  We quantize $sl_n$ Toda field theories in a periodic lattice. We find the
quantum exchange algebra in the diagonal monodromy (Bloch wave) basis in the
case of the defining representation. In the $sl_3$ case we extend the analysis
also to the second fundamental representation. We clarify, in particular, the
relation of Jimbo and Rosso's quantum $R$ matrix with the quantum $R$ matrix in
the Bloch wave basis.
