensional systems.

Contribution

It characterizes the parameter space of quasiperiodic potentials, distinguishing regions with ordered and random features and analyzing their impact on atomic transport and partial integrability.

Findings

Identification of parameter regions with ordered and random potential features

Analysis of transport properties at different energies in quasiperiodic potentials

Observation of partial integrability phenomena in ultracold atom systems

Abstract

We consider here quasiperiodic potentials on the plane, which can serve as a "transitional link" between ordered (periodic) and chaotic (random) potentials. As can be shown, in almost any family of quasiperiodic potentials depending on a certain set of parameters, it is possible to distinguish a set (in the parameter space) where, according to a certain criterion, potentials with features of ordered potentials arise, and a set where we have potentials with features of random potentials. These sets complement each other in the complete parameter space, and each of them has its own specific structure. The difference between "ordered" and "chaotic" potentials will manifest itself, in particular, in the transport properties at different energies, which we consider here in relation to systems of ultracold atoms. It should be noted here that the transport properties of particles in the considered potentials can be accompanied by the phenomena of "partial integrability" inherent in two-dimensional Hamiltonian systems.