Mean-field description of ultracold bosons on disordered two-dimensional optical lattices

In the present communication, we describe the properties induced by disorder on an ultracold gas of bosonic atoms loaded into a two-dimensional optical lattice with global confinement ensured by a parabolic potential. Our analysis is centred on the spatial distribution of the various phases, focusing particularly on the superfluid properties of the system as a function of external parameters and disorder amplitude. In particular, it is shown how disorder can suppress superfluidity, while partially preserving the system coherence.