Thermometry of ultracold fermions by (super)lattice modulation spectroscopy

We theoretically consider non-interacting fermions confined to optical lattices and apply a lattice amplitude modulation that we choose to be either homogeneous or of superlattice geometry. We study the atom excitation rate to higher Bloch bands which can be measured by adiabatic band mapping. We find that the atom excitation rate shows a clear signature of the temperature dependent Fermi distribution in the lowest band of the equilibrium lattice as excitations are quasimomentum-resolved. Based on typical experimental parameters and incorporating a trapping potential, we find that thermometry of one- and two-dimensional systems is within the reach of nowadays experiments. Our scheme is valid down to temperatures of a few percent of the hopping amplitude comparable to the N\'eel temperature in interacting systems.