  Ultranarrow superconductors are in the strong quantum confinement regime with
formation of multiple coherent condensates associated with the many subbands of
the electronic structure. Here we analyze the multiband BCS-BEC crossover
induced by the chemical potential tuned close to a subband bottom, in
correspondence of a superconducting shape resonance. The evolution of the
condensate fraction and of the pair correlation length in the ground state as
functions of the chemical potential demonstrates the tunability of the BCS-BEC
crossover for the condensate component of the selected subband. The extension
of the crossover regime increases when the pairing strength and/or the
characteristic energy of the interaction get larger. Our results indicate the
coexistence of large and small Cooper pairs in the crossover regime, leading to
the optimal parameter configuration for high transition temperature
superconductivity.
