  We report on a combined experimental and theoretical study of the low-entropy
Mott transition for interacting bosons trapped in a three-dimensional (3D)
cubic lattice -- namely, the interaction-induced superfluid-to-normal phase
transition in the vicinity of the zero-temperature Mott transition. Our
analysis relies on the measurement of the 3D momentum distribution, which
allows us to extract the momentum-space density $\rho({\bf k}={\bf 0})$ at the
center of the Brillouin zone. Upon varying the ratio between the interaction
$U$ and the tunnelling energy $J$ across the superfluid transition, we observe
that $\rho({\bf k}={\bf 0})$ exhibits a sharp transition at a value of $U/J$
consistent with the bulk prediction from quantum Monte Carlo. In addition, the
variation of $\rho({\bf k}={\bf 0})$ with $U/J$ exhibits a critical behavior
consistent with the expected 3D XY universality class. Our results show that
the tomographic reconstruction of the momentum distribution of ultracold bosons
can reveal traits of the critical behavior of the superfluid transition even in
an inhomogeneous trapped system.
