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We study a method to induce resonant transitions between antihydrogen($\bar{H}$) quantum states above a material surface in the gravitational fieldof the Earth. The method consists of applying a gradient of magnetic field,which is temporally oscillating with the frequency equal to a frequency oftransition between gravitational states of antihydrogen. A correspondingresonant change in the spatial density of antihydrogen atoms could be measuredas a function of the frequency of applied field. We estimate an accuracy ofmeasuring antihydrogen gravitational states spacing and show how a value of thegravitational mass of the $\bar{H}$ atom could be deduced from such ameasurement. We also demonstrate that a method of induced transitions could becombined with a free-fall-time measurement in order to further improve theprecision.

A spectroscopy approach to measure the gravitational mass of antihydrogen