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We study the influence of a periodic perturbation of the effective masses ofthe nucleons, due to the assumed semi-classical ultra-light dark matterbackground, on the motion of neutrons in a gravitational quantum well. Ourfocus is on the transition probability between the lowest two energy states,with the Rabi frequency in the kHz region corresponding to the series of "sweetspot" dark matter masses in the $10^{-11}$eV ballpark. The relevant probabilityis written in terms of the specific mass and of the effective coupling to theordinary matter. These parameters can be constrained by the non-observation ofany significant deviations of the measured transition probabilities from thedark-matter-free picture.

Effects of ultra-light dark matter on the gravitational quantum well