  Exceptional points (EPs), early arising from non-Hermitian physics,
significantly amplify the system's response to minor perturbations, and act as
a useful concept to enhance measurement in metrology. In particular, such a
metrological enhancement grows dramatically with the EP's order. However, the
Langevin noises intrinsically existing in the non-Hermitian systems diminish
this enhancement. In this study, we propose a protocol for quantum metrology
with the construction of higher-order EPs (HOEPs) in atom-cavity system through
Hermitian magnon-photon interaction. The construction of HOEPs utilizes the
atom-cavity non-Hermitian-like dynamical behavior but avoids the external
Langevin noises via the Hermitian interaction. A general analysis is exhibited
for the construction of arbitrary $n$-th order EP (EPn). As a demonstration of
the superiority of these HOEPs in quantum metrology, we work out an EP3/4-based
atomic sensor with sensitivity being orders of magnitude higher than that
achievable in an EP2-based one. We further unveil the mechanism behind the
sensitivity enhancement from HOEPs. The experimental establishment for this
proposal is suggested with potential candidates. This EP-based atomic sensor,
taking advantage of the atom-light interface, offers new insight into quantum
metrology with HOEPs.
