  We describe a diabatic protocol to prepare a strongly-interacting
Bose-Einstein condensate in a regime where neither an adiabatic ramp nor a
direct diabatic quench are desirable. This protocol is expected to achieve a
nearly unit population transfer to the strongly-interacting ground state for
realistic experimental parameters for $^{85}$Rb. The protocol matches the
initial and final density profiles by modifying the trap along with the
scattering length during the quench. The protocol should reveal several
properties of the strongly-interacting Bose gas, and enable further
investigation of beyond mean-field corrections to the Gross-Pitaevskii
equation.
