Arnold web and dynamical tunneling in a four-site Bose-Hubbard model

TL;DR

This paper investigates the complex dynamics of a four-site Bose-Hubbard model, revealing a strong link between quantum states and classical phase space structures, and highlighting the role of dynamical tunneling in condensate behavior.

Contribution

It introduces a minimal bipartite Bose-Hubbard model and uncovers a direct correspondence between quantum states and classical Arnold web structures, emphasizing dynamical tunneling effects.

Findings

Quantum states map onto classical Arnold web structures.

Dynamical tunneling influences Fock state dynamics near resonance junctions.

Transport within the trimer can be manipulated via weak coupling to the monomer.

Abstract

We present the quantum and classical study of a four-well trapped Bose-Einstein condensate (BEC) modeled by the Bose-Hubbard Hamiltonian. The model used is fashioned as a minimal bipartite system consisting of a trimer coupled weakly to a monomer. Semiclassical insights into the fragmentation dynamics of the condensate is obtained by mapping out the Arnold web of the high dimensional classical phase space. A remarkable one-to-one correspondence between the quantum state space in occupation number representation and the classical Arnold web in action space is observed. The relevance of dynamical tunneling for the dynamics of Fock states near resonance junctions on the Arnold web is highlighted. We also predict the possibility of manipulating the transport within the trimer subsystem due to the weak coupling to the monomer.