We study the response of trapped two dimensional cold bosons to time dependent lattices. We find that in lattice ramps from 11 (superfluid, $\hbar/U_{ \text{ i}} = 3$ms, $\hbar/J_{ \text{ i}} = 45$ms) to 16 recoils (Mott, $\hbar/U_{ \text{ f}} = 2$ms, $\hbar/J_{ \text{ f}} = 130$ms) the local number fluctuations remains at their equilibrium values if ramps are slower than 3 ms. Global transport, however, is much slower (1s), especially in the presence of Mott shells. This separation of timescales has practical implications for cold atom experiments and cooling protocols.
Categories: cond-mat.quant-gas