From the superfluid to the Mott regime and back: triggering a non-trivial dynamics in an array of coupled condensates

We consider a system formed by an array of Bose-Einstein condensates trapped in a harmonic potential with a superimposed periodic optical potential. Starting from the boson field Hamiltonian, appropriate to describe a dilute gas of bosonic atoms, we reformulate the system dynamics within the Bose-Hubbard model scenario. Then we analyse the effective dynamics of the system when the optical-potential depth is suddenly varied according to a procedure applied in many of the recent experiments on superfluid-Mott transition in Bose-Einstein condensates. Initially the condensate array generated in a weak optical potential is assumed to be in the superfluid ground state which is well described in terms of coherent states. At a given time, the optical-potential depth is suddenly increased and, after a waiting time, it is quickly decreased so that the initial depth is restored. We compute the system-state evolution and show that the potential jump brings on an excitation of the system, incorporated in the final condensate wavefunctions, whose effects are analysed in terms of two-site correlation functions and of on-site population oscillations. Also we show how too long a waiting time can destroy completely the coherence of the final state, making it unobservable.