  In this work, we consider the effects of the Lorentz-violating (LV) term $
v_{\mu}\bar{\psi}\gamma ^{\mu}\psi $ belonging to the fermion sector of the
extended standard model on the dynamics of a quantum two-level system. We
examine how its non-relativistic counterpart, ${(\mathbf{p}-e \mathbf{A})\cdot
}\mathbf{v}/{m_{e},}$ affects the Rabi oscillations of a two-level atom coupled
with a quantum cavity electromagnetic field. Taking an initial coherent field
state in a resonant cavity, it was found that the LV background increases the
Rabi frequency and the time interval between collapses and revivals of the
population inversion function. It was found that initial field states with low
mean number of photons are better probes in order to establish more stringent
upper bounds on the background magnitude. In particular, for an initial vacuum
state in the cavity the upper limit $\text{v}_{x}<10^{-10}eV$ was attained.
