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

We study the influence of a periodic perturbation of the effective masses of fermions, due to the assumed semiclassical ultra-light dark matter (ULDM) background, on the motion of neutrons in a gravitational quantum well (GQW). Our focus is on the transition probability between the lowest two energy states, with the Rabi frequency in the kHz region corresponding to the series of "sweet spot" DM masses in the 10-11eV ballpark. The relevant probability is written in terms of the specific mass and of the effective coupling to the ordinary matter. These parameters can be constrained by the nonobservation of any significant deviations of the measured transition probabilities from the DM-free picture.