  We use the results of ultra-precise cold-atom-recoil experiments to constrain
the form of the energy-momentum dispersion relation, a structure that is
expected to be modified in several quantum-gravity approaches. Our strategy of
analysis applies to the nonrelativistic (small speeds) limit of the dispersion
relation, and is therefore complementary to an analogous ongoing effort of
investigation of the dispersion relation in the ultrarelativistic regime using
observations in astrophysics. For the leading correction in the nonrelativistic
limit the exceptional sensitivity of cold-atom-recoil experiments remarkably
allows us to set a limit within a single order of magnitude of the desired
Planck-scale level, thereby providing the first example of Planck-scale
sensitivity in the study of the dispersion relation in controlled laboratory
experiments. For the next-to-leading term we obtain a limit which is a few
orders of magnitude away from the Planck scale, but still amounts to the best
limit on a class of Lorentz-symmetry test theories that has been extensively
used to investigate the hypothesis of "deformation" (rather than breakdown) of
spacetime symmetries.
