Heating dynamics of bosonic atoms in a noisy optical lattice

We analyze the heating of interacting bosonic atoms in an optical lattice due to intensity fluctuations of the lasers forming the lattice. We focus in particular on fluctuations at low frequencies below the band gap frequency, such that the dynamics is restricted to the lowest band. We derive stochastic equations of motion, and analyze the effects on different many-body states, characterizing heating processes in both strongly and weakly interacting regimes. In the limit where the noise spectrum is flat at low frequencies, we can derive an effective Master equation describing the dynamics. We compute heating rates and changes to characteristic correlation functions both in the perturbation theory limit, and using a full time-dependent calculation of the stochastic many-body dynamics in 1D based on time-dependent density-matrix-renormalization-group methods.