An analytical solution is obtained for a system consisting of two atoms interacting
with a nondegenerate parametric amplifier of a cavity field containing a Kerr like medium
in the presence of Stark shift terms. The nonlinearity of the interaction leads to the generation
of different nonlocal correlations (NLCs) beyond entanglement concurrence, which
are measured by uncertainty-induced quantum nonlocality and maximal Bell’s function. It
is found that the generation of the NLCs, due to the atom-cavity unitary interaction, can be
controlled by the nonlinearity of the Kerr like medium and the Stark shift. The Kerr like
medium and the Stark shift lead to reduce the regularity and the amount of the generated
nonlocal correlations. The reduction in the generated nonlocal correlations, due to the Kerr
like medium, is increased by the increase in the Stark shift parameter and vice versa.