  Within the Bose-Hubbard model, we theoretically determine the stationary
states of two distinguishable atoms in a one-dimensional optical lattice and
compare with the case of two identical bosons. A heterodimer has odd-parity
dissociated states that do not depend on the interactions with the atoms, and
the lattice momenta of the two atomic species may have different averages even
for a bound state of the dimer. We discuss two possible methods of detecting
the dimer. First, the different distributions of the quasimomenta of the two
species may be observed in suitable time-of-flight experiments. Also, an
asymmetry in the line shape as a function of the modulation frequency may
reveal the presence of the odd-parity dissociated states when a heterodimer is
dissociated by modulating the depth of the optical lattice.
