  Based on the coalescence model for light nuclei production, we show that the
yield ratio $\mathcal{O}_\text{p-d-t} = N_{^3\text{H}} N_p / N_\text{d}^2$ of
$p$, d, and $^3$H in heavy-ion collisions is sensitive to the neutron relative
density fluctuation $\Delta n= \langle (\delta n)^2\rangle/\langle n\rangle^2$
at kinetic freeze-out. From recent experimental data in central Pb+Pb
collisions at $\sqrt{s_{NN}}=6.3$~GeV, $7.6$~GeV, $8.8$~GeV, $12.3$~GeV and
$17.3$~GeV measured by the NA49 Collaboration at the CERN Super Proton
Synchrotron (SPS), we find a possible non-monotonic behavior of $\Delta n$ as a
function of the collision energy with a peak at $\sqrt{s_{NN}}=8.8$~GeV,
indicating that the density fluctuations become the largest in collisions at
this energy. With the known chemical freeze-out conditions determined from the
statistical model fit to experimental data, we obtain a chemical freeze-out
temperature of $\sim 144~$MeV and baryon chemical potential of $\sim 385~$MeV
at this collision energy, which are close to the critical endpoint in the QCD
phase diagram predicted by various theoretical studies. Our results thus
suggest the potential usefulness of the yield ratio of light nuclei in
relativistic heavy-ion collisions as a direct probe of the large density
fluctuations associated with the QCD critical phenomena.
