  The crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to
Bose-Einstein condensation (BEC) is difficult to realize in quantum materials
because, unlike in ultracold atoms, one cannot tune the pairing interaction. We
realize the BCS-BEC crossover in a nearly compensated semimetal
Fe$_{1+y}$Se$_x$Te$_{1-x}$ by tuning the Fermi energy, $\epsilon_F$, via
chemical doping, which permits us to systematically change $\Delta /
\epsilon_F$ from 0.16 to 0.5 were $\Delta$ is the superconducting (SC) gap. We
use angle-resolved photoemission spectroscopy to measure the Fermi energy, the
SC gap and characteristic changes in the SC state electronic dispersion as the
system evolves from a BCS to a BEC regime. Our results raise important
questions about the crossover in multiband superconductors which go beyond
those addressed in the context of cold atoms.
