In the experiment each of the atoms was exposed to three laser pulses. The first pulse placed the atom into a superposition of two equally probable states — either leaving it alone to decelerate and then fall back down to Earth under gravity’s pull or giving it an extra kick so that it reached a greater height before descending. A second pulse was then applied at just the right moment so as to push the atom in the second state back faster toward Earth, causing the two superposition states to meet on the way down. At this point the third pulse measured the interference between these two states brought about by the atom’s existence as a wave, the idea being that any difference in gravitational redshift as experienced by the two states existing at difference heights above the Earth’s surface would be manifest as a change in the relative phase of the two states.
The virtue of this approach is the extremely high frequency of a caesium atom’s de Broglie wave — some 3x1025 Hz. Although during the 0.3 s of freefall the matter waves on the higher trajectory experienced an elapsed time of just 2x10-20 s more than did the waves on the lower trajectory, the enormous frequency of their oscillation, combined with the ability to measure amplitude differences of just one part in 1000, meant that the researchers were able to confirm gravitational redshift to a precision of 7x10-9.
But what's more interesting, at least to me, is the name of one of the author of this paper. Someone by the name of "Steven Chu"! :)
This is the 2nd paper that has been published by him after he has assumed his role at the Secretary of DOE. Still, unless I missed something, this must be the first time an active DOE Secretary published a paper in something as prestigious as Nature. The other one appeared in PRL, which is nothing to sneeze at either!