  We apply the Bose-Hubbard Hamiltonian to a three-well system and show
analytically that coherent transport via adiabatic passage (CTAP) of $N$
non-interacting particles across the chain is possible. We investigate the
effect of detuning the middle well to recover CTAP when on-site interparticle
interactions would otherwise disrupt the transport. The case of small
interactions is restated using first-order perturbation theory to develop
criteria for adibaticity that define the regime where CTAP is possible. Within
this regime we investigate restricting the Hilbert space to the minimum
necessary basis needed to demonstrate CTAP, which dramatically increases the
number of particles that can be efficiently considered. Finally, we compare the
results of the Bose-Hubbard model to a mean-field three-mode Gross-Pitaevskii
analysis for the equivalent system.
