Abstract
We study the quantum dynamics of the Bose-Hubbard model on a ladder formed by two rings coupled by the tunneling effect. By implementing the Bogoliubov approximation scheme, we prove that, despite the presence of the inter-ring coupling term, the Hamiltonian decouples in many independent sub-Hamiltonians associated with momentum-mode pairs . Each sub-Hamiltonian is then shown to be part of a specific dynamical algebra. The properties of the latter allow us to perform the diagonalization process, to find the energy spectrum and the conserved quantities of the model, and to derive the time evolution of important physical observables. We then apply this solution scheme to the simplest possible closed ladder, the double trimer. After observing that the excitations of the system are weakly populated vortices, we explore the corresponding dynamics by varying the initial conditions and the model parameters. Finally, we show that the inter-ring tunneling determines a spectral collapse when approaching the border of the dynamical-stability region.
2 More- Received 14 April 2017
DOI:https://doi.org/10.1103/PhysRevA.96.013620
©2017 American Physical Society