  This work presents an experimental test of Lorentz invariance violation in
the infrared (IR) regime by means of an invariant minimum speed in the
spacetime and its effects on the time when an atomic clock given by a certain
radioactive single-atom (e.g.: isotope $Na^{25}$) is a thermometer for a
ultracold gas like the dipolar gas $Na^{23}K^{40}$. So, according to a Deformed
Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where
there emerges an invariant minimum speed $V$ in the subatomic world, one
expects that the proper time of such a clock moving close to $V$ in thermal
equilibrium with the ultracold gas is dilated with respect to the improper time
given in lab, i.e., the proper time at ultracold systems elapses faster than
the improper one for an observer in lab, thus leading to the so-called {\it
proper time dilation} so that the atomic decay rate of a ultracold radioactive
sample (e.g: $Na^{25}$) becomes larger than the decay rate of the same sample
at room temperature. This means a suppression of the half-life time of a
radioactive sample thermalized with a ultracold cloud of dipolar gas to be
investigated by NASA in the Cold Atom Lab (CAL).
