Correlated noise in cold-atom quantum simulation

We point out that, when a Hubbard model is simulated by an optical-lattice system with noise in the laser controller, there is generically a correlation between the fluctuations of the hopping amplitude, J, and those of the on-site repulsion, U. We analyse a toy model of such correlated noise. We also show, in a more realistic model, that such correlations lead to a non-trivial ramp-time-independent value of the fidelity in the case of strong noise.