  In Thouless pump, the charge transport in a one-dimensional insulator over an
adiabatic cycle is topologically quantized. For nonequilibrium initial states,
however, interband coherence will induce a previously unknown contribution to
Thouless pumping. Though not geometric in nature, this contribution is
independent of the time scale of the pumping protocol. In this work, we perform
a detailed analysis of our previous finding [Phys. Rev. B 91, 085420 (2015)] in
an already available cold-atom setup. We show that initial states with
interband coherence can be obtained via a quench of the system's Hamiltonian.
Adiabatic pumping in the post-quench system are then examined both
theoretically and numerically, in which the interband coherence is shown to
play an important role and can hence be observed experimentally. By choosing
adiabatic protocols with different switching-on speeds, we also show that the
contribution of interband coherence to adiabatic pumping can be tuned. It is
further proposed that the interband coherence induced correction to Thouless
pumping may be useful in capturing a topological phase transition point. All
our results have direct experimental interests.
