  The BEC-BCS crossover in QCD at finite baryon and isospin chemical potentials
is investigated in the Nambu--Jona-Lasinio model. The diquark condensation in
two color QCD and the pion condensation in real QCD would undergo a BEC-BCS
crossover when the corresponding chemical potential increases. We determined
the crossover chemical potential as well as the BEC and BCS regions. The
crossover is not triggered by increasing the strength of attractive interaction
among quarks but driven by changing the charge density. The chiral symmetry
restoration at finite temperature and density plays an important role in the
BEC-BCS crossover. For real QCD, strong couplings in diquark and vector meson
channels can induce a diquark BEC-BCS crossover in color superconductor, and in
the BEC region the chromomagnetic instability is fully cured and the ground
state is a uniform phase.
