Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions

Abstract

We study the 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 ground state and localized state configurations. 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 Poincaré 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 as well as collective and emergent nonlinear dynamics of BECs with long-range interactions.

Signatures of Quantum Chaos of Rydberg-Dressed Bosons in a Triple-Well Potential

“…Before discussing many-body calculations of the EBHM, we show the signature of chaos of this model in the semiclassical limit [31,37]. In the semiclassical (mean-field) calculation, one replaces the bosonic operators a i (a † i ) with complex classical fields ψ i (ψ * i ).…”

“…The mean-field calculation is relatively simple, as the number of complex fields is equal to the number of site L. More details of the semiclassical calculations can be found in Refs. [31,37]. A key figure of merit in the mean-field calculation is Lyapunov exponents.…”

“…In Refs. [31,37], we studied nonlinear and chaotic dynamics of Rydberg-dressed bosons in finite potential wells in the semiclassical regime. In the quantum regime, it is known that the BHM is non-integrable in general, where quantum chaos can be triggered by the competition between coherent hopping and on-site interactions [38][39][40][41][42].…”