Hyperchaos in a Bose-Hubbard chain with Rydberg-dressed interactions

TL;DR

This paper investigates chaos and hyperchaos in Rydberg-dressed Bose-Einstein condensates within a one-dimensional optical lattice, revealing how long-range interactions induce complex dynamical behaviors and depend on system parameters.

Contribution

It introduces a detailed analysis of hyperchaotic dynamics in a long-range interacting BEC system using Lyapunov exponents and explores the effects of quenches on chaos.

Findings

Multiple positive Lyapunov exponents indicate hyperchaotic behavior.

The largest Lyapunov exponent scales with phase space area.

Quenches lead to distinct chaotic and hyperchaotic dynamics.

Abstract

We study chaos and hyperchaos of Rydberg-dressed Bose-Einstein condensates (BECs) in a one-dimensional optical lattice. Due to the long-range soft-core interaction between the dressed atoms, the dynamics of the BECs are described by the extended Bose-Hubbard model. In the mean-field regime, we analyze the dynamical stability of the BEC by focusing on the groundstate and localized state configuration. Lyapunov exponents of the two configurations are calculated by varying the soft-core interaction strength, potential bias and length of the lattice. Both configurations can have multiple positive Lyapunov exponents, exhibiting hyperchaotic dynamics. We show the dependence of the number of the positive Lyapunov exponents and the largest Lyapunov exponent on the length of the optical lattice. The largest Lyapunov exponent is directly proportional to areas of phase space encompassed by the associated Poincar\'e sections. We demonstrate that linear and hysteresis quenches of the lattice potential and the dressed interaction lead to distinct dynamics due to the chaos and hyperchaos. Our work is relevant to current research on chaos, and collective and emergent nonlinear dynamics of BECs with long-range interactions.