  We report on a new experiment that tests for a violation of Lorentz
invariance (LI), by searching for a dependence of atomic transition frequencies
on the orientation of the spin of the involved states (Hughes-Drever type
experiment). The atomic frequencies are measured using a laser cooled
$^{133}$Cs atomic fountain clock, operating on a particular combination of
Zeeman substates. We analyze the results within the framework of the Lorentz
violating standard model extension (SME), where our experiment is sensitive to
a largely unexplored region of the SME parameter space, corresponding to first
measurements of four proton parameters and improvements by 11 and 13 orders of
magnitude on the determination of four others. In spite of the attained
uncertainties, and of having extended the search into a new region of the SME,
we still find no indication of LI violation.
