  Using a relativistic transport model to describe the evolution of the quantum
chromodynamic matter produced in Au+Au collisions at $\sqrt{s_{NN}}=3-200$ GeV,
we study the effect of a first-order phase transition in the equation of state
of this matter on the yield ratio $N_tN_p/ N_d^2$ ($tp/d^2$) of produced proton
($p$), deuteron ($d$), and triton ($t$). We find that the large density
inhomogeneities generated by the spinodal instability during the first-order
phase transition can survive the fast expansion of the subsequent hadronic
matter and lead to an enhanced $tp/d^2$ in central collisions at
$\sqrt{s_{NN}}=3-5$ GeV as seen in the experiments by the STAR Collaboration
and the E864 Collaboration. However, this enhancement subsides with increasing
collision centrality, and the resulting almost flat centrality dependence of
$tp/d^2$ at $\sqrt{s_{NN}}=3$ GeV can also be used as a signal for the
first-order phase transition.
