A bound on Planck-scale modifications of the energy-momentum composition rule from atomic interferometry

High sensitivity measurements in atomic spectroscopy were recently used in Amelino-Camelia et. al. to constraint the form of possible modifications of the energy-momentum dispersion relation resulting from Lorentz invariance violation (LIV). In this letter we show that the same data can be used successfully to set experimental bounds on deformations of the energy-momentum composition rule. Such modifications are natural in models of deformed Lorentz symmetry which are relevant in certain quantum gravity scenarios. We find the bound for the deformation parameter $κ$ to be a few orders of magnitude below the Planck scale and of the same magnitude as the next-to-leading order effect found in Amelino-Camelia et. al. We briefly discuss how it would be possible to distinguish between these two scenarios.