The sensitivity of local quantum Fisher
information and the Bures distance entanglement as
quantifiers of the non-classical correlations, is examined
for an atomic system interacting nonlinearly with
a single cavity field. The general behavior shows that,
the amount of the nonclassical correlation between the
atomic subsystems that are depicted by the local quantum
Fisher information is larger than that detected by Bures
distance entanglement. It is shown that, the long-lived
non-classical correlations between the atomic subsystems
is depicted in the presence of the intrinsic coherence
and enhanced by switching on the dipole-dipole
interaction. However, the upper bounds of these correlations
decreases if the field is initially prepared
in an even coherent state. Although the long-lived
the behavior of these correlations disappear at large values
of the mean photon numbers, but the maximum and minimum bounds of these correlations are enhanced.