By means of a temporal-periodic modulation of the s-wave scattering length, a procedure to control the evolution of an initial atomic coherent state associated with a Bosonic Josephson junction is presented. The scheme developed has a remarkable advantage of avoiding the quantum collapse of the state due to phase and number diffusion. This kind of control could prove useful for atom interferometry using BECs, where the interactions limit the evolution time stage within the interferometer, and where the modulation can be induced via magnetic Feshbach resonances as recently experimentally demonstrated.

The possibility of using nanoelectromechanical systems as a simulation tool for quantum many-body effects is explored. It is demonstrated that an array of electrostatically coupled nanoresonators can effectively simulate the Bose-Hubbard model without interactions, corresponding in the single-phonon regime to the Anderson tight-binding model. Employing a density matrix formalism for the system coupled to a bosonic thermal bath, we study the interplay between disorder and thermalization, focusing on the delocalization process. It is found that the phonon population remains localized for a long time at low enough temperatures; with increasing temperatures the localization is rapidly lost due to thermal pumping of excitations into the array, producing in the equilibrium a fully thermalized system. Finally, we consider a possible experimental design to measure the phonon population in the array by means of a superconducting transmon qubit coupled to individual nanoresonators. We also consider the possibility of using the proposed quantum simulator for realizing continuous-time quantum walks.