Cooling neutral atoms in optical traps can be a difficult task under some experimental conditions, like when optical trapping potentials are state-dependent. We report on a theoretical study showing that cooling can be achieved even if the internal states of the atoms experience different potential depths as long as a well-tailored frequency sweep is applied to the cooling laser. We develop a master rate equation and a Monte Carlo simulation for atoms of Li and Yb trapped in optical lattices and tweezers and we find that the average occupation number of the vibrational levels is drastically reduced under feasible experimental conditions. Our findings provide an alternative cooling scheme that can be applied in principle to any particle that is optically trappable, e.g. atoms, molecules or ions, and can provide a faster route to cooling atoms to condensation or degeneracy. F. Berto, et al. |