Effects of dephasing on quantum adiabatic pumping with nonequilibrium initial states

Thouless's quantum adiabatic pumping is of fundamental interest to condensed-matter physics. It originally considered a zero-temperature equilibrium state uniformly occupying all the bands below a Fermi surface. In light of recent direct simulations of Thouless's concept in cold-atom systems, this paper investigates the dynamics of quantum adiabatic pumping subject to dephasing for rather general initial states with nonuniform populations and possibly interband coherence. Using a theory based on pure-dephasing Lindblad evolution, we find that the pumping is contributed by two parts of different nature: a dephasing-modified geometric part weighted by initial Bloch state populations and an interband-coherence-induced part compromised by dephasing, both of them being independent of the pumping time scale. The overall pumping reflects an interplay of the band topology, initial state populations, initial state coherence, and dephasing. Theoretical results are carefully checked in a Chern insulator model coupled to a pure-dephasing environment, providing a useful starting point to understand and coherently control quantum adiabatic pumping in general situations.