  We study the tunneling of a small ensemble of strongly repulsive bosons in a
one-dimensional triple-well potential. The usual treatment within the
single-band approximation suggests suppression of tunneling in the strong
interaction regime. However, we show that several windows of enhanced tunneling
are opened in this regime. This enhanced tunneling results from higher band
contributions, and has the character of interband tunneling. It can give rise
to various tunneling processes, such as single-boson tunneling and two-boson
correlated tunneling of the ensemble of bosons, and is robust against
deformations of the triple well potential. We introduce a basis of generalized
number states including all contributing bands to explain the interband
tunneling, and demonstrate various processes of interband tunneling and its
robustness by numerically exact calculation.
