  Quantum weak measurement, measuring some observable quantities within the
selected subensemble of the entire quantum ensemble, can produce many
interesting results such as the superluminal phenomena. An outcome of such a
measurement is the weak value which has been applied to amplify some weak
signals of quantum interactions in lots of previous references. Here, we apply
the weak measurement to the system of relativistic cold atoms. According to
mass-energy equivalence, the internal energy of an atom will contribute its
rest mass and consequently the external momentum of center of mass. This
implies a weak coupling between the internal and external degrees of freedom of
atoms moving in the free space. After a duration of this coupling, a weak value
can be obtained by post-selecting an internal state of atoms. We show that, the
weak value can change the momentum uncertainty of atoms and consequently help
us to experimentally measure the weak effects arising from mass-energy
equivalence.
