  We predict novel inter-band physics for bosons in a double-well lattice. An
intrinsic coupling between the s and px band due to interaction gives rise to
larger Mott regions on the phase diagram at even fillings than the ones at odd
fillings. On the other hand, the ground state can form various types of
condensates, including a mixture of single-particle condensates of both bands,
a mixture of a single-particle condensate of one band and a pair-condensate of
the other band, and a pair-condensate composed of one particle from one band
and one hole from the other band. The predicted phenomena should be observable
in current experiments on double-well optical lattices.
