Tracking quasi-classical chaos in ultracold boson gases

TL;DR

This paper investigates how ultracold boson gases in a lattice transition to chaos under a constant force, using mean position measurements to identify chaos thresholds linked to nonlinearity.

Contribution

It demonstrates a method to detect the onset of chaos in many-body boson gases through experimentally accessible mean position data, connecting nonlinear dynamics with observable quantities.

Findings

Chaos threshold determined by nonlinearity matches Lyapunov exponent calculations

Mean position effectively signals the transition to chaos

KAM theory provides a theoretical framework for chaos onset

Abstract

We study the dynamics of a ultra-cold boson gas in a lattice submitted to a constant force. We track the route of the system towards chaos created by the many-body-induced nonlinearity and show that relevant information can be extracted from an experimentally accessible quantity, the gas mean position. The threshold nonlinearity for the appearance of chaotic behavior is deduced from KAM arguments and agrees with the value obtained by calculating the associated Lyapunov exponent.