  A general coupled representation is proposed for bosonic atoms in double well
optical lattices. Based on such a representation, we investigate the excitation
spectra and thermodynamics of bosonic atoms in the optical lattices. We find
excitation spectra of the double well system with filling factor equal to one
can be described by simultaneous excitations composed of pseudo particles
corresponding to doubly occupied and empty double wells. It is demonstrated
that hard-core bosonic statistics must be taken into account in order to
properly describe the equilibrium properties at finite temperatures. For this
we calculate the temperature dependence curves of particle numbers and heat
capacity, in which the hard-core features are clearly shown. At last, the cases
with filling factors unequal to one are also briefly discussed.
