It has been a great success to use cold atoms in optical lattices to simulate various theoretical models in condensed matter physics in the last decade. On the other hand, current studies have been focusing on single band physics. In this talk, I will discuss how novel macroscopic quantum phenomena can be induced by inter-band interaction in a double-well optical lattice. Generally, the ground state can form various unconventional 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. Moreover, the formation of the last type of condensates has a deep connection with p-wave superconductors in one dimension, where Z2 symmetry breaking is essential.