  The state of a quantum system acquires a phase factor, called the geometric
phase, when taken around a closed trajectory in the parameter space, which
depends only on the geometry of the parameter space. Due to its sensitive
nature, the geometric phase is instrumental in capturing weak effects such as
the acceleration-induced non-inertial quantum field theoretic effects. In this
paper, we study the geometric phase response of a circularly rotating detector
inside an electromagnetic cavity. Using the cavity, the non-inertial
contribution to the geometric phase can be isolated from or strengthened
relative to the inertial contribution. We show that the accumulative nature of
the geometric phase may facilitate the experimental observation of the
resulting, otherwise feeble, non-inertial contribution to the modified field
correlations inside the cavity. Specifically, we show that the atom acquires an
experimentally detectable geometric phase at accelerations of the order of
$\sim 10^{7}$ m/s$^2$ which is experimentally feasible.
